[crashzzz]

back to question 51...

let's calculate our EV if we've gone all-in...

Say, we have reason to believe he could be bluffing (and why not after all? we've both shown sign of weakness by checking the turn). So there is a 10~20% chance he could be bluffing, let's make it 10%.

If we push all-in, he'll definitely call with AA, probably call with 89, he'll be more hesitant with 88, if he did have a flush, he would be more incline to fold.

Of the possible hands we've put him on the flop, he could have: AhAd,8s8h,8d8h,8s8d,8s9h,8d9h,8h9h,TsJs,JsQs. So a total of 9 possible hands.

1 out of 9(11%), he'll calls with AA.
3 out of 9(33%), he'll call ~30% of the time with 88
3 out of 9(33%), he'll call ~50% of the time with 89
2 out of 9(22%), he'll fold with his flush.

so he'll fold 50% of the time when he doesn't have AA.

EV=(19550$)(.10) + (-49000$)(.11)(.90) + (19550$)(.50)(.90) + (53550$)(.38)(.9) == +24215$

let's be conservative, and say he's bluffing 10% of the time, has AA 33% of the time, a weaker full house the rest of the time (57%). To which, he'll only call with his 89 only half of the time (he has 6 possible weaker full house, 3 of which are with 89, ie 1.5out6 he'll call), so (.57)(.25)= 14.25%

EV=(19550$)(.10) + (-49000$)(.33) + (19550$)(.57-.1425) + (53550$)(.1425) = 1955$ - 16170$ + 8357$ + 7630$ == +1772$

still making it a positive EV going all-in in a conservative scenario.

If it wasn't our entire saving on the line, all-in is the right call. Since our entire saving is on the line, hey! I'm allowed to be conservative and just call no? [img]/images/graemlins/grin.gif[/img]