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I started playing tournament blackjack almost two years ago. I prepared myself by studying every written word on the topic I could get my hands on. Confident that I had a huge advantage over the "ploppies" where I played, I pressed forward. Unfortunately, this huge advantage didn’t materialize. I barely won more than my share, based on the numbers of winners versus the number of players. It seemed as if the strategies I’d studied so diligently weren’t working. I’ve come to the conclusion that the mathematically optimal betting and playing decisions recommended in the literature often aren’t optimal against ploppies.

This is because of assumptions you work from when you apply the strategies in the available literature. The main assumption is that your opponents are strong players who themselves are likely to make optimal decisions. Ploppies often make suboptimal decisions, or even give it away to you. Many good players I’ve talked to adjust their play for this, drawing upon their experience and gut instincts. But I became interested in the idea of quantifying these uncertain factors in a systematic way. A 20^th-century innovation in the philosophy of logic – fuzzy logic – seems to offer some answers.

You might have a negative impression of this whole idea of using "fuzzy logic" for any kind of rigorous mathematical analysis. Don’t get this confused with the disparaging use of the term "fuzzy math" that’s been used in politics. Fuzzy logic is a school of thought used extensively in mathematical modeling, computer programming, and many other fields.

A detailed discourse in the mechanics of fuzzy logic is beyond the scope of this article, and would be boring. Instead let’s just say that you can assign percentages to the possibility of each decision within the set of all possibilities for this decision. For example, if a player is deciding whether to play craps or roulette, you can assign a value of 0.5 to the possibility of each choice if you have no other information about this player. If past experience with this player has shown that he/she likes craps more, you can assign 2/3 to the possibility that craps will be played, and 1 minus 2/3, or 1/3, to the possibility of roulette being played. Note the similarity to probability theory, in which 1 is used as the sum of the probabilities of all possible events being examined. In fact, the mathematical treatment of the quantities in fuzzy logic is practically identical to that of probability theory.

How is all this important in tournament blackjack? I’ll start with the example I feel is the most important to your win rate.

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