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[Kuildeous]

I don't generally play with people who make a big deal about post-shuffle card distribution, but I've seen them around. It seems that some people think that the cards will be even more randomized if you deal one per player at a time. Even I do that a lot when playing cards. It's a habit, I guess.

It would be faster to just deal each hand out. Using poker as an example, you hand each person the top five cards of the deck. If the deck is properly shuffled, then it should be just as uncertain as dealing one card to each person*.

So, in the games where you distribute cards, how do you handle it?

* Unless you're playing euchre, where you deal 2/3/2/3 cards and then 3/2/3/2 cards at a time.

[pingpongsam]

I have always dealt 1 card per player in rotation from the top of the deck only. I was of the impression you could get shot doing otherwise.

[WanderingWinder]

Depends on the game. Typically it's one-at-a-time, Euchre it's the 2-3 thing, 500 (which is a spin-off of euchre and my favouritest card game) is typically either 3-4-3 or 3-2-2-3, Casino is 2-2... but in any case, if you've shuffled well enough, it totally doesn't matter.

[DStu]

If the deck is properly shuffled, then it should be just as uncertain as dealing one card to each person*.

When I play Skat, I deal 3/(2)/4/3, because those are the rules. When playing other games where I have to distribute 10 cards, I deal 3/4/3, because that's how you deal at Skat. Or 3/2/3/2.
More than 2, but not 10 cards, I usually do 2/2/2/2/2/.../2/[1], and two cards 1/1.

[Kuildeous]

I have always dealt 1 card per player in rotation from the top of the deck only. I was of the impression you could get shot doing otherwise.

With some people, I think you might. Some folks get real antsy about that sort of thing. I still remember making a wrong call while playing blackjack. A person down the table busted. He blamed me; if I had played it according to the charts, he would not have busted. Technically true, but we didn't know what card was coming up. It's possible that my bad call could have saved his bacon, but he chose to berate me for costing him money.

One advantage I see to spreading cards around is that it can lessen the effect of a poorly shuffled deck. This can be important in games like Uno where you don't necessarily want to give someone a huge clump of color (note, I'm no Uno expert so I'm only guessing that this is a bad idea). A properly shuffled deck shouldn't matter, but an improperly shuffled deck could use the one-per method to alleviate that problem.

[WanderingWinder]

I have always dealt 1 card per player in rotation from the top of the deck only. I was of the impression you could get shot doing otherwise.

With some people, I think you might. Some folks get real antsy about that sort of thing. I still remember making a wrong call while playing blackjack. A person down the table busted. He blamed me; if I had played it according to the charts, he would not have busted. Technically true, but we didn't know what card was coming up. It's possible that my bad call could have saved his bacon, but he chose to berate me for costing him money.

One advantage I see to spreading cards around is that it can lessen the effect of a poorly shuffled deck. This can be important in games like Uno where you don't necessarily want to give someone a huge clump of color (note, I'm no Uno expert so I'm only guessing that this is a bad idea). A properly shuffled deck shouldn't matter, but an improperly shuffled deck could use the one-per method to alleviate that problem.

While a common perception, it isn't actually true that it randomizes a non-randomized deck. It only gives you specifically-biased set of cards A, rather than differently-specifically biased but still specifically-biased set of cards B. So maybe you have cards that are more different from each other, as opposed to having cards that are all the same - but having a mix of different cards isn't more random than having all the same cards.

[DG]

Logically, there is no point in choosing a method of dealing to suit a random deck. Any method would be sufficient. We know however that most shuffled decks are not entirely random so we choose a dealing method for 'near random' decks. Cards put together in groups to form the deck are more likely after a typical shuffle to be near cards from that group than near to other cards. This is especially true if the cards are not uniform or have a tendency to stick to each other. Dealing cards one at a time will distribute these clustered cards amongst the players. For most games this is an ideal solution to the failings of human shuffling.

[Ozle]

The 1 card per person at a time thing is to make it harder to rig a deck isn't it?

If you are dealing the top 5 cards to one person in a game its a lot easier to get 5 required cards to one person than if you had to do every 5th card down.

[pingpongsam]

I believe the top deck single card deal is primarily an anti-cheat mechanism. I cannot prove this but it makes sense.

Properly shuffled it should be impossible to know the top card of the deck. Dealt singly it should be exceedingly difficult to stack a deck without detection. Other manners of dealing open up a range of possibilities for stacking and cherry picking.

[WanderingWinder]

Logically, there is no point in choosing a method of dealing to suit a random deck. Any method would be sufficient. We know however that most shuffled decks are not entirely random so we choose a dealing method for 'near random' decks. Cards put together in groups to form the deck are more likely after a typical shuffle to be near cards from that group than near to other cards. This is especially true if the cards are not uniform or have a tendency to stick to each other. Dealing cards one at a time will distribute these clustered cards amongst the players. For most games this is an ideal solution to the failings of human shuffling.

There's no such thing as a 'near random' deck. It's either random, or it isn't. Again, similar cards being spread out is NOT the same thing as random.

[pingpongsam]

Out of all the possible permutations of a random deck having all the cards in order by suit as they came out of the shrink wrap is one of them. In this sense every deck is random.

[DStu]

Logically, there is no point in choosing a method of dealing to suit a random deck. Any method would be sufficient. We know however that most shuffled decks are not entirely random so we choose a dealing method for 'near random' decks. Cards put together in groups to form the deck are more likely after a typical shuffle to be near cards from that group than near to other cards. This is especially true if the cards are not uniform or have a tendency to stick to each other. Dealing cards one at a time will distribute these clustered cards amongst the players. For most games this is an ideal solution to the failings of human shuffling.

There's no such thing as a 'near random' deck. It's either random, or it isn't. Again, similar cards being spread out is NOT the same thing as random.

Replace "near random" by "nearly uniformly random".
And I think the point is that you are happier with similar cards being spread out than having them not spread out.

In all* games, you are not interested having an exact uniform random distribution after shuffling. What matters is that the hands people draw have the proper probabilities. For example: Say you play with 3 players, and after an imperfect shuffle, card B has has probability of being i cards below card A is 20%, 30%, 20%, 15%, 5%, 5%, 3%, 1%, 1%, for i=1,...,9. Zero afterwards.
Now if you give 6 cards at once to player 1, and cardA is the first card, the probability of him also getting cardB is 90%.
If you give only one card at once, and card A is the first card, the probability of him also getting cardB is 20%+5%+1%=26% which is much closer to the 5/17=29.4% Player 2 is 20%+15%+4%=38% (needs 35.3%; instead of 10% with the first method), player 3 is 30%+5%+1%=36% (needs 35.3%, instead of 0%)

Now I made all this up, and the numbers are a bit extreme of course, but exactly this pattern (cards not getting the 'right' distance) is the biggest problem when shuffling, and by distributing small numbers of cards at once you distribute the probabilities that are too high and the once that are too low among the players, so that they can average out at least a bit. You can do this because the order in which you get the cards usually don't matter.

[WanderingWinder]

Logically, there is no point in choosing a method of dealing to suit a random deck. Any method would be sufficient. We know however that most shuffled decks are not entirely random so we choose a dealing method for 'near random' decks. Cards put together in groups to form the deck are more likely after a typical shuffle to be near cards from that group than near to other cards. This is especially true if the cards are not uniform or have a tendency to stick to each other. Dealing cards one at a time will distribute these clustered cards amongst the players. For most games this is an ideal solution to the failings of human shuffling.

There's no such thing as a 'near random' deck. It's either random, or it isn't. Again, similar cards being spread out is NOT the same thing as random.

Replace "near random" by "nearly uniformly random".
And I think the point is that you are happier with similar cards being spread out than having them not spread out.

In all* games, you are not interested having an exact uniform random distribution after shuffling. What matters is that the hands people draw have the proper probabilities. For example: Say you play with 3 players, and after an imperfect shuffle, card B has has probability of being i cards below card A is 20%, 30%, 20%, 15%, 5%, 5%, 3%, 1%, 1%, for i=1,...,9. Zero afterwards.
Now if you give 6 cards at once to player 1, and cardA is the first card, the probability of him also getting cardB is 90%.
If you give only one card at once, and card A is the first card, the probability of him also getting cardB is 20%+5%+1%=26% which is much closer to the 5/17=29.4% Player 2 is 20%+15%+4%=38% (needs 35.3%; instead of 10% with the first method), player 3 is 30%+5%+1%=36% (needs 35.3%, instead of 0%)

Now I made all this up, and the numbers are a bit extreme of course, but exactly this pattern (cards not getting the 'right' distance) is the biggest problem when shuffling, and by distributing small numbers of cards at once you distribute the probabilities that are too high and the once that are too low among the players, so that they can average out at least a bit. You can do this because the order in which you get the cards usually don't matter.

"Nearly unifromly random" also doesn't mean anything. But I take it you mean you want to have similar cards spread out.
And I actually strongly disagree on what the point of shuffling is. If what you say the point is really were the point, stacking the deck for a spread-out distribution would not only be fine, but good. The real point of shuffling is not knowing what is coming.

[DStu]

Waht do you mean by "doesn't mean anything". Where's the problem? "Nearly"?  Shall we start define everythin mathematically before we talking about it? Because there is definitely no problem in defining "nearly" in the context of probability measures, but I don't think that will get fun here.
So by "nearly uniformly random" I mean: "A probability measure which, in some suitable metric, has a small (for a suitable definition of 'small') distance to the uniform distribution". At least for me, that means quite a lot, although of course it's not very precise...

For the second point, no time now, more on it later or tomorrow.

[theorel]

@WanderingWinder:
That's just ridiculous.  There is not some point where a deck magically goes from non-random to random.  There are different distributions the cards take as you start to shuffle them.  Good shuffling should lead in the limit to a uniform card distribution, but we don't have infinite time to shuffle.  So, we do what we can to help it along.

What is the goal of shuffling?
It is to "randomize" the deck.  Which is to say, for any given position in the deck each card has an equal probability of being in that position.  What is the result of a randomized deck?  For each card there is a given probability of it being dealt to each player.  If the deck is properly randomized then each card should have an equal probability of being given to each player.  So, the actual goal of shuffling and dealing is to get as close as possible to giving each card an equal probability of being in each players' hand...this is a less stringent condition then having each position in the deck be equally likely.  Therefore we do not need to attain some computer-level randomization of the deck, if we try to take steps to mitigate the lack of uniformity in the distribution of the cards.

