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Unformatted text preview: Atlantic Electronic http://aejm.ca Journal of Mathematics http://rema.ca Volume 1 , Number 1 , Summer 2006 pp. 14 HOW DO MATHEMATICS AND POKER MIX? Brian Alspach Department of Mathematics and Statistics University of Regina Regina, SK S4S 082 I am asked frequently how I view the role of mathematics in poker. I see three distinct ways in which mathematics relates to poker. The first is through the mathematics one actually uses while playing the game. The second is through the mathematics that changes or reinforces how one thinks about the game. The third is via the wide range of mathematical questions that arise from poker. I shall discuss each of these in turn. Also, I am assuming that the reader has some familiarity with the standard poker games and terminology. Anyone who wishes to brush up on poker information should go to the Canadian Poker Player Magazine website (http://www.canadianpokerplayer.com) and follow some of the links. Issues involving pot odds form the broadest application of mathematics during actual play. The idea is straightforward. When a player is facing a bet of $x and the pot has $y in it, we say the pot is offering her pot odds of y-to-x. If she estimates that the odds of winning the pot are better than y-to-x, then calling the bet of $x is going to be profitable in the long run. Here is a typical example. A player has A-J of hearts and the board has 2-6-8-Q of which two are hearts. If the pot has $100 and she is facing a bet of $10, then the pot is offering her 10-to-1 pot odds. The odds against catching a heart on the river are about 4-to-1. The odds against catching a heart that doesnt pair the board are about 5.5-to-1. She can expect to catch a heart about one in every five times she is in this situation. Thus, she will make a profit of $100 about one-fifth of the time and lose her $10 about four-fifths of the time. This means she is averaging about a $12 profit for every bet. This assumes she wins if a heart comes and she loses if it doesnt. This is a simplification, but in any case, it is a very profitable situation and she should call the bet. The preceding example is clearcut but that is not always the case. Sometimes it can be tricky to figure out the odds against winning. You must estimate the strengths of your opponents hands. You also must estimate what kind of future action you might get should you hit a card you need. Making these estimates is part of the mathematical approach. Players also can manipulate the pot odds being offered to other players. For example, if there are two players left and the first to act suspects her opponent is on a flush draw, then a raise roughly equal to the size of the pot means that her opponent is getting pot odds of only about 2-to-1. Thus, she has placed her opponent in the position of not having the proper odds to call should her opponent be on some kind of draw. Of course, this applies mostly to pot limit and no-limit 1 2...
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