omaha odds

On the flop, how many bets have to be in the pot to justify calling with only an uncounterfeitable nut low draw? Ex: you hold A-2-3-x, flop is 8-J-K.

Lets first find how often you make the nut low and lets say your hand is A 2 3 9.


P(two low cards w/no A 2 3)= 4C2 (16)/45C2


P(two low cards w/exactly one A 2 3)=


9(16)/45C2


P(making nut low= 96 +144/ 45C2


=240/990.


So a naiver answer would be 12/99 or 87 to 12.

But you may get quartered and you often have to pay another bet on the turn.


SO if you only have to pay a bet on the flop, if you make the nut low you win half, and you don't get anything if you don't make the nut low draw the 87-12 figure is correct.

Steve - There can be no distinct answer as to how many bets are needed in the pot to continue with A239 after a flop of KJ8. The reason is there are four betting rounds during which chips may be added to the pot.


What it boils down to is that if the pot is raised before the flop and if at least four opponents call the raise, then I think you’re stuck seeing another card with A239 after a flop of KJ8. If the turn is favorable, then I think you’re probably stuck seeing the river.


With no pre-flop raise or with less than four opponents seeing the pre-flop raise, then I think you’re off the hook.


Following is some of the reasoning.


If there were no raises on the second and third betting rounds, but if there was a single bet on the second and third betting rounds, then over 1980 times of continuing with this hand after this flop, you might expect to lose a total of 880 small bets by folding when the turn made low impossible. You might expect to lose another 1860 small bets by folding when the river made low impossible for you.


Over 1980 times, your total loss, by folding on the turn or river when low became impossible for you, would be 2740 small bets.


To show a profit playing the hand your gain would have to be 2740 small bets on the 480 times (out of the 1980) you made the nut low.


You can see that you’d want to show an average win of 2740/480 or about 6 small bets when you did make the nut low.


In a ten handed game you would have sole possession of the nut low 57% of the time, you would be quartered for low 38% of the time, and be sixthed for low 5% of the time. Your average pot equity with the nut low would be 0.57*0.5 + 0.38*0.25 + 0.05*0.17 = 0.3885.


In other words, when you made the nuts for low you wouldn’t always be awarded half the pot, because of the quartering and sixthing effects, but instead your average award would be 0.3885 of the pot.


Let P be the amount already in the pot from the first betting round plus your opponent’s contributions on the 2nd, 3rd and 4th betting rounds. Let Y be your contribution on the 2nd, 3rd and 4th betting rounds. Then


(P+Y)*0.3885 - Y = 2740/480.


If Y = 5, then

(P+5)*0.3885 - 5 = 2740/480

P = 22.6


If those equations are correct (and no guarantees there) then it looks like you want 28 small bets in the pot at the showdown with 5 of those small bets being bets you, yourself, have contributed after the first betting round.


How could there come to be 28 small bets in the pot at the showdown, with only five of them coming from you after the flop?


Stack 23 chips of one color and another 5 chips of a different color in front of you, each chip representing one small bet. Anyone else’s contribution after the flop will be the same as you, yourself, contribute after the flop.


It’s easier going backwards. If there came to be 18 chips in the pot before the flop, then you’d only need one opponent going with you to the showdown. With 13 chips in the pot before the flop, then you’d need two opponents going with you to the showdown. With 8 chips in the pot before the flop, then you’d need three opponents going with you to the showdown.


With 10 chips in the pot before the flop, then you’d need three opponents seeing the turn and river and two opponents seeing the showdown with you.


And there are many, many other ways to do it. Thus there is no distinct answer to your question.


Buzz