David_Nicoson
Thursday, September 21st, 2006, 6:29 PM
QUOTE (Sefaje @ Thursday, September 21st, 2006, 10:15 PM)

nico, why would you want top pair to fold? that's a hand that we're ahead of.
Because then I get the money in the pot.
EDIT.
OK, I can give the long answer, too. If our opponent has a hand like AJ such that we 3 outs for queens we're about a 1.5:1 favorite. If we both had a billion dollars in front of us and the pot was still just $10, I'd want him to call as much as possible.
Here, though, the pot size is large enough that even if the hero pushes after the villain's raise on the flop, the villain is still getting the correct odds to call. He makes money by calling. There are only two players. Therefore the hero loses money.
The preflop pot is 2. Hero and villain put in 4 each on the flop. 2 + 4 x 2 = 10.
Then the hero pushes for 15.70. 15.70 + 10 = 25.70. Villain has to call 15.70. So his pot odds are 25.70:15.70 or 1.63:1. 1.63 > 1.5, therefore he should call.
Looking at it another way, he trades $15.70 for 40.3% equity in a $41.40 pot or $16.68. So he makes about a buck. He's putting additional money in as a dog, but it's right for him to do so because the pot is laying him sufficient odds.
There's a stack size at which we prefer that he call our all-in for these known hands.
amount he has to put in = his equity in the pot
amount he has to put in = (his hand's chances) (the size of the pot)
Let b = our bet size
Let p = pot size before our bet
Let c = the chance the villain has to win the hand
b = c(p + 2b)
b = cp + 2bc
b - 2bc = cp
b(1-2c) = cp
b = cp/(1-2c)
(I note at this point that as c approaches 50% our bet size becomes infinite. That's an encouraging sign toward my math being right.)
In our case:
c=0.403
p=$2 + $4x2 = $10
b = (0.403)($10) / (1 - 2 * 0.403)
b = $20.77
So if he has more than $20.77, we want him to call our push with AJ.
Checking:
-----------
Pot is $10 + 2($20.77) = $51.55
His equity is (0.403)($51.55) = $20.77.
That was fun and all, but queens are far from clean outs without knowing the hands.