4/180 W/TT, Not sure I'm ahead enough to continue

[Jeff76]

[ QUOTE ]
Betting flop is a bluff. But an ace is clearly in your range, so folding out JJ-KK is ev.

[/ QUOTE ]I bet an ace here 100% because he isn't check/folding JJ-KK on this flop.

[Jeff76]

[ QUOTE ]
Let's say that he never calls on the river with an unpaired hand (i.e. K high). Let us then assume that he has a PP (not unreasonable given his line).

Let us further assume that 50% of the time he has JJ-KK and 50% of the time he has a lower pair (that did not make a set). These numbers are hypothetical and arbitrary.

Let us then assume that he will call our river bet 50% of the time and fold 50% of the time.

So 1/4 of the time we fold out a worse hand and pick up the pot. 1/4 of the time we fold out a better hand and pick up the pot.

1/4 of the time he calls with a worse hand and we gain EV. 1/4 of the time he calls with a better hand and we lose EV.

Using these very crude estimates, it seems that betting is the only reasonable option on the river.

If he has a worse hand, we gain nothing by checking (and obvioulsy lose value when he would have called). If he has a better hand and will sometimes fold to a river bet, we gain. Thus, betting on the river is the obvious play IMO. The only question that remains is how much.

[/ QUOTE ]My head just exploded thank you. Math is hard. Let me think about this when I'm not too sleepy to think straight.