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[Grujah]

I find it interesting to hear/realize that pile shuffling is reversible, because that could have a crazy application for MtG:  if someone plays a game, pile shuffles, then riffle/mash shuffles only one or two times, then when the other opponent takes their right to shuffle the deck, they could perform a procedure that reverses the pile shuffle, then perform no other randomization.  The player who underrandomized would then have a very high likelihood of getting clumpy draws.

.. and the other player gets DQed for cheating.
Stacking your opponents deck intentionally is illegal.

[pacovf]

This is a "spirit of the law" thing, right? The other player doesn't look at the cards, in a well-shuffled deck what he is doing is not going to affect the deck at all.

[Kirian]

Which brings up the question, what is the purpose of pile shuffling?  If the intent is not to randomize the cards, then why do it at all?

I'm not meaning this rhetorically either, I don't pile shuffle and I'm genuinely curious.

It's to make the order dramatically different. When you overhand shuffle the Silver and Gold piles together, if any given card from that pile is a Gold, the odds are that the card directly underneath it is another Gold and everybody in your casual playgroup knows this even if they're not trying to exploit it. Pile shuffle it a couple of times (in addition to the overhand shuffles that you already did in step 1), and it's still possible to give yourself pretty good odds of predicting the card correctly, but now it requires effort, and in a casual game, it can generally be assumed that nobody's going to put in that effort.

But this is just another argument that overhand shuffling is a bad idea.  Shuffle the Silvers and Golds together with two or three mash shuffles, and you've done just as well but in a lot less time.

[Awaclus]

But this is just another argument that overhand shuffling is a bad idea.  Shuffle the Silvers and Golds together with two or three mash shuffles, and you've done just as well but in a lot less time.

And ruined your cards.

[Rabid]

Which brings up the question, what is the purpose of pile shuffling?  If the intent is not to randomize the cards, then why do it at all?

I'm not meaning this rhetorically either, I don't pile shuffle and I'm genuinely curious.

It's to make the order dramatically different. When you overhand shuffle the Silver and Gold piles together, if any given card from that pile is a Gold, the odds are that the card directly underneath it is another Gold and everybody in your casual playgroup knows this even if they're not trying to exploit it. Pile shuffle it a couple of times (in addition to the overhand shuffles that you already did in step 1), and it's still possible to give yourself pretty good odds of predicting the card correctly, but now it requires effort, and in a casual game, it can generally be assumed that nobody's going to put in that effort.

But this is just another argument that overhand shuffling is a bad idea.  Shuffle the Silvers and Golds together with two or three mash shuffles, and you've done just as well but in a lot less time.

I use a pile reordering when shuffling in MTG.
Mostly to count the deck, but the other benefit is breaking up cards the are physically stuck together.

[Chris is me]

I overhand the first few shuffles, then switch to a gentle mash shuffle plus some overhands. With just 10 - 15 cards, I can do about a dozen overhand shuffles in the time it would take me to mash 4 or 5 times, and it's probably random enough, maybe. I don't like the riffle shuffle for such small decks, really. It's too easy to just miss entirely and waste your time. But really, I like overhand shuffling mainly because it just feels satisfying to do.

I don't know if anyone else does this, but I usually alternate which side of the deck the overhand shuffle tosses cards to? Dunno if that helps.

I never pile shuffle. I do in Magic before several regular shuffles just to make the order different before i start shuffling, but it's neither random nor fast, so what's the point?

[Kirian]

But this is just another argument that overhand shuffling is a bad idea.  Shuffle the Silvers and Golds together with two or three mash shuffles, and you've done just as well but in a lot less time.

And ruined your cards.

Do you not sleeve your cards?  Obviously the mash shuffle only works for sleeved cards.

[Awaclus]

But this is just another argument that overhand shuffling is a bad idea.  Shuffle the Silvers and Golds together with two or three mash shuffles, and you've done just as well but in a lot less time.

And ruined your cards.

Do you not sleeve your cards?  Obviously the mash shuffle only works for sleeved cards.

Not my Dominion cards, there are too many of them.

[enfynet]

But this is just another argument that overhand shuffling is a bad idea.  Shuffle the Silvers and Golds together with two or three mash shuffles, and you've done just as well but in a lot less time.

And ruined your cards.

Do you not sleeve your cards?  Obviously the mash shuffle only works for sleeved cards.

Not my Dominion cards, there are too many of them.

Same here. Overhand shuffle is the most delicate way to handle unsleeved paper cards.

[werothegreat]

But this is just another argument that overhand shuffling is a bad idea.  Shuffle the Silvers and Golds together with two or three mash shuffles, and you've done just as well but in a lot less time.

And ruined your cards.

Do you not sleeve your cards?  Obviously the mash shuffle only works for sleeved cards.

Not my Dominion cards, there are too many of them.

Same here. Overhand shuffle is the most delicate way to handle unsleeved paper cards.

I always mash shuffle.  Never sleeved.  Cards are fine.  There's a way to do it that just slides them between each other.

EDIT: It's also easier with fewer cards.  Once I go over about 20 cards in my deck, I start riffling.

[popsofctown]

I find it interesting to hear/realize that pile shuffling is reversible, because that could have a crazy application for MtG:  if someone plays a game, pile shuffles, then riffle/mash shuffles only one or two times, then when the other opponent takes their right to shuffle the deck, they could perform a procedure that reverses the pile shuffle, then perform no other randomization.  The player who underrandomized would then have a very high likelihood of getting clumpy draws.

.. and the other player gets DQed for cheating.
Stacking your opponents deck intentionally is illegal.

