Probability in Poker

#1 11-10-2005, 3:59 PM

This article might be useful.

Probability in PokerA popular way to figure out if you should draw or not in Texas hold’em is to think of probability in an negative way. If you know the relationship between the odds of not making your hand and the money you will win if you hit your draw, you will be playing good statistical poker and be on your way to being a long term winner. This is called pot odds.

Figuring out pot odds is very easy. Just follow the steps below:

1. Figure out number of unknown cards in deck

52 - board cards - your hole cards = A

2. Decide on number of cards that will help make your hand = B

3. A-B = number of cards that won’t help your hand = C

4. Odds against making your hand is C : B

Example:

You are on a nut heart flush draw with only the river card to come.

1. Your unknown cards are 52 - 4 -2 = 46. This is A.

2. Since there are four hearts known (two on board and two in your hand) and thirteen

hearts in total, there are still nine cards that can help you. So B = 9.

3. 46 - 9 = 37 = C

4. Odds against making your hand is 37:9 or 37 divided by 9 which is 4.11 to 1 ( 4.11 : 1 )

So, if the pot is at least 4.11 times your bet, then you should call, otherwise fold.

If you do not make your hand approximately 4 times for every one time you do, then you must make your hand one out of every five times approximately or about 1 : 5. 1 divided by 5 = .20 or 20%.

This is using probability in a positive sense to figure out if you should draw or not. There is an easy way to approximate this as you play, so there is no need to memorize your percentage chance of making your draw. The following is a chart to show you how to calculate these approximations at a moments notice.

Turn and River to Come:

1-9 Outs: # outs x 4

10 -12 Outs (# of outs x 4) - 2

13-15 Outs (# of outs x 4) - 4

River to Come:

1-3 Outs: # of outs x 2

4-8 Outs: (# of outs x 2) + 1

9-15 Outs: (# of outs x 2) + 2

Example:

If you are on a nut flush heart draw with only the river to come you have 9 outs that will allow you to make your hand. Using the charts above, use the following formula:

9 x 2 + 2 = 20% which is real close to the actual 19.6%.

So in this case, you have a 20% chance of getting your flush. Ergo, the cost of your call should not be more than 20% of the pot’s total. In other words, you can call a bet up to 20% of the size of the pot since you win the pot about one in five times or 1 : 5.


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