So, the question is are there steps we can take to more closely approximate a uniform distribution of cards to players, without the deck having a uniform distribution.  The answer is "yes" -if we know something about the distribution of the deck (and given that the deck is not completely deterministic).  As others have pointed out, the actual problem with insufficient shuffling tends to be "clumping".  What this means is that given that card A is in some position in the deck, the cards which were near card A are likely to still be near it.  Choosing a dealing method which involves giving everyone their whole hand will result in a higher likelihood of the cards which were near A being dealt to the same player.  However, choosing a one-at-a-time method will reduce this probability, which is good because it will likely bring it closer to uniform random.  Now, it might take it beyond uniform random, which would also be bad.  So there is still some minimum amount of shuffling necessary to get a distribution which can take on a result closer to uniform random...you can't just pick up the cards and start dealing them, that won't work.  (although it does "spread out former hands"...as you point out, that's not the goal)

[WanderingWinder]

Waht do you mean by "doesn't mean anything". Where's the problem? "Nearly"?  Shall we start define everythin mathematically before we talking about it? Because there is definitely no problem in defining "nearly" in the context of probability measures, but I don't think that will get fun here.
So by "nearly uniformly random" I mean: "A probability measure which, in some suitable metric, has a small (for a suitable definition of 'small') distance to the uniform distribution". At least for me, that means quite a lot, although of course it's not very precise...

For the second point, no time now, more on it later or tomorrow.

Right but 'random' does not mean 'the uniform distribution'. In fact, a uniform distribution is highly ordered, very much not random. Which is the crux, I think, of our misunderstanding.
Random basically means without a pattern. There either is a pattern, or there isn't. I don't see how you can 'almost' or 'nearly' have a pattern. If you want to enlighten me, please go ahead.

Also, if jonts26 wants to bust some mathy statsy goodness, I would definitely appreciate it.

[eHalcyon]

People instinctively consider clumps or streaks to be non-random.  The truth is, randomness produces clumps and streaks as often as it doesn't.  If I flip a coin 4 times, it is just as likely for me to flip HHHH as it is for me to flip HTTH or HTHT or TTHT, even though HHHH "feels" less random.

[Ozle]

I was completely on the side of something can't be 'partially random'

However, then I thought at it like this:

So, if I take three cards from the bottom, shuffle them around and put it into the middle of the deck.

Are the three cards I put in random when considered on thier own??
Is the rest of the deck random without including those 3 cards?
Is the deck as a whole random?

[Ozle]

Although people massively over use the word random in everyday life I have noticed.
"Wow that was completely random"
"Just throwing in a random thought here"
and so on

[Lekkit]

So, if I take three cards from the bottom, shuffle them around and put it into the middle of the deck.

Are the three cards I put in random when considered on thier own??

If the deck was randomized before taking them aside, then, yeah. They are random. Just like a hand drawn from the top of a randomized deck.

Is the rest of the deck random without including those 3 cards?

It's not a complete deck, but the deck is still randomized, right?

Is the deck as a whole random?

If it was random before taking the cards out, then, yeah. It still is.

If you roll a die, the outcome is random. It doesn't really matter if you shake the die in your hand before you roll it, it doesn't make it more random. It's the same here, if the deck is random, then reorganizing the cards won't change that. Unless you flip the deck over and reorganize them while looking at the cards.

[Teproc]

1 card from the top of the deck usually, sometimes 2 if there are a lot of cards to deal, like in Great Dalmuti.

Also, there's a traditional game in France called Tarot. Yes, it's originally somewhat related to the divination cards, except it's really just a sophisticated trick-taking game that is very popular here, and it has weird dealing rules, because you do not ever shuffle the cards. You deal cards three by three, counterclockwise, and you have to deal a separate deck of 3 or 6 cards, depending on how many players there are. Those 3/6 separate cards must not be dealt all at the same time, but at "random" points during the shuffle, and the last card of the deck can't be put in there. This is probably not clear at all, but basically the game has all those weird rules regarding the dealing of the cards because of the absence of shuffling.

This is because the game actually encourages starting hands to be unbalanced. The game kinda needs one or two players to have stronger hands than the other, because, and I won't get deeper into the rules because they're somewhat complicated, basically player wager at the start of the game, and then have to complete the wager while playing against the other players. If 4 people are playing, one person will play against the three others, and if 5 people are playing, it will be 2vs3. During the game, strong cards will often end up in the same tricks, which is extremely relevant as, again, you do not shuffle between games (you do cut the deck though).

All that to say, I find it interesting that the game actually uses dealing rules as a way of "unbalancing" the game in order to basically make it interesting and fair, which is not something that seems to be used in modern card games.

[Eevee]

So, in the games where you distribute cards, how do you handle it?

I play card games for money with my friends A LOT. Sometimes for more meaningful amounts. Not once have anyone complained about not dealing individually. Heck, we even have a name for it, "varianssipötkö" (="a string of variance" or something like that for all of you who dont speak finnish).

I make sure to deal like that every couple of orbits just to hear someone enthusiastically shout "varianssipötkylä!".

[Insomniac]

I don't generally play with people who make a big deal about post-shuffle card distribution, but I've seen them around. It seems that some people think that the cards will be even more randomized if you deal one per player at a time. Even I do that a lot when playing cards. It's a habit, I guess.

It would be faster to just deal each hand out. Using poker as an example, you hand each person the top five cards of the deck. If the deck is properly shuffled, then it should be just as uncertain as dealing one card to each person*.

So, in the games where you distribute cards, how do you handle it?

* Unless you're playing euchre, where you deal 2/3/2/3 cards and then 3/2/3/2 cards at a time.

I play quite a bit of euchre with my family, who learned in Ontario and we've never heard of 2/3/2/3 and just deal 1 to each person till everyone has 5 leaving 4 cards which you check before flipping to make sure you didnt misdeal

[qmech]

Right but 'random' does not mean 'the uniform distribution'. In fact, a uniform distribution is highly ordered, very much not random. Which is the crux, I think, of our misunderstanding.
Random basically means without a pattern. There either is a pattern, or there isn't. I don't see how you can 'almost' or 'nearly' have a pattern. If you want to enlighten me, please go ahead.

Good news: the problem here is only one of terminology.  The uniform distribution on the set of all possible deck orderings is the one that assigns each one an equal probability.  There seem to be a lot of mathematicians around here, who don't think twice about using this (very useful) terminology, but thinking it refers in some sense to spreading copies of the same card out evenly is totally understandable.

The sense in which you can be close to (uniformly) random is this.  There are 52! possible orderings of a standard deck of cards, so with perfect shuffling the probability that you see any particular ordering is 1/52!.  If we have some shuffling method that gives different probabilities to each ordering then we can add up the difference between that probability and 1/52! over all orderings of the deck to obtain a measure of "distance from the uniform distribution" in the technical sense used above.  If this is small then are close to random in the sense that only a very small adjustment to our probabilities would be needed to become "completely random".

To mathematicians, randomness doesn't mean "without patterns" (in fact it's frequently the case that random objects have some approximate structure with very high probability).  It turns out to be much more useful to think about the space of all possible outcomes, and how likely each of those is to occur, rather than looking at a particular instance and trying to decide whether it is "sufficiently random".

[theorel]

Good news: the problem here is only one of terminology.  The uniform distribution on the set of all possible deck orderings is the one that assigns each one an equal probability.  There seem to be a lot of mathematicians around here, who don't think twice about using this (very useful) terminology, but thinking it refers in some sense to spreading copies of the same card out evenly is totally understandable.

I totally would never have thought that a uniform distribution could be thought of that way.  Thank you qmech for cutting to the crux of the matter .

Here's a different point of view on what qmech wrote from a probabilistic rather than combinatorial view:
"deterministic" means that the deck order is determined.  This would be a stacked deck, or the deck in the order you picked it up before shuffling at all.  This is the height of "not-random."  Given a position in the deck you can determine with 100% probability which card appears there (hence "determin"-istic)

Once you start shuffling, the deck ceases to be deterministic.  However the cards still possess a lingering pattern due to how they were cleaned up.  The goal of shuffling is to remove this "pattern".  But the process of shuffling could create any patterns...one possible outcome for the deck is exactly as it was before you shuffled it.  So, we characterize this by saying that the cards appear in a "probability distribution" meaning that given any position in the deck there is a certain probability that a card will appear at that position.

A "uniform probability distribution" means that given a point in the deck each card has a 1/52 probability of appearing there.  Another example of a uniform probability distribution is a non-weighted die, which has a uniform probability distribution for all its numbers (1/6).  This is a fully randomized deck.

My point from before is that a deck does not need to be fully randomized, only "sufficiently randomized".  Which means that it can take on some probability distribution between deterministic and uniform probability.  And that by taking measures to increase the probabilities at given points and decrease them at others you can approximate the uniform probability.  (DStu gave an excellent example before, I suggest anyone who didn't understand re-read it).

[jonts26]

Also, if jonts26 wants to bust some mathy statsy goodness, I would definitely appreciate it.

Well, I don't have much to add the the previous few posts. A lot of the problems here seem to stem from how we define random. Which I guess is a hard thing to pin down and I don't feel like attempting now. Anyway, here are some random thoughts and fun facts!

The purpose of dealing 1 at a time is not to further randomize the deck, but because it's harder to cheat that way since most deck stacking techniques rely on forced clumping of cards during the shuffle. It is much, much easier to stack the deck in euchre than bridge.

There are indeed 1/52! card combinations. That is a lot. For perspective, if you start with a random deck, every time you give it a shuffle, you have almost certainly created a deck ordering which has never happened before. That still blows my mind.

@theorel: The wannabe philosopher in me wants to point out that maybe there is no such thing as random and everything is deterministic.

After 8 perfect shuffles, you return a deck to its original ordering.

[DStu]

First, thanks qmech, I think most of I wanted to write is not neccessary any more (or yet, lets see how the thread goes).

A "uniform probability distribution" means that given a point in the deck each card has a 1/52 probability of appearing there.  Another example of a uniform probability distribution is a non-weighted die, which has a uniform probability distribution for all its numbers (1/6).  This is a fully randomized deck.

