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Sunday, May 9, 2010

Outs in Omaha poker


Now let's talk about outs in Omaha poker. Out is a card that can come on turn on river and bring you win. Consider example from previous post. Player 1 has A♠A♣72♠, second player has KJT9 .. Flop is AQ4. Player 2: has 17 outs: 9 hearts, 3 kings, 3 jacks and 2 tens.
But how to calculate the probability of winning knowing number of outs?  First let's see how it's done only with one card to come (i.e. after turn). We know that deck consists of 52 cards. Four of them are our hole cards and three are on the flop, that's why we don't know 52-4-3=45 cards. And probability of winning having 17 outs is 17*100/45%=37,78%. In general probability of winning with one card to come is n*100/45%, where n is number of outs.
When there are two cards to come (i.e. after river) it's a bit more complicated to calculate probability. Let n be number of outs. First we calculate probability, that none of our outs will come. So, we have n out and 45-n outs. Probability, that none of our outs will come after turn is (45-n)/45, after turn brought non-out there are 45-n-1 non outs and 44 cards in deck and probability of hitting non-out on the river is (44-n)/44. So probability not drawing out on turn and river is (45-n)(44-n)/(45*44).
And probability of drawing 1 of n outs is 1-(45-n)(44-n)/(45*44). If we have 17 outs than probability is 0,618 or 61,8%.
Below is table with outs and % of winning:
№ of outs% of winning after turn% of winning after turn and river
12,22%4,44%
24,44%8,79%
36,67%13,03%
48,89%17,17%
511,11%21,21%
613,33%25,15%
715,56%28,99%
817,78%32,73%
920,00%36,36%
1022,22%39,90%
1124,44%43,33%
1226,67%46,67%
1328,89%49,90%
1431,11%53,03%
1533,33%56,06%
1635,56%58,99%
1737,78%61,82%
1840,00%64,55%
1942,22%67,17%
2044,44%69,70%
2146,67%72,12%
2248,89%74,44%
2351,11%76,67%
2453,33%78,79%
2555,56%80,81%


As you see you should invest as much as possible money in pot after the flop if number of your outs is greater or equal 14 (i.e. probability of winning is greater 50%).

1 comment:

  1. Very interesting really enjoyed your tips, tricks and strategies for the ultimate poker game...

    ReplyDelete

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