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ON RANDOMNESS, RUSHES, HOT SEATS, AND BAD LUCK Dealers

Some of the most persistent fallacies in the poker world revolve around notions that the cards fall in predictable patterns.

Three of the most common fallacies are:

1. You can be on a rush during which you can expect better cards than usual.
2. A seat in which a player has been receiving good cards can be expected to continue to receive good cards.
3. Certain dealers can be expected to deal a player especially good or bad cards.

Each of these notions reflects a lack of appreciation of the concept of randomness. (*To avoid needlessly expanding the scope of this essay I will not address the variations which exist in the definition of “randomness.” Some of these variations seems to have come about more for practical purposes of obtaining useful research samples than for their logical precision as definitions of randomness. Here I am conceptualizing randomness as a feature of the sampling process (e.g., the shuffle and deal of the cards). It follows and this essay will elaborate on this – that a set of data (e.g., a series of dealt poker hands ) obtained by a random sampling process may appear quite unrandom. That is to be expected some of the time. (See Randomness, 1998, chap.9, by Deborah J. Bennett, for further discussion of this matter.)

A COIN TOSS RUSH

One of the simplest ways to illustrate the idea of randomness is the coin toss. I will use coin toss analogies to show the irrationality of each of the fallacious notions I have mentioned. First, consider the idea of being on a rush. Many (perhaps most?) poker players believe that they can identify when they are on a rush. They believe that they can then play substandard hands because, since they are on a rush, they will tend to make good hands on the flop or later, at a frequency greater than what could normally be expected. This is an illusion. To understand why, one must first understand that the cards you receive are random. The cards are scrambled and shuffled to create unpredictable sequences each deal.

Now the astute reader might note that a player is more likely to be dealt certain combinations of cards, or to make certain kinds of hands, but this still does not say that the deal of the cards is not random. It means only that the resulting combinations are not equally likely. It is rather like throwing two dice. The outcome is random, though certain numbers are more likely to come up than others. (See e.g., the discussions in the book Randomness by Deborah J. Bennet ). An implication of the randomness of the cards dealt is that you cannot accurately predict what cards you will receive next. You can accurately say, for example, that you are more likely to be dealt AK than AA.

But you cannot predict better than statistical probability when you will receive one or the other. But what if you were to pick a period when you happen to have been receiving a highly unusual assortment of poker cards. Say that for a half hour you happen to have been dealt a far greater than average number of “premium” starting hands such as big pairs, AK, AQs and the like. At that point, can you not predict that you are especially likely to receive a premium hand on the next deal? Well, this is a good time to look for enlightenment in a coin toss. Say you begin to toss a fair coin over and over. Beginning on the 458th toss you happen to have a streak of 17 tails in a row. Would you be willing to lay odds that it will come up a tail on the next toss? Would you agree to bet, say two dollars to someone else’s one dollar that the next toss will produce a tail?

To do so you would have to be convinced that the chance of a tail coming up on the next toss is no longer 50 percent. You would have to believe that it has somehow risen to over 66 percent. Think about that. As you looked at the coin sitting in your hand prior to the next toss, you would actually have to believe that some force was present making it over 66 percent likely to come up a tail. Let’s look at the issue another way. Say you record the results of several million coin tosses in a row. Now you go back and look at the outcomes in sequence. Now suppose that you pick out 100 sequences within the several million in which the first ten tosses of the sequences produced a head.

You don’t look beyond the tenth toss of each sequence. Since each of these sequences has least ten heads in a row, is it reasonable to assume that they should, on average, be more likely to show a head on the next toss than would be the case for sequences of, say, three heads in a row? Bear in mind that if you answer yes to this question you must believe that the ten head sequence has caused the coin to change in some way.

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