Poker Math

[GTSamIAm]

I meant for more complex situations, like being able to calculate your equity such as:

Villain: Kx
Hero: 45

Flop: K5J rainbow

What are my chances of winning by showdown? I can make my two pair or trips and still be outdrawn.

Or using combinatorics to find out which combinations and how many of certain hands multiple opponents might have. You put your two opponents on two separate ranges of hands. Then from that, calculating your equity.

Hero: 45
Villain 1: Kx, AA, QQ
Villain 2: JQs-J9s, AJs, QJ-QTo (suit is one on the board)

Flop is: KJ5 rainbow

[Luzion]

You can learn enough in the first few chapters of a probability book to do those problems. In fact, you dont even need to know how to do basic probability to do the problems you put up.

You could separate everything into groups.

1) You improve on the turn, and again on the river
2) You and your opponent dont improve on the turn, you improve on the river
3) You improve on the turn, and no one improves on the river

Add them all up

Or you could find the probability of you improving by the river, and divide that by the probability your opponent also improves.

[GTSamIAm]

Isn't there a much faster way to do that?

[Luzion]

I already told you how in first post at the end.

Figure out the probability you will improve by the river, and multiply by the probability your opponent will improve by the river. This works pretty well, but its approximately. You are still better off calculating each possibility imo; there are times were you may share outs or have hidden outs.


Your 1st problem is reasy. Just calculate the probability that you trip/2pair on the turn, and any non-King plus his kicker on the river and add the probability that the turn doesnt have a King or his kicker, and you improve on the river. Thats your pot equity.

Villain: K8
Hero: 45

Flop: K5J rainbow

Ill assume your opponent has 8 as a kicker. Your pot equity right now is...

Improve on the turn and/or on the river while your opponent doesnt on the river
5/45 * 39/44 = 0.0985
Improve on the river only while your opponent doesnt on the turn
35/45 * 5/44 = 0.0884

Equity = 18.7%

[AaronBrown]

While it's not hard to learn how to solve these questions exactly, it's not much help to your game. In the first place, most people can't do these in their heads exactly, and in the second place, you don't have precise information. You may put your opponent on certain hands with certain probabilities, but you don't know for sure. You also don't know how the betting will go.

Experienced players have broken down the situations you might face into a manageable number. In your first case, you've got the top pair. In the second you've got the low pair and are assuming each of your opponents has a different higher pair, and every unpaired card in their hands and on the board is higher than either card in your hand. You have to know how to play both situations, the precise cards that make them up affect the odds a little, but not enough to matter. Other people have worked them out, and you can read about it.

Clearly in the first situation you have a big advantage, and in the second you should suggest a switch to lowball. The exact size of the advantage is nowhere near as important as your strategy. In the first hand, you want to extract as much money as possible if your opponent is unpaired or has Jacks or 5's, while not losing too much if he has a pocket pair of Jacks or 5's or J5. That's what you should be thinking about, not whether your chance of winning if the hand is played to showdown is 81.62% (which it is) or 81.63%.

[spaminator101]

lets just say very small

however if you ever get up to the point where you play 5000-10000 then you definately need phycology on your side
also in large tourneys phycology can be more important if your up against half decent opponents

[Luzion]

I like how you pulled the number 5000/10000 out of your ass. [img]/images/graemlins/confused.gif[/img]

I also like how you make your speculation sound like fact.

Also, can you spell psychology correctly for once? You spelled it wrong like 6x in a row.

[spaminator101]

[ QUOTE ]
Also, can you spell psychology correctly for once? You spelled it wrong like 6x in a row.

[/ QUOTE ]

ill try