Well, there's two thing here, theory, and practice.  In practice, I think you'd have a really hard time proving malicious intent from the person who reversed the pile shuffle.  I don't think anyone would ever get DQed for reversing a pile shuffle.  At the RELs that are high enough where a DQ like that would happen, both players are going to be megarandomizing their decks so much this will not be not really be a thing. 


In theory, apart from what may be Wizards of the Coast policy because I don't always agree with that, when your opponent presents their deck to you, it's already random, and it was their responsibility to make sure of that, and if I don't look at the faces of the cards there's nothing I can do to make it nonrandom.  If you reverse a procedural reordering on the cards, you can't possibly make your opponent's draws any better or any worse unless he didn't randomize his deck in the first place.  If he didn't randomize his deck in the first place, then you stacked his deck with a procedural method, but that by necessity means that he did too when he pile shuffled procedurally.  The only way a rational arbiter could DQ the second player to touch the cards is if he also DQ'ed the first player to touch the cards.  Double DQing could be an internally consistent position to have on that though.


Philosophically, I don't really think that a form of "cheating" that in its absolute best case reverses the amount of cheating an opposing player did can really be considered cheating.


As a specific exception, if someone performed the "semirandom pile shuffle", where they try to pick which pile gets each card as arbitrarily as they possibly can, and you managed to watch and remember what they chose for each pile, which would be impressive, and then reversed -that-, that would be cheating, because there was some amount of randomness and disorder in how those piles were created (even though human random number generation is really weak, which is why that method shouldn't relied upon), and you've reversed that randomness and disorder deliberately.

[Witherweaver]

F.DS: Your source for shuffle analysis.

[DStu]

The operation that reverses pile shuffling is more pile shuffling.

If you pile-shuffle n card in k piles, and do this i(n,k) times, you get back to the original order.  That this is true is trivial, there are at most n! orderings, and as it is deterministic, it must repeat itself eventually*.  But i(n,k) is way smaller than n!.
Also, you could revert a pile shuffle by taking the "shuffled" deck, take k cards each, put them into a pile and than draw 1 card from each pile rotating. So just think on what you have to do to perform the pile shuffle backwards.

But shuffling is not commutative, so if you plan to get a bad deck by doing a reverse pile shuffle, after "pile shuffling then bad shuffling", so have P*B*P^(-1),you won't get B (just bad shuffle).


So why pile shuffling at all? In Dominion, it also has it's merit even if it does not add randomness. This is because you have many similar cards, and usual shuffling techniques will work better if these similar cards are distributed around the deck. See David desJardins explaining it to Donald

:e Forgot the *: Of course just by this it is not entierly clear that the cricle starts at the beginning, this is left as exercise to the reader.

[Witherweaver]

What if you change the number of piles per iteration, and does this assume equal size piles?

[Grujah]

I find it interesting to hear/realize that pile shuffling is reversible, because that could have a crazy application for MtG:  if someone plays a game, pile shuffles, then riffle/mash shuffles only one or two times, then when the other opponent takes their right to shuffle the deck, they could perform a procedure that reverses the pile shuffle, then perform no other randomization.  The player who underrandomized would then have a very high likelihood of getting clumpy draws.

.. and the other player gets DQed for cheating.
Stacking your opponents deck intentionally is illegal.

Well, there's two thing here, theory, and practice.  In practice, I think you'd have a really hard time proving malicious intent from the person who reversed the pile shuffle.  I don't think anyone would ever get DQed for reversing a pile shuffle.  At the RELs that are high enough where a DQ like that would happen, both players are going to be megarandomizing their decks so much this will not be not really be a thing. 


In theory, apart from what may be Wizards of the Coast policy because I don't always agree with that, when your opponent presents their deck to you, it's already random, and it was their responsibility to make sure of that, and if I don't look at the faces of the cards there's nothing I can do to make it nonrandom.  If you reverse a procedural reordering on the cards, you can't possibly make your opponent's draws any better or any worse unless he didn't randomize his deck in the first place.  If he didn't randomize his deck in the first place, then you stacked his deck with a procedural method, but that by necessity means that he did too when he pile shuffled procedurally.  The only way a rational arbiter could DQ the second player to touch the cards is if he also DQ'ed the first player to touch the cards.  Double DQing could be an internally consistent position to have on that though.


Philosophically, I don't really think that a form of "cheating" that in its absolute best case reverses the amount of cheating an opposing player did can really be considered cheating.


As a specific exception, if someone performed the "semirandom pile shuffle", where they try to pick which pile gets each card as arbitrarily as they possibly can, and you managed to watch and remember what they chose for each pile, which would be impressive, and then reversed -that-, that would be cheating, because there was some amount of randomness and disorder in how those piles were created (even though human random number generation is really weak, which is why that method shouldn't relied upon), and you've reversed that randomness and disorder deliberately.

First, assuming that just because somebody is playing at Comp/Pro REL he is more likely to "megarandomize" his deck is false. If you watch the competitive scene, there have been quite a few banning recently for deck manipulations. Also, this GPTs and PPTQ are both Competative REL and we have them very often here at our LGS, so it is not unusual to get a newer player who doesn't know the rules the best at one of them.

Thing is, you are not "reverting the cheating". If your opponent didn't shuffle right unintentionally, it doesn't qualify as cheating, and he will get a Game Loss at most (from what I recall, can't bother to check the rules ATM). If you intentionally stuck his deck, it is cheating.

Of course, it's up judge to correctly interpret the intentions, but if you are presented with a non-randomized deck, you either ask your opponent to shuffle it correctly or call a judge, depending on REL and how casual the atmosphere is.

[popsofctown]

I don't understand how the judge could possibly discern intentions in practice, especially when a reverse pile shuffle is a pile shuffle.