Improper shuffling - how to exploit?

[tpir90036]

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This does not create good randomness from the original.

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That is why there is a wash, a box and a cut. Like I said before.... there is no way any human being could use the way casinos shuffle to gain any sort of edge.

However, assuming they did not use these shuffling steps... it would be very easy to predict some cards from straight riffling. Paul Phillips had a story on his livejournal about playing poker in Barcelona where they did not box the cards and he theorized one could figure out one of the board cards with some degree of certainty if they worked at it:

http://extempore.livejournal.com/45230.html

[GuitarMarc]

Thanks tpir, that's along the lines of what I was looking for. So the wash and the box play a pretty important role in randomization. It was interesting what one of the posters over there said.

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I'm a shuffle nut, and have been since early in my poker career. I've read some of Persei Diaconis's work on shuffling, and it's eye-opening. I get bitchy in places where the house shuffle doesn't include a wash -- at least Casino Barcelona does. While you were barred from Binion's, two years ago, their house shuffle was changed, for the duration of the WSOP, to: gather cards, riffle, strip, riffle. No wash, except in cash games when a player asked for it. Only two riffles. One wound up seeing some interesting deals. (I laugh when I hear people complain about the dealing on online sites.)

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[Derek in NYC]

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Example - I was at the Oaks Club this weekend and in the back room they do not use automatic shufflers. The dealer takes the muck and unused cards, spreads them out and mixes them a bit before putting the deck back together. Then 3 rifle shuffles followed by a quick hand mix then 1 more rifle shuffle.

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It is my understanding this is the proper method to use.

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This cannot be the correct technique, as it is missing a 1 handed box cut.

[bobman0330]

Can you call someone an anti-intellectual and a know-it-all in the same post? It's good to know your perjoratives are fully randomized.

No sequence of perfect cuts and perfect riffles is going to work in a poker game, obviously. if that were the case, a computer simulation could be worked out beforehand that would tell a player where various cards would end up after the shuffle sequence, based on knowing where they started. for example, if we know that the top card becomes the turn after the shuffles, the shuffle is badly broken and can be exploited by any player.

One important point is to distinguish between practical shuffle requirements in a game like poker and a game like bridge. In bridge, all the cards will be dealt, what's important is that all card combinations are equally likely. Thus, a bridge shuffle is bad if adjacent cards in the unshuffled deck tend to remain adjacent (never dealt together) or remain an odd number of spaces apart (dealt to same partnership). In a game of poker, relative position is still important, but absolute position is important as well (if all the top cards [usually cards dealt in the prior hand] remained the top cards, then there would be serious failures of randomness. In a bridge game, it doesn't matter what order you get the cards in. Hypothetically, you could divide the deck into a top half and a bottom half, shuffle them thoroughly, then restack the deck in the same order and deal. This works fine for bridge, but horribly horribly for bridge.) Also, bridge cards have a tendency to become ordered during play, whereas poker does not involve any change in the relative orientation of the cards.

My point from all that is... there are two aspects of randomness, one of which (absolute position) is not preserved by any perfect sequence.

Another relevant point is that a discussion of shuffle efficiency shouldn't make you really mad...

[TheNoodleMan]

I would love to play poker against those of you who believe that you can beat the shuffle.

OT: What is the over under on the number of times this is quoted?

[GuitarMarc]

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Can you call someone an anti-intellectual and a know-it-all in the same post? It's good to know your perjoratives are fully randomized.


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Yes, you can. They're not mutually exclusive or random. He was "anti-intellectual" because he was questioning the merits of a well-known ground breaking study that experts in the field readily accept. He was a "know-it-all" because though he didn't really understand the study, he felt he could BS about it.

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Another relevant point is that a discussion of shuffle efficiency shouldn't make you really mad...

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Of course not since I'm the one who started the thread. It was the unnecessary confrontational manner of a few people who then needed to personalize it instead of discussing it in theory.

[fluff]

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I'm pretty surprised at some of these answers. It is a real phenomena that happens with shuffling. Sorry Joshua, but you're absolutely wrong in what you said. The study proves 7 shuffles create randomness. Also you can't work backwards saying that 7 shuffles will now be predictable since 8 shuffles returns the deck to its original.

The point is that most brick and mortars DO NOT shuffle enough to create true randomness and I was wondering if there was a way to take advantage of this. There's no point debating the merits of a 13 year old study that was a major math breakthrough. I assumed anyone responding here would be familiar enough with it before attempting an answer.

