a holdem math problem.

[NYplayer]

Imagine you have AK with no pair on the turn and are out of position, you check and he bets. given the following information how big does the pot have to be to call and how should you play (imagine you have 6 outs to 1 pair).
On the river he will have worse than 1 pair 5% of the time. 1 pair 45% and better than 1 pair 50% of the time.
He will check behind on the river with worse than 1 pair or 1 pair 60% of the time (he will bet worse than 1 pair and 1 pair 40% of the time). he will call a bet from you with 1 pair or better. he folds no pair to a bet.

[AaronBrown]

Let me make sure I understand.

5% of the time he has nothing on the river. Presumably he was going for a straight or flush, or he had two high cards. Ignoring the chance that he holds AK, you win all of these showdowns.

45% of the time he has a pair. He could have started with one or hit one of the board cards. We're not counting pairs on the board here. If you pair you will win (unless you pair Kings and he has pocket Aces, or he also has AK and you tie). Let's ignore that and say you win if you pair in these cases, lose otherwise.

50% of the time he will have better than a pair. That could be a stright or flush, in which case you're beaten for sure assuming you have no possibilities for those hands, two pair or trips. I'm going to assume that's half the cases, and you win if both the turn and river are Aces or Kings, and lose otherwise.

Anytime you bet or raise, he will fold the 5% of the time he has no pair, otherwise he will call. If you check to him, he will bet 70% of the time. That 70% consists of 50% betting with two pair or better, 18% betting with one pair and 2% betting with no pair.

Your options are:

Fold, get zero.

Raise and bet each round. 5% of the time he folds and you win P, the amount in the pot (after his bet, but before you match it or raise). The other 95% of the time you reach showdown. You win 47%*45% + 1%*25% = 21% of the time. You get P + SB + 2*BB when you win, you lose 2*SB + 2*BB when you lose. At $10/$20 the pot would have to be $178 to make that positive expection, which isn't going to be true.

Call and check for the rest of the hand. 30% of the time you get away with risking only on SB. You win P 3%+27%*47% = 16% of the time and lose SB 14% of the time. The other 70% you win P+2*BB 25%*1% + 18%*47% + 2% = 11% of the time and lose SB + 2*BB 59% of the time. This is even worse, the pot has to be $223 for this to make sense.

Call and check unless you hit a pair, if you do hit, raise thereafter. 95%*53% of the time you don't hit and lose, 5%*53% you don't hit and win, 46%*50% you hit and lose, 46*50% of the time you hit and win, 1%*25% of the time you hit double and lose, 1%*75% of the time you hit double and win. That's 73% of the time you lose, 27% you win. When you lose you put in an average SB + 1.2 BB, which of course you lose. When you win, you win an average of P + SB + 1.7 BB. That's break-even if P = $48.

Call now, check until you get a pair, raise thereafter but fold on the river if you don't pair. This saves 0.53 BB over the strategy above, but raises your losing percentage to 76%. That makes sense with $28 or more in the pot.

The only downside to this strategy is it is completely predictable. It's the best way to play this hand, but if you always play predictably, other people will figure out how to beat you. So mix it up a little to encourage your opponent to make more mistakes.

[DesertCat]

[ QUOTE ]

The only downside to this strategy is it is completely predictable. It's the best way to play this hand, but if you always play predictably, other people will figure out how to beat you. So mix it up a little to encourage your opponent to make more mistakes.

[/ QUOTE ]



I'm not gay or nothing, but I really enjoy your posts...

[AaronBrown]

I always heard there were two people who like Orgazmo, I finally meet the other one. But I think the line is "Now I don't wanna sound like a queer or nothing."

Thanks for the kind words.

[Ole16]

You can now add the third person [img]/images/graemlins/laugh.gif[/img]

[AaronBrown]

Wow! We should form a club.

[jonesyb]

you can add a 4th person to that list also.

[img]/images/graemlins/cool.gif[/img]