It's even stricter. You don't only want to each card to have it's propor position, you want to have each of the 52!=8x10^67 possible permutations of the deck is equally likely. And 10^67 is a large number, the sun has 10^55 atoms (accorting to Wolfram Alpha). So that's nearly a trillion times the number of atoms in the sun.
Do you really come near this distribution? I don't know, it's hard to tell, it's really hard to generate significantly more than 10^67 shuffles to compare the outcome with the uniform distribution. At least if you are limited by the lifetime of the universe...

The good thing is that, when playing most card games, you are not really interested in the exact permutation. You care for what cards come to your hand. So when you distribute your 52card deck to 4 persons, each one getting 13 cards, you don't care in which cards they get first, what matter is which one come to their hand. That mean out the 8x10^67 permutations, you map (13!x13!x13!x13!)=1.3x10^39 permutations to one and the same hands.

And as described above, you can either use this large contraction to try to cancle out any distance from the uniform distribution of all hands, or you you can leave it. Typical shuffles tend to leave cards that where close before the shuffle also close together after the shuffle. Which means, the probability of permutations where these two cards have a smaller distance from each other is 'a bit' larger than it should be, and the ones where they have a large distance is 'a bit' smaller. Where 'a bit' depends on how often you shuffle, but is always larger than 0.

So you want to give each player cards from all parts of the deck to compensate for this behaviour. If you don't, and A and B where next to each other before the shuffle, and he has card A, it's 'highly' likely that he also has B. At least more likely than it should be. If you do, it's significantly lower. See example (with extreme numbers for demonstration effect) above.

[Davio]

Actual randomness: Every permutation is possible with the same likeliness. The chances of the deck being A-2(diamond),A-2(heart),A-2(spade),A-2(club) is the same as 2-A(diamond),2-A(heart),etc and the same as specifically Ac3s8d4h5s....

Human randomness: No two cards of the same suit and a rank higher or lower should be near each other.

In random distributions, clustering (grouping) will appear.

[Kirian]

* Unless you're playing euchre, where you deal 2/3/2/3 cards and then 3/2/3/2 cards at a time.

I play quite a bit of euchre with my family, who learned in Ontario and we've never heard of 2/3/2/3 and just deal 1 to each person till everyone has 5 leaving 4 cards which you check before flipping to make sure you didnt misdeal

Crazy Canadians.  Here in OH it's 2/3, and you'd damned well better count the four cards left before flipping.  Also, no "partner's best" BS, if you're playing alone, play alone.

[Davio]

In the Netherlands with the game "Klaverjassen" the de facto standard is 3-2-3.

In fact, when playing with an older crowd in a competitive setting (tournament), the players can get pretty mad if you divert from this standard. Those players can also get mad when someone grabs their cards before everyone has 8. They can be pretty tough, those Benidorm bastards.
And if you shuffle too much you even get the complaint that "you're shuffling the faces off the cards". 

[Kuildeous]

I play quite a bit of euchre with my family, who learned in Ontario and we've never heard of 2/3/2/3 and just deal 1 to each person till everyone has 5 leaving 4 cards which you check before flipping to make sure you didnt misdeal

I never played euchre. I only learned about it about 3 years ago when I did a show that takes place in the UP ("that's Upper Peninsula for all ya flat-landers"). I researched the game on Wikipedia.

I get the impression that the traditional game sticks with 2/3/2/3, but I'm sure more casual players don't worry about it. Kind of like how pre-Hinterlands, our group would draw the first hand, know what the second hand was and just combine our first two purchases. It would have bugged a Dominion purist ("What? But why would you buy your second card without knowing what the other players are planning?!"), but it worked for our casual group.

[WanderingWinder]

Actual randomness: Every permutation is possible with the same likeliness. The chances of the deck being A-2(diamond),A-2(heart),A-2(spade),A-2(club) is the same as 2-A(diamond),2-A(heart),etc and the same as specifically Ac3s8d4h5s....

Human randomness: No two cards of the same suit and a rank higher or lower should be near each other.

Yeah, but this is the problem. That should happen sometimes.

[WanderingWinder]

Right but 'random' does not mean 'the uniform distribution'. In fact, a uniform distribution is highly ordered, very much not random. Which is the crux, I think, of our misunderstanding.
Random basically means without a pattern. There either is a pattern, or there isn't. I don't see how you can 'almost' or 'nearly' have a pattern. If you want to enlighten me, please go ahead.

Good news: the problem here is only one of terminology.  The uniform distribution on the set of all possible deck orderings is the one that assigns each one an equal probability.  There seem to be a lot of mathematicians around here, who don't think twice about using this (very useful) terminology, but thinking it refers in some sense to spreading copies of the same card out evenly is totally understandable.

Indeed, I do math work at a university, I'm quite aware of what the formal definition of the uniform distribution means. I just thought that you couldn't possibly be referring to the uniform distribution on the set of all deck orderings, because this is impossible to get.
At any given moment in time, the deck has one, particular, distinct order. The probably distribution is 1 that it is in this distinct order, and 0 that it's in any other order. I guess you can say that the deck has achieved this uniform distribution if you put it into a process that leaves you with equal probabilities of every ordering (even this is a stretch really), however, Im pretty sure that such processes don't exist. Though, if you believe the Copenhagen quantum mechanics people (and I don't, but I'll humour you), such a process could exist, but I'm fairly sure the amount of time it would take would take is going to be well longer than the amount of time you'd expect the cards to exist without breaking down, being destroyed, or at least becoming indistinguishable from each other. So, yeah....
I stand by my assertion that for all intents and purposes, the randomization of card decks refers to the inability of humans to predict which card comes at any point, better than giving random equal weight to every card they know to remain in the deck. For most card games, anyway.

[DStu]

But you can model many processes to be random, and even if it is deterministic on some layer, the model will represent what you know about the process. If you don't know how the fingers moved, you can as well assume the distribution is "uniformly random", and probably that is your best guess on how to describe you knowledge of the state of the deck.

It's deterministic in some state I don't know, and all states are from my perspective equally likely is perhaps true, but what do you get from the fact that it is (maybe) deterministic. You know as much about it as if it where random, so you can model it as being random.

It's kind of like, for every-day life, not using the 'fact' that our enviroment can be modelled to be R^3, because Heisenberg uncertainity, and Einstein space curvature, and thus, so it's not "true" that the space is R^3. But you will get to work much easier if you assume it is.

[WanderingWinder]

But you can model many processes to be random, and even if it is deterministic on some layer, the model will represent what you know about the process. If you don't know how the fingers moved, you can as well assume the distribution is "uniformly random", and probably that is your best guess on how to describe you knowledge of the state of the deck.

It's deterministic in some state I don't know, and all states are from my perspective equally likely is perhaps true, but what do you get from the fact that it is (maybe) deterministic. You know as much about it as if it where random, so you can model it as being random.

It's kind of like, for every-day life, not using the 'fact' that our enviroment can be modelled to be R^3, because Heisenberg uncertainity, and Einstein space curvature, and thus, so it's not "true" that the space is R^3. But you will get to work much easier if you assume it is.

This is my point almost exactly (though you can model anything to be anything... ) The point is that people don't know it any different from random. Which is not the same as random, if you want to be precise. But it cuts against the 'almost' random thing. Because either you have some idea as to what cards are where, or you don't. Binary.

[DStu]

This is my point almost exactly (though you can model anything to be anything... ) The point is that people don't know it any different from random. Which is not the same as random, if you want to be precise. But it cuts against the 'almost' random thing. Because either you have some idea as to what cards are where, or you don't. Binary.

It's not 'almost random' is 'almost uniformly random', which the 'almost' bounded to 'uniform', not to random. So it describes a random distribution, which differes a bit from the uniform distribution. (Or some deterministic state which people don't know different from a distribution which is almost uniform).

(But I like to appreviate 'deterministic state the people don't differen from random' by 'random state' in the future, if you don't mind, also I see that there might be some interesting philosopical question (which I don't find interesting) behind it)

Edit: I also see that people have said "nearly random", but this should be parsed to "nearly uniformly random", or maybe "nearly in the obvious distribution" (in case the obvious one is not the uniform distribution).

[WanderingWinder]

This is my point almost exactly (though you can model anything to be anything... ) The point is that people don't know it any different from random. Which is not the same as random, if you want to be precise. But it cuts against the 'almost' random thing. Because either you have some idea as to what cards are where, or you don't. Binary.

It's not 'almost random' is 'almost uniformly random', which the 'almost' bounded to 'uniform', not to random. So it describes a random distribution, which differes a bit from the uniform distribution. (Or some deterministic state which people don't know different from a distribution which is almost uniform).

(But I like to appreviate 'deterministic state the people don't differen from random' by 'random state' in the future, if you don't mind, also I see that there might be some interesting philosopical question (which I don't find interesting) behind it)

But almost uniformly random doesn't mean anything if uniformly random doesn't mean anything, and uniformly random doesn't mean anything if you don't take the strict mathematical definition, and if you DO, then you aren't 'almost' there at all - you either are or aren't. Again. But we're arguing in circles here.
I do mind you calling that random, but 'seemingly random' or 'apparently random' seem fine to me.

[DStu]

But almost uniformly random doesn't mean anything if uniformly random doesn't mean anything, and uniformly random doesn't mean anything if you don't take the strict mathematical definition, and if you DO, then you aren't 'almost' there at all - you either are or aren't

First, uniformly random means quite a lot, if there is a question than if the deck is in this state.

I'm in this field for some years now, and my impression is that the mathemtics quite elgantly ignore this philosphical question of trying to adress "what is 'random'", so I would be curious to see this definition, where 'uniform random' does not mean anything.

Concerning the 'almost', it depends on the definition of almost. I remeber this also already to be in the thread, but there is no problem to define a metric for probability measures, and than "almost" means "some probability measure with small distance with respect to the metric".
If you like to have the discrete metric (you are either there or not, have either distance 1 if you are there, and distance 0 if you are not), than I wonder why you want to use it for probability measures, but not if you talk about your distance on your way home. You can't be almost at home, you either are there or are not.

[DStu]

Doublepost, want to understand where the terminology differ: maybe here?

Because either you have some idea as to what cards are where, or you don't. Binary.

Also if you have "some" information on the cards, I would still call them "random". A coin that shows head 99% of the time is still a random coin, just on which is quite "far" away from the ideal one that shows head 50% of the time. But I can not know the output until it falls, so it's random.