Dave Bayer and Persi Diaconis, "Trailing the Dovetail Shuffle to its Lair", Ann. Appl. Probab. 2(1992), 294-313

http://www.math.hmc.edu/funfacts/ffiles/20001.4-6.shtml

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Maybe this is a definition problem, but a perfect riffle is something like this:

Say you have 16 cards, 1 2 3 4 5 6 7 8 a b c d e f g h i j.

Then for one prefect riffle you'll get 1 a 2 b 3 c 4 d 5 e 6 f 7 g 8 h 9 i.

The next one you get 1 5 a e 2 6 b f 3 7 c g 4 8 d h

As you can see there is ABSOLUTELY NOTHING RANDOM about a *perfect* riffle. No matter how many times you riffle prefectly, you can track EXACTLY where each card will be. They are NOT ALLOWED to be in any other state.

The study you cite introduces some randomness when the deck is cut, hence they are not talking about purely perfect riffles (read the damn thing). Also it says nothing about guaranteeing randomness after 7 riffles, it says that a *minimum* of 7 riffles is required to allow for all possible states a 52 card deck can attain.

Moreover, believing that a sequence of 7 perfect riffles creates a random deck, then an 8th perfect riffle will return it to its original state and calling other people "anti-intellectual" is the height of irony.

[GuitarMarc]

Some of you are getting denser and denser. It's not about whether you can track the position of the cards after n shuffles. In that case, the 9th shuffle results will equal the 2nd shuffle results. The point is that the 7th shuffle will create sufficient randomness from the original order to not bias the next hand. It could be a perfect or imperfect set of shuffles. Once again, it's not the point.

You could create an algorithm that shuffles the cards anyway you want, then perform it over 1000 permutations, then have your program tell you the exact location of every card. Based on what you just said, that would be not random enough because there would still be a way to know the location of every card. Just because a computer could track the card locations doesn't mean in a real life environment that it's not random enough.

And enough with the anti-intellectual stuff. The real irony lies in you trying to be cutesy about referring to it yet still not understanding the heart of the matter. Some pros seem to think the shuffle is insufficient in some places. Be aware of it, don't be aware of it. 3 or 4 shuffles is not sufficiently random according to the study. That's what this post is about.

[JoshuaD]

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Sorry Joshua, but you're absolutely wrong in what you said. The study proves 7 shuffles create randomness. Also you can't work backwards saying that 7 shuffles will now be predictable since 8 shuffles returns the deck to its original.

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I must not be understanding what you said, because it sounds like nonsense.

You're saying if you take a deck and do a perfect shuffle -- that's placing one card from your right, one from your left, one from your right, one from your left.. etc -- seven times, the result will be random? That's just nonsense.

In each perfect shuffle, I will be able to track each and every card. If I split exactly in the middle and put the top half in my left hand, and then proceed to shuffle, placing a card from my right hand first, I will know where every single card was re-located to:

From the top of the deck:

1, 27, 2, 28, 3, 29, 4, 30, ....

Now, I do anohter perfect shuffle. Same steps as before.

1, 14, 27, 40, 2, 15, 28, 41 ...

This process is trackable for any number of shuffles, there is absolutely nothing random about it. The deck may LOOK thoroughly shuffled at step 7, but it is in a very predictable and althogether non-random state.

edit: Reading over the thread now, I see you addressed this.

[JoshuaD]

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You're right, I wrote that incorrectly. Obviously it should be that you fail to understand the point which you still do. Where do you get off saying I am changing my statements. If you were here I would slap you silly. Why do aholes like you exist.

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What in gods name are you talking about?

YOU said:

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Right. That famous study said 8 perfect rifle shuffles will return the deck to its original state but 7 creates good randomness from the original.

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That is flat out, 100%, absolutely, positively, without a doubt wrong. We understand now that you mispoke when you said this, but your initial response shows a gross misunderstanding of this issue:

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Sorry Joshua, but you're absolutely wrong in what you said. The study proves 7 shuffles create randomness. Also you can't work backwards saying that 7 shuffles will now be predictable since 8 shuffles returns the deck to its original.

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If the 8th shuffle will ALWAYS return the deck to it's original ordering then the position of every card is known after the 7th shuffle. If that wasn't the case, then there would be now way we could predict that the 8th shuffle returns the deck to normal.

You have said a great deal of blantantly wrong things in this thread, don't get mad when people call you on it.