stud hi/lo odds question. yes, i'm serious.

[fisherman112]

a few friend of mine play mixed games from time to time and i got involved in a large stud 8ob pot with an interesting 6th street decision.

i had started out with a monster draw A /images/graemlins/club.gif4 /images/graemlins/club.gif5 /images/graemlins/club.gif2 /images/graemlins/diamond.gif, caught air on 5th and made an 8 low on 6th. my friend raised my bet with 4 low cards showing. i was positive he had 6 low cards and 2 pair. i have, best case, 3 outs to the high, how big does the pot have to be for it to be +EV to call, hope he whiffs on his low draw 7th st and we split the pot? assume im always showing it down.

[AaronBrown]

One problem is in seven card stud there are a lot of other cards you've seen, these would affect the calculation. Also is this a declare game (as usually played in private games) or a cards talk (as usually played in commercial establishments)?

If I understand, your flush has busted, but there are still four 3's in the deck to give you a straight. Or maybe he has one of the 3's, so that's why you say "best case, 3 outs to the high." If one of his pairs is 3's, then you have only two outs. You've seen your six cards and four of his, plus some others (how many others matters).

Anyway, you have a small chance to get a 3 and hit high/low plus a good chance that he either pairs one of his small cards or gets a nine or higher. Let's say for sake of the argument that it's 1/12 to get high/low, 7/12 to get low only and 4/12 to lose both.

If you win both, you know it, so you bet after the last card. But otherwise you don't know it, so you have to call after the last bet. Assuming he calls when you get a 3, we can just add one more bet into the mix.

If there are N bets in the pot, you have to pay 2 more bets in the hope of winning N+2. Your expectation is:

(N+2)/12 + 7*N/2*12 - 2*4/12 = 7(N-1)/24

which is positive as long as there is at least one bet in the pot. But fiddle with the odds, and you'll get a different answer.