Pedanticly, also deterministic states are probability measure which just happen to have all mass on one state, but I accept to not use the word "random" when something is deterministic to avoid confusion.

[WanderingWinder]

But almost uniformly random doesn't mean anything if uniformly random doesn't mean anything, and uniformly random doesn't mean anything if you don't take the strict mathematical definition, and if you DO, then you aren't 'almost' there at all - you either are or aren't

First, uniformly random means quite a lot, if there is a question than if the deck is in this state.

I think this sentence got away from you. Certainly the second half is a conglomeration of words that doesn't mean much anything to me.

I'm in this field for some years now, and my impression is that the mathemtics quite elgantly ignore this philosphical question of trying to adress "what is 'random'", so I would be curious to see this definition, where 'uniform random' does not mean anything.

Did you fully read my post? I said it doesn't mean anything IF it doesn't mean the strict mathematical definition. I'm saying that is the only definition. I'm not saying that that is not a definition. But you can't ignore the philosophical question, and you don't grasp it if you think you can. The only way to try to 'ignore' it is to accept one side of the argument, which is of course not ignoring it at all. The whole philosophical question is what you mean when you say that. If you truly ignore it, you can't communicate.

Concerning the 'almost', it depends on the definition of almost. I remeber this also already to be in the thread, but there is no problem to define a metric for probability measures, and than "almost" means "some probability measure with small distance with respect to the metric".
If you like to have the discrete metric (you are either there or not, have either distance 1 if you are there, and distance 0 if you are not), than I wonder why you want to use it for probability measures, but not if you talk about your distance on your way home. You can't be almost at home, you either are there or are not.

I reject the notion of the distance metric for a concept such as randomness. Similarly, something is either chaotic or not. Jimmy is either in love with Alice, or he isn't. For certain things, distance makes sense. For others, it does not. I am positing that randomness belongs to the latter class, rather than to the former.

[WanderingWinder]

Doublepost, want to understand where the terminology differ: maybe here?

Because either you have some idea as to what cards are where, or you don't. Binary.

Also if you have "some" information on the cards, I would still call them "random". A coin that shows head 99% of the time is still a random coin, just on which is quite "far" away from the ideal one that shows head 50% of the time. But I can not know the output until it falls, so it's random.

Pedanticly, also deterministic states are probability measure which just happen to have all mass on one state, but I accept to not use the word "random" when something is deterministic to avoid confusion.

The coin that shows heads .99 is of course random around its .99 mean. But the deck of cards is not random about any mean state. It's a false analogy. The more apropos analogy is to a coin which is normally .5 like a normal coin, but given the circumstances of a particular toss, you're able to determine say a .7 chance it lands heads. For this particular toss, the results will be random about a .7 mean of course, but this is certainly not a 'random' toss of the coin.

[DStu]

Concerning the 'almost', it depends on the definition of almost. I remeber this also already to be in the thread, but there is no problem to define a metric for probability measures, and than "almost" means "some probability measure with small distance with respect to the metric".
If you like to have the discrete metric (you are either there or not, have either distance 1 if you are there, and distance 0 if you are not), than I wonder why you want to use it for probability measures, but not if you talk about your distance on your way home. You can't be almost at home, you either are there or are not.

I reject the notion of the distance metric for a concept such as randomness. Similarly, something is either chaotic or not. Jimmy is either in love with Alice, or he isn't. For certain things, distance makes sense. For others, it does not. I am positing that randomness belongs to the latter class, rather than to the former.

So things are either random or they aren't. So far we agree, I think. Now if they are random, (or if I model them as random because all I know of them is as much as I know of some random distribution), there are different probability distributions. There is the uniform distribution, and there are other distribtions. These distributions can have a distance.

So now I can model shuffling. This model is how I imagine shuffling to work, so in a sense that is "what I know" on shuffling. Under this model, I can calculate the distribution of the permutations of the cards. Again that is all I know on the state of the cards, so I can as well asume the cards are in the random state with the distribution I just calculated.  This distribition now again has some distance to the uniform distribtion. So now I'm that bold that if this distance is "small", I would call my cards "almost uniformly random".

[DStu]

The coin that shows heads .99 is of course random around its .99 mean. But the deck of cards is not random about any mean state. It's a false analogy. The more apropos analogy is to a coin which is normally .5 like a normal coin, but given the circumstances of a particular toss, you're able to determine say a .7 chance it lands heads. For this particular toss, the results will be random about a .7 mean of course, but this is certainly not a 'random' toss of the coin.

Why not? With this knowledge, it behaves like a coin with a .7 mean? A coin with .7 mean you consider as random. Why shouldn't you use the same notion for something that behaves exactly the same?

A conditional probability is still a probability.

[WanderingWinder]

The coin that shows heads .99 is of course random around its .99 mean. But the deck of cards is not random about any mean state. It's a false analogy. The more apropos analogy is to a coin which is normally .5 like a normal coin, but given the circumstances of a particular toss, you're able to determine say a .7 chance it lands heads. For this particular toss, the results will be random about a .7 mean of course, but this is certainly not a 'random' toss of the coin.

Why not? With this knowledge, it behaves like a coin with a .7 mean? A coin with .7 mean you consider as random. Why shouldn't you use the same notion for something that behaves exactly the same?

A conditional probability is still a probability.

If I flip the penny I have sitting  next to my keyboard, I am flipping a particular coin rather than a random one. Same reason.

[DStu]

The coin that shows heads .99 is of course random around its .99 mean. But the deck of cards is not random about any mean state. It's a false analogy. The more apropos analogy is to a coin which is normally .5 like a normal coin, but given the circumstances of a particular toss, you're able to determine say a .7 chance it lands heads. For this particular toss, the results will be random about a .7 mean of course, but this is certainly not a 'random' toss of the coin.

Why not? With this knowledge, it behaves like a coin with a .7 mean? A coin with .7 mean you consider as random. Why shouldn't you use the same notion for something that behaves exactly the same?

A conditional probability is still a probability.

If I flip the penny I have sitting  next to my keyboard, I am flipping a particular coin rather than a random one.

And where's the problem in flipping a particular coin?

[WanderingWinder]

The coin that shows heads .99 is of course random around its .99 mean. But the deck of cards is not random about any mean state. It's a false analogy. The more apropos analogy is to a coin which is normally .5 like a normal coin, but given the circumstances of a particular toss, you're able to determine say a .7 chance it lands heads. For this particular toss, the results will be random about a .7 mean of course, but this is certainly not a 'random' toss of the coin.

Why not? With this knowledge, it behaves like a coin with a .7 mean? A coin with .7 mean you consider as random. Why shouldn't you use the same notion for something that behaves exactly the same?

A conditional probability is still a probability.

If I flip the penny I have sitting  next to my keyboard, I am flipping a particular coin rather than a random one.

And where's the problem in flipping a particular coin?

There isn't any problem with it. It's just not random.

[WanderingWinder]

Concerning the 'almost', it depends on the definition of almost. I remeber this also already to be in the thread, but there is no problem to define a metric for probability measures, and than "almost" means "some probability measure with small distance with respect to the metric".
If you like to have the discrete metric (you are either there or not, have either distance 1 if you are there, and distance 0 if you are not), than I wonder why you want to use it for probability measures, but not if you talk about your distance on your way home. You can't be almost at home, you either are there or are not.

I reject the notion of the distance metric for a concept such as randomness. Similarly, something is either chaotic or not. Jimmy is either in love with Alice, or he isn't. For certain things, distance makes sense. For others, it does not. I am positing that randomness belongs to the latter class, rather than to the former.

So things are either random or they aren't. So far we agree, I think. Now if they are random, (or if I model them as random because all I know of them is as much as I know of some random distribution), there are different probability distributions. There is the uniform distribution, and there are other distribtions. These distributions can have a distance.

So now I can model shuffling. This model is how I imagine shuffling to work, so in a sense that is "what I know" on shuffling. Under this model, I can calculate the distribution of the permutations of the cards. Again that is all I know on the state of the cards, so I can as well asume the cards are in the random state with the distribution I just calculated.  This distribition now again has some distance to the uniform distribtion. So now I'm that bold that if this distance is "small", I would call my cards "almost uniformly random".

While this is still not how I would look at things, it's eminently reasonable, and I don't think we really have substantive disagreements at this point.

[carstimon]

I think that you guys are thinking about two different things- the deck itself, and the process of taking a deck and shuffling.  When WW says

There's no such thing as a 'near random' deck. It's either random, or it isn't. Again, similar cards being spread out is NOT the same thing as random.

he's talking about the deck itself.  Whereas DStu is talking about shuffling.

WW, tell me if this is on track to what you're trying to say:  Imagine I hand you two decks of cards, and I ask you "Which is more random?".  This is not meaningful.

And I think DStu is saying this:  I shuffle one deck once, and I shuffle the other deck 17 times.  The second deck is "more random" in the following sense:  the probabilities of which-card-is-where are closer to that of the uniform distribution.

[WanderingWinder]

I think that you guys are thinking about two different things- the deck itself, and the process of taking a deck and shuffling.  When WW says

There's no such thing as a 'near random' deck. It's either random, or it isn't. Again, similar cards being spread out is NOT the same thing as random.

he's talking about the deck itself.  Whereas DStu is talking about shuffling.

WW, tell me if this is on track to what you're trying to say:  Imagine I hand you two decks of cards, and I ask you "Which is more random?".  This is not meaningful.

And I think DStu is saying this:  I shuffle one deck once, and I shuffle the other deck 17 times.  The second deck is "more random" in the following sense:  the probabilities of which-card-is-where are closer to that of the uniform distribution.

I think DStu and I understand each other pretty well. Less sure you do. Most of all, don't think it matters too much at this point.

[timchen]

Because either you have some idea as to what cards are where, or you don't. Binary.

This I don't agree. Can you not have some idea about where are some of the cards? Say you have a deck with stashes, as a trivial example?

What I see you are saying is that you either know completely about a deck (not random), or you know it from partially to none (random). That is sure binary, but a rather useless statement.

Going to the original discussion, different shuffle and dealing definitely matters. Different shuffle gives you different random distributions (which hopefully all converges to the uniform distribution if you shuffle infinitely many times), but with a finite number of shuffles probably some methods converge faster than the others.

