Atlantic Electronic
http://aejm.ca
Journal of Mathematics
http://rema.ca
Volume
1
, Number
1
, Summer
2006
pp.
1–4
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 ytox. If she estimates
that the odds of winning the pot are better than ytox, then calling the bet of $x
is going to be profitable in the long run. Here is a typical example. A player has
AJ of hearts and the board has 268Q of which two are hearts. If the pot has
$100 and she is facing a bet of $10, then the pot is offering her 10to1 pot odds.
The odds against catching a heart on the river are about 4to1. The odds against
catching a heart that doesn’t pair the board are about 5.5to1.
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 onefifth of the time and lose
her $10 about fourfifths 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 doesn’t.
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 2to1.
Thus, she has placed her
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 Spring '10
 Jeremy
 Glossary of poker terms, backtoback pocket aces

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