Practical Poker Math

From a Game Theory Perspective
While it is important to know the money odds and the odds
of improvement, to see the total picture a player must also
consider certain aspects of opposing players’ hands, as well
as their likely actions and reactions.
To have a true idea of expectation in any given hand, a player
needs to know only 3 pieces of information:
1. The likely size of the pot at the end
2. The cost to continue to the end
3. A player’s Total Odds of winning the pot.
Sometimes calculating a player’s Total Odds of winning the
pot can be one of the most complex calculations in all of
poker. This is because it involves far more than knowing the
odds of whether or not a certain hand will improve. In addition,
a player must also consider:
1. The possibility that he is drawing dead
2. The possibility that his hand is already the Nuts
3. The possibility that any of his opponents might
either have him beat or out-draw him
4. The possibility that his opponents might be manipulated
out of the hand by well placed bets or raises.
For example, assume you’re in a game where you have good
knowledge of your opponents, you are on the button before
the last card and have a 25% or 1 in 4 chance of completing
a draw to what will surely be the best hand.
A 25% probability of drawing the winning hand is equal to
odds of 3 : 1 against. With odds of 3 to 1 against, a player
95
After the Flop