Also depending on the game, we might not distinguish some ordering from others. Say in bridge, cards from 2 to 8 are not going to matter that much usually, but the suit always matters. Therefore, a shuffle/dealing that does not exchange positions of numbers in the same suit is more forgivable than a shuffle/dealing that does not exchange suits. In this particular game, since the cards in the same suit are more likely to be played together, it is beneficial to deal it one card at a time to compensate for insufficient shuffle.

[WanderingWinder]

Because either you have some idea as to what cards are where, or you don't. Binary.

This I don't agree. Can you not have some idea about where are some of the cards? Say you have a deck with stashes, as a trivial example?

What I see you are saying is that you either know completely about a deck (not random), or you know it from partially to none (random). That is sure binary, but a rather useless statement.

No, you misread me. In that case where you know something, I'm saying it's not random. So either you know absolutely nothing about the deck (effectively random) or you know something about the deck (not random).

Going to the original discussion, different shuffle and dealing definitely matters. Different shuffle gives you different random distributions (which hopefully all converges to the uniform distribution if you shuffle infinitely many times), but with a finite number of shuffles probably some methods converge faster than the others.

No, this is the whole point. This doesn't give you different random distributions. It gives you different NOT random distributions.

Also depending on the game, we might not distinguish some ordering from others. Say in bridge, cards from 2 to 8 are not going to matter that much usually, but the suit always matters. Therefore, a shuffle/dealing that does not exchange positions of numbers in the same suit is more forgivable than a shuffle/dealing that does not exchange suits. In this particular game, since the cards in the same suit are more likely to be played together, it is beneficial to deal it one card at a time to compensate for insufficient shuffle.

Again, I don't think anything compensates for insufficient shuffling except for sufficient shuffling.

And the larger point, I maintain, is that the only important thing (for most games anyway; there may be some exception) is that people don't know which cards are where at all. If people don't know, you're good, if they do, you have a problem.

[DStu]

No, you misread me. In that case where you know something, I'm saying it's not random. So either you know absolutely nothing about the deck (effectively random) or you know something about the deck (not random).

The story is, as I have experienced the last two pages, WanderingWinder has a extremly strict notion on "random", which basically means "uniformly random" for him.
Every other person I've met so far, including a lot of people working in probability theory, also call other distributions "random distribution". I'm a little bit curious where this strict notion comes from.
I also find this notion a little bit exhausting, because you basically can't speak about things-that-are-not-deterministic-but-are-not-uniformly-random, because you have to invent a new word to describe this state, but have two ("random" and "uniformly random") for "uniformly random".
As said, usually I would call things-that-are-not-deterministic-but-are-not-uniformly-random "random", because they are not deterministic.  And especially it is difficult to talk about why certain things might help shuffling, because all you want to talk about then is things-that-are-not-deterministic-but-are-not-uniformly-random-but-should-get-as-uniform-random-as-possible.

[WanderingWinder]

No, you misread me. In that case where you know something, I'm saying it's not random. So either you know absolutely nothing about the deck (effectively random) or you know something about the deck (not random).

The story is, as I have experienced the last two pages, WanderingWinder has a extremly strict notion on "random", which basically means "uniformly random" for him.
Every other person I've met so far, including a lot of people working in probability theory, also call other distributions "random distribution". I'm a little bit curious where this strict notion comes from.
I also find this notion a little bit exhausting, because you basically can't speak about things-that-are-not-deterministic-but-are-not-uniformly-random, because you have to invent a new word to describe this state, but have two ("random" and "uniformly random") for "uniformly random".
As said, usually I would call things-that-are-not-deterministic-but-are-not-uniformly-random "random", because they are not deterministic.  And especially it is difficult to talk about why certain things might help shuffling, because all you want to talk about then is things-that-are-not-deterministic-but-are-not-uniformly-random-but-should-get-as-uniform-random-as-possible.

Well, my problem goes back to the philosophical question - are there really things that aren't deterministic like that? Well, I think so, but they're effectively quite rare when we're talking about a physical process like shuffling, especially on a macroscopic scale.
I use the 'effectively random' label to talk about things which I know are deterministic, but which none of the pertinent actors are actually consciously determining. If that makes sense.

[DStu]

But in my opionion this philospophical question is quite offtopic, because wether the deck is "random" or not (and what exactly this means) is not the one you are more interested in when shuffling. What you are interested in is that your knowledge on the state of the deck (or what you can at maximum know about it, when you would think really hard), and this can be described as random distribution (not neccesarily uniform).

And that was what I wanted to talk about, but lost the motivation a bit...

[timchen]

No, you misread me. In that case where you know something, I'm saying it's not random. So either you know absolutely nothing about the deck (effectively random) or you know something about the deck (not random).

Sorry, but I don't see how this sentence means anything different from what I said as below:(aside from the claim that I made this distinction is useless)

What I see you are saying is that you either know completely about a deck (not random), or you know it from partially to none (random). That is sure binary, but a rather useless statement.

Ok I guess I need to elaborate.
By your definition, for a shuffled 52-card deck, if I somehow only know where SA is, is this random? I guess not.
How about that I only know SA is among the upper half 26 cards? I guess not.
Or if I only know that SA is next to SK? not random.
How about that I only know SA has a higher than usual probability let's say (25%) next to SK? still not random.
If you agree with my distinction here (which I assume so), then practically any hand-shuffled deck is not random. Even random generators in the strict sense does not generate random numbers. This distinction is thus useless.

(note that in the above discussion "random" means "uniformly random", as there is no ambiguity)

No, this is the whole point. This doesn't give you different random distributions. It gives you different NOT random distributions.

Now here the terminology changes. When you say "random" without further specifications, depending on context it can mean a few things, including a uniform distribution, as the above discussion. But when you say "random distributions" (especially when I have cited "uniform distribution" as a special kind of random distribution), in any scientific context I have seen, it just mean something can take certain values with certain probabilities. Come on, if you work in Physics you must know about expontential distribution, Gaussian, or Maxwell distributions right? They are all random distributions, but not uniform in any sense.

Again, I don't think anything compensates for insufficient shuffling except for sufficient shuffling.

Well, we can still play word games here. Sure, shuffle more is better. And probably I shouldn't use the word "compensate". But my point (and the question from the open post) is, ok, given insufficient shuffle, do different ways of dealing give different results? And the answer I think is yes, and in most cases dealing one card at a time will deal you hands which are statistically more likely from a uniform random distribution, for the purpose of the game.

Well, my problem goes back to the philosophical question - are there really things that aren't deterministic like that? Well, I think so, but they're effectively quite rare when we're talking about a physical process like shuffling, especially on a macroscopic scale.
I use the 'effectively random' label to talk about things which I know are deterministic, but which none of the pertinent actors are actually consciously determining. If that makes sense.

I don't think this has anything to do with the philosophical question-- and it is even not a philosophical question (unless you take the side saying everything is a philosophical question.)
For all practical random things we see in a game, they are actually all deterministic. When you throw a dice, which face ends up on top is completely determined by the initial and boundary conditions. The "randomness" comes about by both the sensitivity to the initial and boundary conditions, and the inability to control those conditions. For a shuffled deck it is similar; the deck once dealt is of course fixed. It is just that we neither control the precise way we shuffle nor remember the starting deck before shuffle so that we have no idea how it will order. The reason why both cases a uniform random distribution emerges is because all the factors that determine the outcome is somewhat insensitive to the spots of the dice or the numbers and drawings on the card so by symmetry we can deduce that if we shuffle long enough or when we throw the dice from high enough the outcome will be uniformly random.

This certainly has nothing to do with whether a Gaussian distribution is random or not random. This also has nothing to do with quantum mechanics and Copenhagen interpretation.

[WanderingWinder]

No, you misread me. In that case where you know something, I'm saying it's not random. So either you know absolutely nothing about the deck (effectively random) or you know something about the deck (not random).

Sorry, but I don't see how this sentence means anything different from what I said as below:(aside from the claim that I made this distinction is useless)

What I see you are saying is that you either know completely about a deck (not random), or you know it from partially to none (random). That is sure binary, but a rather useless statement.

Ok I guess I need to elaborate.
By your definition, for a shuffled 52-card deck, if I somehow only know where SA is, is this random? I guess not.
How about that I only know SA is among the upper half 26 cards? I guess not.
Or if I only know that SA is next to SK? not random.
How about that I only know SA has a higher than usual probability let's say (25%) next to SK? still not random.
If you agree with my distinction here (which I assume so), then practically any hand-shuffled deck is not random. Even random generators in the strict sense does not generate random numbers. This distinction is thus useless.

(note that in the above discussion "random" means "uniformly random", as there is no ambiguity)

Okay. The stuff where you elaborate matches what I've been saying, though probably I am a little wrong here, and the 25% chance kind of situations are indeed random. The reason I resist saying this is because insofar as this matters for a card game, it is not sufficient to have it randomized to this extent - what is needed is the players having absolutely no idea about cards, their placement relative to each other, etc.
The big thing is, what you say in the quoted section above seems to me to be the opposite of what you say in the unquoted section. Maybe I was misunderstanding. But if the 'let me elaborate' stuff is how you understand, then your understanding of what I'm saying is right.

No, this is the whole point. This doesn't give you different random distributions. It gives you different NOT random distributions.

Now here the terminology changes. When you say "random" without further specifications, depending on context it can mean a few things, including a uniform distribution, as the above discussion. But when you say "random distributions" (especially when I have cited "uniform distribution" as a special kind of random distribution), in any scientific context I have seen, it just mean something can take certain values with certain probabilities. Come on, if you work in Physics you must know about expontential distribution, Gaussian, or Maxwell distributions right? They are all random distributions, but not uniform in any sense.

Well, you have thousands of kinds of distributions, and I in no way mean to imply that uniform is the only kind of random distribution in general. Insofar as a card deck is concerned though, it's the only meaningful one. Of course you can have other distributions, and whether they really are random or not IS in fact the philosophical question - there is a big question about about whether random number generators really are random or not, and you can say that's stupid, whatever, but I don't think it is, and there are lots of philosophers at universities who don't either. Now, I realize I'm weird, and that's fine, but it's not a settled thing and not just a 'come on, that's stupid' thing either.

Again, I don't think anything compensates for insufficient shuffling except for sufficient shuffling.

