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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).