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gergery
01-18-2005, 09:09 PM
Hereís a common situation in low-limit Omaha

Iím dealt AAQJ preflop from early position and raise. I get a bunch of callers and then get a meaningless flop, say 622 rainbow. I need to decide whether to bet out or not.

For simplicity, lets say Iíll bet potsize and everyone will fold unless they have 66xx or 2xxx. What are the odds someone has one of those holdings, and how many opponents must there be before the odds of someone having one of those two hands goes over 50% (meaning my potsize bet then becomes EV-)?

I figure this as:
Combinations of 1 player having 66xx: C(3,2)*C(43,2) = 2709 or 1.8%
Combinations of 1 player having 2xxx: C(2,1)*C(44,3) = 26488 or 17.7%
Total possible: C(45,4) = 148,995
Or, chance of 1 player having it is 19.6%, meaning chances of NOT having it is 80.4%

Solving for 80.4% ^X=50%, then X=3 players, so the bet is profitable with 3 opponents but not with 4. (leaving aside people calling to bluff later, etc.).

Is my logic/methodology/calculations correct here?

--Greg