Well, we can still play word games here. Sure, shuffle more is better. And probably I shouldn't use the word "compensate". But my point (and the question from the open post) is, ok, given insufficient shuffle, do different ways of dealing give different results? And the answer I think is yes, and in most cases dealing one card at a time will deal you hands which are statistically more likely from a uniform random distribution, for the purpose of the game.

Of course they give you different results! And my large point is this - these shuffling methods give you hands which more closely resemble VARIED hands, but people associate randomness with these varied hands, when randomness indeed gives you more clumped hands than people think. The same reason why if I ask a million people to come up with a random number between 1 and 1000, the numbers like 100, 200, etc. won't come up as often as they 'ought' to, because people don't think of these as 'random' numbers, just because they're round.

Well, my problem goes back to the philosophical question - are there really things that aren't deterministic like that? Well, I think so, but they're effectively quite rare when we're talking about a physical process like shuffling, especially on a macroscopic scale.
I use the 'effectively random' label to talk about things which I know are deterministic, but which none of the pertinent actors are actually consciously determining. If that makes sense.

I don't think this has anything to do with the philosophical question-- and it is even not a philosophical question (unless you take the side saying everything is a philosophical question.)
For all practical random things we see in a game, they are actually all deterministic. When you throw a dice, which face ends up on top is completely determined by the initial and boundary conditions. The "randomness" comes about by both the sensitivity to the initial and boundary conditions, and the inability to control those conditions. For a shuffled deck it is similar; the deck once dealt is of course fixed. It is just that we neither control the precise way we shuffle nor remember the starting deck before shuffle so that we have no idea how it will order. The reason why both cases a uniform random distribution emerges is because all the factors that determine the outcome is somewhat insensitive to the spots of the dice or the numbers and drawings on the card so by symmetry we can deduce that if we shuffle long enough or when we throw the dice from high enough the outcome will be uniformly random.

This certainly has nothing to do with whether a Gaussian distribution is random or not random. This also has nothing to do with quantum mechanics and Copenhagen interpretation.

1. Who said anything about a Gaussian distribution?
2. It does have something to do with quantum mechanics and the Copenhagen interpretation, because Copenhagen will tell you that the first thing, which you take for granted, about things being deterministic, is in fact wrong, and you actually CAN get things which are TRULY random. Of course this is impractical, but I never tried to bring this up as an actual practical consideration, only in the philosophical realm.

Again, my larger point is that it's not really a uniform distribution that emerges, but the important thing is that the people playing can't tell the difference between the actual distribution and the truly uniform distribution, that people can't predict the distribution better than by guessing how they would via a uniform distribution of the cards. And what I am saying regarding shuffling here is that stacking the cards in some particular way does not help achieve this goal at all. How you shuffle thereafter, how non-standardized your shuffling pattern is, how long you shuffle, etc. WILL help achieve this goal, but stacking the similar cards does not, because it doesn't actually make your guessing of the thing closer to random, but rather you replace your rough ability to estimate that SK and SA are near to each other with a rough ability to estimate that they're far apart.

[carstimon]

I think DStu and I understand each other pretty well. Less sure you do. Most of all, don't think it matters too much at this point.

Ah, I was confused.  Thanks for clearing that up!

[timchen]

The big thing is, what you say in the quoted section above seems to me to be the opposite of what you say in the unquoted section.

Sorry, apparently a hole in my brain or at least in my writing there. I meant either you know completely or partially about a deck (not random), or none (random).

Of course you can have other distributions, and whether they really are random or not IS in fact the philosophical question - there is a big question about about whether random number generators really are random or not, and you can say that's stupid, whatever, but I don't think it is, and there are lots of philosophers at universities who don't either. Now, I realize I'm weird, and that's fine, but it's not a settled thing and not just a 'come on, that's stupid' thing either.

I have no intention saying anyone is stupid or implying so, but I don't understand this stuff. For the question whether random number generators really are random or not, I don't see how this can be a philosophical question. For any random number generator, given the same seed it will always generate the same sequence of numbers. The "randomness" of the random number generator is measured by different correlations within that sequence of numbers, for every given seed. Thus random number generators, at conceptual levels are not random. At technical levels you can measure how "random" it is. And how to build a good random number generator can be a good research problem. Don't see from any aspect can this be a philosophical question.

Of course they give you different results! And my large point is this - these shuffling methods give you hands which more closely resemble VARIED hands, but people associate randomness with these varied hands, when randomness indeed gives you more clumped hands than people think. The same reason why if I ask a million people to come up with a random number between 1 and 1000, the numbers like 100, 200, etc. won't come up as often as they 'ought' to, because people don't think of these as 'random' numbers, just because they're round.

This I agree, but I don't see people arguing on the opposite side in this thread...
And in the case we are interested, given some insufficient shuffle, dealing 13 cards at a time will tend to deal out more clumped hands than random, while dealing 1 card at a time my tend to deal out more varied hands than random. But I still think the degree of "more varied" is less than the degree of "more clumped." See David's reply in BGG's thread for a related example. (It is stacking your deck before shuffle whereas here I am talking about dealing. But I believe the effect is similar.)

2. It does have something to do with quantum mechanics and the Copenhagen interpretation, because Copenhagen will tell you that the first thing, which you take for granted, about things being deterministic, is in fact wrong, and you actually CAN get things which are TRULY random. Of course this is impractical, but I never tried to bring this up as an actual practical consideration, only in the philosophical realm.

No. The evolution in quantum mechanics is deterministic, but measurements from a deterministic state can give random results. The Copenhagen interpretation is a philosophical way trying to explain why measurements themselves are NOT described by evolution in quantum mechanics. This is an outdated argument anyway, as modern theories understand measurement as disentanglement via environment.

Nevertheless, there are intrinsic randomness in quantum mechanics (unless you are A T'hooft...). This has nothing to do with our present discussion however, due to the fact that quantum mechanical random fluctuations are suppressed by thermal (high energy) and statistical (large number of degrees of freedom) fluctuations. So in an effective theory describe dice throwing and shuffling there is effectively no intrinsic randomness. Researchwise I believe it is an interesting topic trying to find instances where the "quantumness" can survive at higher temperature.

And what I am saying regarding shuffling here is that stacking the cards in some particular way does not help achieve this goal at all. How you shuffle thereafter, how non-standardized your shuffling pattern is, how long you shuffle, etc. WILL help achieve this goal, but stacking the similar cards does not, because it doesn't actually make your guessing of the thing closer to random, but rather you replace your rough ability to estimate that SK and SA are near to each other with a rough ability to estimate that they're far apart.

Having some hard time grasping what you are saying. But I think what you mean is that if you stack the cards, you replace one not-so-random distribution by another. Sure, but my point is that there is one which is closer to the uniform distribution. For example, suppose you deliberately keep SA and SK far away when you stack them. Let's say you therefore reduce the chance for them to be together from the uniform distribution case (~4%) to 3%. If you don't put them far away when you see they are next to each other, then they will have a much higher chance of being together ~25% as opposed to how they should be. (~4%) It is obvious to me that the former is closer to uniform distribution and is therefore better.

[WanderingWinder]

Of course you can have other distributions, and whether they really are random or not IS in fact the philosophical question - there is a big question about about whether random number generators really are random or not, and you can say that's stupid, whatever, but I don't think it is, and there are lots of philosophers at universities who don't either. Now, I realize I'm weird, and that's fine, but it's not a settled thing and not just a 'come on, that's stupid' thing either.

I have no intention saying anyone is stupid or implying so, but I don't understand this stuff. For the question whether random number generators really are random or not, I don't see how this can be a philosophical question. For any random number generator, given the same seed it will always generate the same sequence of numbers. The "randomness" of the random number generator is measured by different correlations within that sequence of numbers, for every given seed. Thus random number generators, at conceptual levels are not random. At technical levels you can measure how "random" it is. And how to build a good random number generator can be a good research problem. Don't see from any aspect can this be a philosophical question.

There are a number of ways of generating random numbers without specific seeds that you just give it. Largely, they're still algorithmic around some kind of seed, but the point is whether the seed is or is not random. Practically, people tend not to use random number generators that are very based on this. But occasionally there's some entropic stuff going on, or taking a bit which has its state determined by quantum-level fluctuations, at least in hypotheticals. Which is generally what philosophical discussions (at least the ones I have) are - the specific instances are unimportant, because there can be loopholes out. Platonists (and these are very much Platonic discussions) care more about the general, the essence, the form. So ok, you don't see it, it's there; as you don't care about it, I really see no reason to try to force you to understand my viewpoint here. So I'm not going to.

Of course they give you different results! And my large point is this - these shuffling methods give you hands which more closely resemble VARIED hands, but people associate randomness with these varied hands, when randomness indeed gives you more clumped hands than people think. The same reason why if I ask a million people to come up with a random number between 1 and 1000, the numbers like 100, 200, etc. won't come up as often as they 'ought' to, because people don't think of these as 'random' numbers, just because they're round.

This I agree, but I don't see people arguing on the opposite side in this thread...
And in the case we are interested, given some insufficient shuffle, dealing 13 cards at a time will tend to deal out more clumped hands than random,

iff the cards were originally more clumped, but I take your point.

while dealing 1 card at a time my tend to deal out more varied hands than random. But I still think the degree of "more varied" is less than the degree of "more clumped." See David's reply in BGG's thread for a related example. (It is stacking your deck before shuffle whereas here I am talking about dealing. But I believe the effect is similar.)

Okay, read his thing, and obviously there's nothing factually wrong there. As I said earlier in the thread, I reject the distance metric, but I also understand that it's eminently plausible, and from a practical standpoint, I won't bother to argue against it. But I don't see what that has to do with the varied vs. clumped thing. A varied deck and a clumped deck can't be compared to what he's talking about, because he isn't talking about deck orderings - he's talking about randomization processes. These are two entirely different animals. Any particular ordering of the cards does not have a distance form the uniform distribution, because the uniform distribution is not an actual ordered deck of cards. The process of shuffling can be modeled as producing a probabilistic distribution of the cards in the deck, and this probabilistic model can then be compared to the uniform distribution. Hence you have to compare the shuffling process to get your distance metric, not any particular deck.
I have a feeling that ^^that paragraph is confusingly written. Can someone who understands it (if anyone does...) rephrase it more clearly for me?

