So far this Website has provided a systematic outline of the principles for success at Texas Hold'em Poker. What follows is a series of five essays on poker, and gambling, in general. The purpose of these essays is to discuss some counter-intuitive mathematical ideas and their relationship to human behavior that must be understood to succeed over the long run at any gambling endeavor.
The first three essays (starting next page) address probability theory. In my many years teaching math, I have found that probability concepts are among the most difficult for students to grasp. Part of the problem is our human tendency to believe that everything happens for a reason. It is difficult to accept the idea of events happening for no reason.
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Patterns and Sequences
People constantly search for patterns in sequences of random events, and, in fact, find patterns. However, patterns found within random event sequences have no predictive value. You will always be able to find patterns because humans are good at finding patterns - it is how we learn. But patterns found in a sequence of past random events will not predict the outcome of future random events, which is the essential meaning of randomness.
People also have a related tendency to project personal meaning into random events. When playing lotteries, horses and roulette, for example, we pick numbers that have personal meaning, such as our birthday, child's birthday, or anniversary. Because enough people pick meaningful numbers, over time the laws of chance dictate that some of these numbers will win on occasion. But again, accidental coincidence does not mean that these numbers are predictive in any way. It just means that people are good at finding meaning in the events that make up their lives. No one is willing to accept the fact that a good deal of the important events in our lives happen by chance.
Part of the difficulty with accepting the unpredictability of future random events, is that mathematically it is necessary to distinguish between two types of events-independent and conditional. Each time the deck is reshuffled and the cards dealt, all memory of the past is erased. Each starting hand is an independent event with its own unchanged probability.
The first essay in the next pages discusses probability concepts for independent events. Once a hand is dealt, probabilities become conditional. What is the probability of an Ace appearing on the board? If you hold two Aces, that probability is substantially reduced compared to the situation where you hold no Aces. If you hold two Aces and you have good reason to believe your opponents hold the other two, the probability of another Ace appearing has fallen to zero. The second essay discusses these kinds of situations where probabilities are altered because of conditions. Lastly, we will discuss the mathematical requirements for winning over the long run. Randomness means that anything can happen in the short-run, but what happens if you play month after month, year after year?
Discussion of the psychological attributes is necessary for success. Most poker books stress the need for patience.
However, poker requires a different kind of patience than the kind your mother taught. Waiting for an event that can happen at any time is different from waiting for an event that will happen in a given amount of time. The essay about Patience concerns the need for a new understanding of "patience." The last essay elaborates on the need for a flexible, dynamic strategy and how adjustments are made during a day of playing poker.
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