Shuffling

Robbie Strazynski (@cardplayerlife) pointed me to this YouTube video about the mathematics of shuffling a deck of cards into true randomness:




You might watch that and think, "OMG! The way poker dealers shuffle doesn't come anywhere close to meeting that standard!" And you'd be right. But you wouldn't be right to worry about that fact.

When the professor is talking about a deck that is not fully randomized, so that one could guess the next card more often than chance alone would dictate, he's talking about having started from a deck that is as it comes from the factory--or, to use the casino term, a deck that has been "spaded"--with the cards in rank order within each suit.

But if you don't know what order the cards are in before the shuffling begins, it makes no difference how much shuffling you do. Your ability to guess the position of any specified card is 1 out of 52 before the shuffling procedure begins (by definition of what it means not to know what order the cards are in), and it is the same after one riffle shuffle, or two, or ten.

For purposes of a poker game, it makes no difference whether the order of the cards in the deck after the shuffling process can pass a statistical test for random distribution compared to the order they were in before the shuffling process. All that matters is whether any player can know or guess the identity of any card. For example, suppose that I see that the first card I'm dealt is the queen of clubs. Can I guess the identity of the next card--which will be dealt to the player on my left--with any accuracy better than a 1 in 51 guess based on that one piece of information? No. And that's all that matters.

Of course, if one is paying attention, one can know at least roughly the position of some of the cards before the shuffle, because you can watch the dealer turn face-down the board cards and any players' hands that were exposed, and watch where those cards end up in the deck. Suppose you notice that the river card on the previous hand was the ace of diamonds, and the way the dealer gathers up the cards causes that ace to now be on the bottom of the deck before the shuffle.

You could, if you really wanted to, watch what the dealer does, and get a general sense of where that ace ends up. The dealer will typically do two riffle shuffles, which will leave the ace within the bottom few cards. Next he will do a "boxing" shuffle, which is an on-the-table equivalent to the second type of shuffling shown in the video. It moves a few cards at a time as a packet from the top of the deck to the bottom. So now you know that the ace is somewhere near the top of the deck--probably within the top ten cards. Now the dealer does another riffle, which will leave the ace near the top. Finally, the deck is cut, which will put that ace somewhere in the middle.

If you're playing ten-handed hold'em, 20 cards will be dealt to the players. Is that enough that one of the last ones dealt will be that ace of diamonds? Maybe, maybe not--it depends on how large the packets of cards were during the boxing shuffle, and on where the cut was made. If the ace doesn't get to one of the players, will it end up on the board? Maybe, maybe not. The dealer will go through 8 more cards (5 on the board and 3 burn cards), so the river will be what had been the 28th card in the deck at the start of the hand. But the ace might be above or below that point. You can't be sure.

This shuffled deck would not pass every test for randomness, because you could, for example, profitably bet that the ace of diamonds will be found in the middle one-third of the deck, which will prove to be true more than it being in the top or bottom thirds--a condition that would not obtain for a truly randomized deck of cards. But in real-world practice, your ability to track the position of a card is so diluted, and the poker edge you could gain by a general sense of where in the deck that one card will be found is so weak that they might as well be zero.

And all of that is for just one card, and only for a person who is really watching closely. If the dealer does a wash of the cards before the shuffling (some casinos' procedures require that, some leave it up to the dealer, or it may be done at a player's request), it's pretty unlikely that you'll be able to follow the position of even that one card you were trying to track.

Furthermore, if the casino uses a Shufflemaster machine with alternating decks, you have no chance at all, because the machine truly randomizes the deck. It has a random number generator, and moves each card to a randomly selected spot (1 through 52) in the newly ordered deck.

All of which is a very long way of saying this: The standard poker room shuffling procedure, if done correctly, is plenty good enough. It may not pass rigorous statistical tests of randomness, but it effectively leaves every player thoroughly ignorant of where any card is going to show up, which is all that matters.

New setup? You're a moron.

God, how I hate idiots that ask for a new setup because they're in a dry spell for catching good hands. Do they seriously think that getting one or two new decks of cards will change that? It's sheer lunacy. Every hand you're dealt is random, whether it's from an old deck or a new deck. Random is random. Bad streaks are no more likely to end with a new deck than with the current deck. I wouldn't mind so much, except that it's such a waste of time, what with checking the decks for the right number of cards, getting them shuffled, etc.

I really want to ask these imbeciles to explain to me the mechanism by which they believe that a new deck of cards will change the probability that the next hand they're dealt will be a good one. They can't possibly have a cogent answer.

The only advantage is that this is yet another way that we learn which players think that they lose because of bad luck, rather than bad playing. If you ask for a new setup, thinking that it might change your luck, you're an idiot, plain and simple, in the same way that if you blame the dealer for bad hands you're an imbecile. You don't understand or accept randomness, which means that with your current mindset you will never, ever become a consistently winning player. You're a loser because you just don't get it. Thanks for volunteering to announce that to the whole table.

I understand randomness. I accept randomness. In fact, I embrace randomness. In the same way that random genetic mutations are the raw material on which evolutionary forces work to produce new species, random card sequences are the raw material from which I make strong, interesting, and unexpected poker hands. I make my livelihood out of randomness, and I accept that an inevitable consequence of randomness is that there will be long stretches of unplayable hands, and days and weeks when I lose money because I get strong but second-best hands over and over and over again.

That is the nature of the game. And it doesn't change because a new deck of cards is brought to the table, you pinhead. So stop wasting everybody's time. Go for a five-minute walk, and when you come back, we'll tell you that we changed the decks. Just believe it, and the effect will be exactly the same. (In fact, come to think of it, that's exactly what casinos should do: Anybody who asks for a setup is required to leave the room for five minutes. The game will just go on without them, but when they come back, everybody tells them that the decks were changed during their absence.)

Once again, if I had my own casino, asking for a new setup would be deemed proof that you're too stupid to be playing, so you'd be escorted out. But first we'd take a photo of you with a dunce cap on your head, to be added to the file of people not allowed back in for reasons of excessive stupidity.


I should note an exception to the above rant. Sometimes a deck needs to be replaced. This can happen because the cards have become sticky and the auto-shuffler keeps jamming, or the dealer keeps pitching two cards at a time, etc. Also, sometimes the cards are so worn that the backs of some of the cards have developed wear patterns that players can start to identify, or an out-of-spec Shufflemaster is putting distinguishing creases on some cards. If you can show the dealer and the floor person an objective reason that a deck should be replaced, by all means do so. I've done it myself a few times, including once when I spotted an ace that had been deliberately marked by a player. But as anybody who has spent much time in a poker room knows, the vast majority of setup requests are from players who want to change their luck. I frankly don't understand why casinos indulge these idiotic demands. Roy Cooke has it right again in his proposed set of rules: "A player may not request a set-up except for a marred card." ("Cooke's Rules of Real Poker," 14.19, p. 107.) Are you listening, poker-room managers?