2. It does have something to do with quantum mechanics and the Copenhagen interpretation, because Copenhagen will tell you that the first thing, which you take for granted, about things being deterministic, is in fact wrong, and you actually CAN get things which are TRULY random. Of course this is impractical, but I never tried to bring this up as an actual practical consideration, only in the philosophical realm.

No. The evolution in quantum mechanics is deterministic,

No. No it's not. It's probabilistic.

but measurements from a deterministic state can give random results. The Copenhagen interpretation is a philosophical way trying to explain why measurements themselves are NOT described by evolution in quantum mechanics. This is an outdated argument anyway,

It's still the most popular one, though now it may only have a plurality rather than a majority of followers.

as modern theories understand measurement as disentanglement via environment.

Nevertheless, there are intrinsic randomness in quantum mechanics (unless you are A T'hooft...).

I'm not a T'hooft per se, but I don't believe in intrinsic randomness in the universe. Or, in fact, true randomness at all. Which may be part of the problem here?

This has nothing to do with our present discussion however, due to the fact that quantum mechanical random fluctuations are suppressed by thermal (high energy) and statistical (large number of degrees of freedom) fluctuations. So in an effective theory describe dice throwing and shuffling there is effectively no intrinsic randomness.

I assume by 'effectively' you mean to just ignore the incredibly small influence that the supposed quantum effects would have on a macroscopic scale, which, while not zero, is so insanely small that it largely is ignored. In which case, yeah, ok, I have been saying this since the beginning.

Researchwise I believe it is an interesting topic trying to find instances where the "quantumness" can survive at higher temperature.

And I don't. But whatever, we can have different interests, and this is increasingly divergent from the topic.

And what I am saying regarding shuffling here is that stacking the cards in some particular way does not help achieve this goal at all. How you shuffle thereafter, how non-standardized your shuffling pattern is, how long you shuffle, etc. WILL help achieve this goal, but stacking the similar cards does not, because it doesn't actually make your guessing of the thing closer to random, but rather you replace your rough ability to estimate that SK and SA are near to each other with a rough ability to estimate that they're far apart.

Having some hard time grasping what you are saying. But I think what you mean is that if you stack the cards, you replace one not-so-random distribution by another. Sure, but my point is that there is one which is closer to the uniform distribution. For example, suppose you deliberately keep SA and SK far away when you stack them. Let's say you therefore reduce the chance for them to be together from the uniform distribution case (~4%) to 3%. If you don't put them far away when you see they are next to each other, then they will have a much higher chance of being together ~25% as opposed to how they should be. (~4%) It is obvious to me that the former is closer to uniform distribution and is therefore better.

What is obvious to you is obviously wrong to me, cf. the paragraph I've written and labelled as confusingly written above.

[timchen]

There are a number of ways of generating random numbers without specific seeds that you just give it. Largely, they're still algorithmic around some kind of seed, but the point is whether the seed is or is not random. Practically, people tend not to use random number generators that are very based on this. But occasionally there's some entropic stuff going on, or taking a bit which has its state determined by quantum-level fluctuations, at least in hypotheticals. Which is generally what philosophical discussions (at least the ones I have) are - the specific instances are unimportant, because there can be loopholes out. Platonists (and these are very much Platonic discussions) care more about the general, the essence, the form. So ok, you don't see it, it's there; as you don't care about it, I really see no reason to try to force you to understand my viewpoint here. So I'm not going to.

\
Please elaborate. I am interested. Sorry if I say so, but right now I feel it's like a few random opaque words throwing together to create some philosophical atmosphere.

Specifically: a few questions and comments:
 --a very common seed I know used in programming is time. It is not random at all. The random thing is that the sequence of the numbers bears no relation to the value of the seed.
--Sure you can attempt to use quantum-level fluctuations to create a theoretical real random number generator-- but is there anything philosophical about this?
--entropic stuff? What do you mean?

the specific instances are unimportant, because there can be loopholes out. Platonists (and these are very much Platonic discussions) care more about the general, the essence, the form.

And what are you talking about here? Can you be more specific and how is it related to things you said before it anyway?

But I don't see what that has to do with the varied vs. clumped thing. A varied deck and a clumped deck can't be compared to what he's talking about, because he isn't talking about deck orderings - he's talking about randomization processes. These are two entirely different animals. Any particular ordering of the cards does not have a distance form the uniform distribution, because the uniform distribution is not an actual ordered deck of cards. The process of shuffling can be modeled as producing a probabilistic distribution of the cards in the deck, and this probabilistic model can then be compared to the uniform distribution. Hence you have to compare the shuffling process to get your distance metric, not any particular deck.
I have a feeling that ^^that paragraph is confusingly written. Can someone who understands it (if anyone does...) rephrase it more clearly for me?

I think you are wrong here. What we are discussing is to stack the deck before you shuffle or how you deal after you shuffle, which is defining a randomization process, and will result in some random distribution. Any particular shuffle will create a single instance, but the distribution describes the statistics of the deck resulting from using the same procedure again and again. And what I am arguing here is that to declump the cards before you shuffle or to deal cards one by one to each player can result in a randomization procedure which results in a distribution closer to the uniform distribution than say, not do anything or to deal 13 cards at a time. And I thought what you were saying is you disagree. If you are talking about a single instance, a single known deck, I am not sure I understand what you are talking about at all.

No. No it's not. It's probabilistic.

It's not. Given an initial state |\psi>, after time t it becomes exp(iHt)|\psi>. Nothing probabilistic here. The only probabilistic thing is when you measure an observable O, the resulting state will be one of the eigenstate of O, with probability proportional to the absolute value squared of the inner product between that eigenstate and the current state |\psi>.

It's still the most popular one

Most popular in common literature, maybe?

What is obvious to you is obviously wrong to me, cf. the paragraph I've written and labelled as confusingly written above.

Trying to see how can this be obviously wrong to you, but failed. If you wish you can explain.

[WanderingWinder]

There are a number of ways of generating random numbers without specific seeds that you just give it. Largely, they're still algorithmic around some kind of seed, but the point is whether the seed is or is not random. Practically, people tend not to use random number generators that are very based on this. But occasionally there's some entropic stuff going on, or taking a bit which has its state determined by quantum-level fluctuations, at least in hypotheticals. Which is generally what philosophical discussions (at least the ones I have) are - the specific instances are unimportant, because there can be loopholes out. Platonists (and these are very much Platonic discussions) care more about the general, the essence, the form. So ok, you don't see it, it's there; as you don't care about it, I really see no reason to try to force you to understand my viewpoint here. So I'm not going to.

\
Please elaborate. I am interested. Sorry if I say so, but right now I feel it's like a few random opaque words throwing together to create some philosophical atmosphere.

Specifically: a few questions and comments:
 --a very common seed I know used in programming is time. It is not random at all. The random thing is that the sequence of the numbers bears no relation to the value of the seed.
--Sure you can attempt to use quantum-level fluctuations to create a theoretical real random number generator-- but is there anything philosophical about this?
--entropic stuff? What do you mean?

the specific instances are unimportant, because there can be loopholes out. Platonists (and these are very much Platonic discussions) care more about the general, the essence, the form.

And what are you talking about here? Can you be more specific and how is it related to things you said before it anyway?

Sorry, not going to. Tired of this topic anyway, and I don't think there's any progress to be made at this point.

But I don't see what that has to do with the varied vs. clumped thing. A varied deck and a clumped deck can't be compared to what he's talking about, because he isn't talking about deck orderings - he's talking about randomization processes. These are two entirely different animals. Any particular ordering of the cards does not have a distance form the uniform distribution, because the uniform distribution is not an actual ordered deck of cards. The process of shuffling can be modeled as producing a probabilistic distribution of the cards in the deck, and this probabilistic model can then be compared to the uniform distribution. Hence you have to compare the shuffling process to get your distance metric, not any particular deck.
I have a feeling that ^^that paragraph is confusingly written. Can someone who understands it (if anyone does...) rephrase it more clearly for me?

I think you are wrong here. What we are discussing is to stack the deck before you shuffle or how you deal after you shuffle, which is defining a randomization process, and will result in some random distribution. Any particular shuffle will create a single instance, but the distribution describes the statistics of the deck resulting from using the same procedure again and again. And what I am arguing here is that to declump the cards before you shuffle or to deal cards one by one to each player can result in a randomization procedure which results in a distribution closer to the uniform distribution than say, not do anything or to deal 13 cards at a time. And I thought what you were saying is you disagree. If you are talking about a single instance, a single known deck, I am not sure I understand what you are talking about at all.

Great. That's not what I thought you were talking about. No rel disagreements here, just some doubts. I'm not so sure as you are that you're right. But I don't have a huge particular reason that you're wrong. In any case, I think the effect is small with sufficient shuffling, and doesn't do much if anything to change how much shuffling is sufficient. I would guess.

No. No it's not. It's probabilistic.

It's not. Given an initial state |\psi>, after time t it becomes exp(iHt)|\psi>. Nothing probabilistic here. The only probabilistic thing is when you measure an observable O, the resulting state will be one of the eigenstate of O, with probability proportional to the absolute value squared of the inner product between that eigenstate and the current state |\psi>.

This somewhat vaguely-written (possibly your English-as-second-language doesn't help you here) chunk of text does not demonstrate to me that you understand quantum. Of course, I could be the wrong one. I certainly wouldn't try to say I understand quantum either. At any rate, I hate quantum, and tend to try to not refer to it except: 1) with a couple of specific close personal friends or 2) derisively. So I'd rather not get in this big discussion. As you're the only one who really cares about it here, I'll just defer. Like, to my understanding, what you're saying is wrong, but I so don't care, that I'm fine with that being accepted; especially as I believe my own understanding to be incorrect.

It's still the most popular one

Most popular in common literature, maybe?

I can't see a reasonable definition by which it's not the most popular. What definition would you use, and what interpretation is more popular.

What is obvious to you is obviously wrong to me, cf. the paragraph I've written and labelled as confusingly written above.

Trying to see how can this be obviously wrong to you, but failed. If you wish you can explain.
[/quote]
I was trying to see how it could be obvious to you, and I failed as well. But hey, you know, I don't wish. I'm just tired of this thread by this point.

