Thursday, October 25, 2012

Some poker math

So I've tried playing and studying some Pot limit Omaha poker, I've quite enjoyed this format and that encouraged me to dwelve more into it. So I made some calculations on some specific hands and the results surprised me. In my given scenario KQ89 prefers to call the flop and JJ34 prefers to get it in on the flop even if he's got 45% chance to win if he does.

Here are the calculations: 
I've rounded up some values but everything else should be quite accurate.

Player 1 has a 20 out wrap and Player 2 has a bare top set. The pot on flop is 10bb
After the flop, effective remaining stack is 40bb.
I analyzed 3 situations:1st situation: Players get it all in on flop
When Player 1 calls a pot bet on flop it breaks down into two more situations
I analyzed a few outcomes on turn:
-a) Board pairs up and player 1 is drawing dead therefore he folds.
-b) Turn bricks and Player 2 bets pot, both players are flipping.
-c) Player 1 hits and is the favorite to win, so he bets pot and Player 2 folds.
-d) Player 1 hits and is the favorite to win, so he bets pot and Player 2 calls.
so there's 2 more situations , 2nd situation = a+b+c and 3rd situation = a+b+d
Ofc there's more possible situations but those rely a lot on the players behavior so I just analyzed these.

Assuming both players are very straightforward no money gets in on the river since one player has 100% equity and will take down the pot.

EV -> the EV of the 1st situation.
EV1 -> the EV of the 2nd situation.
EV2 -> the EV of the 3rd situation.

The second example also includes a flush, So I added another situation if Player 2 folds only if the turn brings a flush.(EV3)

Of course this poker hand is only theoretical, opponents' tendencies is very important and you can never know his exact range. Using bigger stacks would change the results and it might be that against some opponents it would be better to get it in on the flop(e.g. against the very aggressive ones against which you won't know what hand you're against)

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