[timchen]

This somewhat vaguely-written (possibly your English-as-second-language doesn't help you here) chunk of text does not demonstrate to me that you understand quantum. Of course, I could be the wrong one. I certainly wouldn't try to say I understand quantum either. At any rate, I hate quantum, and tend to try to not refer to it except: 1) with a couple of specific close personal friends or 2) derisively. So I'd rather not get in this big discussion. As you're the only one who really cares about it here, I'll just defer. Like, to my understanding, what you're saying is wrong, but I so don't care, that I'm fine with that being accepted; especially as I believe my own understanding to be incorrect.

It is not the problem of my English. In fact I think these few sentences are probably among the most accurate things I have said in this thread. Unfortunately while it is precise, it is not clear. It could only demonstrate to you that I know (can't say understand!) quantum mechanics if you also know about it (which I thought you do). In any rate, if you have taken a modern undergrad level quantum class you will have a perfect idea what I am talking about. Yeah, but you said you hate it so I guess that's okay.

I can't see a reasonable definition by which it's not the most popular. What definition would you use, and what interpretation is more popular.

I was expecting popularity among physicists. I imagine the disentanglement from environment causing the measurement process to lose unitarity and become random is the dominant point of view nowadays. People also talk about multiverse too, but more from a sci-fi perspective.

I was trying to see how it could be obvious to you, and I failed as well. But hey, you know, I don't wish. I'm just tired of this thread by this point.

At this point if I take your comments seriously, it must be my language problem. I was saying identical things to the above paragraph now you say you have no problem with. Maybe it is because I neglected to say "and then shuffle" after "stacking them"? Anyway I think we understand each other now.

[WanderingWinder]

Sorry, not going to. Tired of this topic anyway, and I don't think there's any progress to be made at this point.

Yeah, I thought there's not much to be explained too. At least nothing based on science and logic.

This somewhat vaguely-written (possibly your English-as-second-language doesn't help you here) chunk of text does not demonstrate to me that you understand quantum. Of course, I could be the wrong one. I certainly wouldn't try to say I understand quantum either. At any rate, I hate quantum, and tend to try to not refer to it except: 1) with a couple of specific close personal friends or 2) derisively. So I'd rather not get in this big discussion. As you're the only one who really cares about it here, I'll just defer. Like, to my understanding, what you're saying is wrong, but I so don't care, that I'm fine with that being accepted; especially as I believe my own understanding to be incorrect.

It is not the problem of my English. In fact I think these few sentences are probably among the most accurate things I have said in this thread. Unfortunately while it is precise, it is not clear. It could only demonstrate to you that I know (can't say understand!) quantum mechanics if you also know about it (which I thought you do). In any rate, if you have taken a modern undergrad level quantum class you will have a perfect idea what I am talking about. Yeah, but you said you hate it so I guess that's okay.

I can't see a reasonable definition by which it's not the most popular. What definition would you use, and what interpretation is more popular.

I was expecting popularity among physicists. I imagine the disentanglement from environment causing the measurement process to lose unitarity and become random is the dominant point of view nowadays. People also talk about multiverse too, but more from a sci-fi perspective.

I was trying to see how it could be obvious to you, and I failed as well. But hey, you know, I don't wish. I'm just tired of this thread by this point.

At this point if I take your comments seriously, it must be my language problem. I was saying identical things to the above paragraph now you say you have no problem with. Maybe it is because I neglected to say "and then shuffle" after "stacking them"? Anyway I think we understand each other now.

There's really no need to insult me, or imply that by not wanting to continue the discussion, I must be wrong.
I really don't think we need another flame war.
Thanks.

[timchen]

I am sorry. I'll edit.

[WanderingWinder]

I don't see the point in editing. I'm not going to un-see it. I just don't much see the point in trying to bait me into an argument where it's very clear neither of us will win, especially as no one else cares, and as I'd said, I don't really care either. I mean, the problem I have isn't with your statement, really- that's just a symptom- and it's not really with the theory, because that just doesn't really matter; it's with the confrontational attitude.

[timchen]

I don't see the point in editing. I'm not going to un-see it. I just don't much see the point in trying to bait me into an argument where it's very clear neither of us will win, especially as no one else cares, and as I'd said, I don't really care either. I mean, the problem I have isn't with your statement, really- that's just a symptom- and it's not really with the theory, because that just doesn't really matter; it's with the confrontational attitude.

For the attitude, I am sorry. The reason why I edited is that I do want you to speak more on that particular subject, and this has nothing to do with whether anyone else is watching or not. Just really want to know what that philosophical question is. But if you take it as sort of a bait or an insult, that is not my original intent so I deleted it, and I am sorry about that. 

On the other hand, your attitude isn't exactly welcome, is it?
The most annoying part to me is this

No. No it's not. It's probabilistic.

comment on quantum mechanics. Clearly you have said blatantly something you later admit that you do not know well. And when I thought you knew well and said something rigorous (if short) then you start to question my English. For me, I never comment anything with authoritative tone unless I am 100% confident. For things I am less sure of you can always read the uncertain-ness in my post. Frankly speaking, I still feel my confrontational attitude is more justified than your cocky ones.

[WanderingWinder]

Because it IS probabilistic, and I'm going to trust my professors, one of whom knew Schroedinger, and all the textbooks and everything I've read more than anything you could say. Now, I'm not trying to say I'm an expert here, and I have not claimed that. But I know experts, and the probabilistic thing is clear. Even if I totally disagree with QM kn a hundred philosophical reasons, which makes it a very hard thing to try to defend. So man, I'm not sure how you get cocky - I am genuinely bewildered - because at every step I am trying to hedge, trying to give you wiggle room, trying to give reasonable explanations for our misunderstandings or disagreements, but all you come back with is that I must be stupid. No dude, I'm just trying to not be an arrogant jerk, trying to give ways for the thing to be ended amicably, but you know, it's a fault of mine, but I have a big problem when somebody just keeps punching me and projecting his own godliness onto me. To be clear you almost never seem to display uncertainty, so given what you said above, I must assume you're certain about a great many things, so good for you.
Incidentally, the reason I know that I don't understand QM and you don't either is that all the leading experts on it almost uniformly state that NO ONE understands it. But I guess you might know better than them, so whatever.
At this point I am just so sick of the whole thing, I don't care if you say I'm as stupid as a lead ball. And as I've probably said too much already, this WILL be the last from me here.

[timchen]

Because it IS probabilistic, and I'm going to trust my professors, one of whom knew Schroedinger, and all the textbooks and everything I've read more than anything you could say.

Well, I think I said pretty clearly that it is the measurement part which is probabilistic. The time evolution part is deterministic. If any of the people you mentioned think otherwise, well, I can't say it's impossible, but then they are wrong. But much more likely to me is that they will know perfectly what I am saying, and it is just you who don't know but still insist. But the point is not who is wrong or who is right. You know, if you think you are right, you should say why it is right, not just throwing names around it. And if you are not sure, you can just say you are not sure.

I am probably a little bit over-reactive on this part. I work on quantum physics, that's probably why.

I am genuinely bewildered - because at every step I am trying to hedge, trying to give you wiggle room, trying to give reasonable explanations for our misunderstandings or disagreements, but all you come back with is that I must be stupid.

On this part, maybe you did, but I don't want a compromise. Maybe that's the main problem of me. You know, I don't care that much who is right, but I want to have things done right. So if something I am certain I am right, and you didn't point anything wrong with it, I just cannot take the hedge in between. But seriously, I didn't think and didn't imply anything about your intelligence. In fact I think you are quite intelligent, but maybe a bit too um how to say, defensive? You know, discussing things with stupid people is not so fun anyway...

No dude, I'm just trying to not be an arrogant jerk, trying to give ways for the thing to be ended amicably, but you know, it's a fault of mine, but I have a big problem when somebody just keeps punching me and projecting his own godliness onto me. To be clear you almost never seem to display uncertainty, so given what you said above, I must assume you're certain about a great many things, so good for you.

Well, things I said in this thread I am indeed pretty certain. Not so much on other threads though... And please don't be sarcastic. I am certain about, really, very few things. But random ensembles and quantum mechanics are probably among the things I am a bit more familiar with. Especially on this forum, you clearly are more certain and better at relevant things (Dominion that is )

[DStu]

Okay, read his thing, and obviously there's nothing factually wrong there. As I said earlier in the thread, I reject the distance metric, but I also understand that it's eminently plausible, and from a practical standpoint, I won't bother to argue against it. But I don't see what that has to do with the varied vs. clumped thing. A varied deck and a clumped deck can't be compared to what he's talking about, because he isn't talking about deck orderings - he's talking about randomization processes. These are two entirely different animals. Any particular ordering of the cards does not have a distance form the uniform distribution, because the uniform distribution is not an actual ordered deck of cards. The process of shuffling can be modeled as producing a probabilistic distribution of the cards in the deck, and this probabilistic model can then be compared to the uniform distribution. Hence you have to compare the shuffling process to get your distance metric, not any particular deck.

Actually, a deterministic state does also has a distance to the uniform distribution, because deterministic states are actually also random distribution that just happen to have all the mass on one certain point. The distance is just nearly 1 (or maybe 2, depending on how exactly it's defined...) given his metric.  Anyway...

I think the point is, when you want to describe how "good" a specific shuffling method is, you need some kind of distance decreases when the shuffling is "better". What "better" means is than obviously point to the modelling. But if you reject a metric, and only look at it binary, a deck is never shuffled, because with every human shuffling method, they are always both in some deterministic but unknown state, and your know (a bit) about them, because you can find out how human shuffling works, what it does with the cards and how likely they end up in which state.  That means in the context, your notation does not help you, because it will always tell you "it's not random", no matter what you do.
So I think rejecting the notion of a distance for probabilty measures, and/or rejecting to model the state of the deck with probability measure, just prevents you to analyze how good certain shuffling methods are. And then it's hard to talk about shuffling methods. And, to come back to the topic, the way how you deal cards can (or should in my opionion) be seen as one step in shuffling the deck.

I think I can kind of understand that probably, when e.g. coming with a Quantum-background, one likes to not call something-which-is-clearly-in-a-defined-state-you-just-don't-know "random", just for the purpose of talking about shuffling of decks calling shuffled decks deterministic is just as practical as using general relativity when talking about quarks. It is just the "wrong" effective model. (Where "wrong" means it does not help you to describe the important features of the considered object as well as another model).