David_Nicoson
Sunday, September 9th, 2007, 7:41 PM
OK, so let me rough this in and see if it goes anywhere.
Acid Knight thinks he can call the turn for pot odds, because the villain's range includes draws. His break-even win percentage is 27%. For the purposes of this exercise, assume that the villain never fires a second bullet with a missed draw on the river.
When he's behind, he's drawing very thin. He's also behind more than he's ahead, so a raise is -EV.
CODE
Board: Js 8h 3c Ah
Dead:
equity win tie pots won pots tied
Hand 0: 07.727% 05.23% 02.50% 46 22.00 { Jc8c }
Hand 1: 92.273% 89.77% 02.50% 790 22.00 { JJ, 88, 33, AJs, A8s, A3s, J8s, AJo, A8o }
When the villain is drawing, the hero is a 3:1 ish favorite.
CODE
Board: Js 8h 3c Ah
Dead:
equity win tie pots won pots tied
Hand 0: 76.136% 76.14% 00.00% 268 0.00 { Jc8c }
Hand 1: 23.864% 23.86% 00.00% 84 0.00 { KhQh, Qh9h, JhTh, Tc9c, Th9h, Ts9s, 9h7h, Jh9d }
Let d = probability the villain is drawing
Let p = pot size
Let b = bet hero has to call
cost to call = ( EV when drawing ) x (probability villain in drawing) + (EV when villain's ahead) x (probability villain is ahead)
b = (3/4)pd + 0.08p(1-d)
(I thought I could neglect the second term, but this turns out to be a poor approximation.)b = 3/4pd + 0.08p-0.08pd
b = (3/4 -0.08)pd + 0.08p
(b-0.08p) / [(3/4 - 0.08)p] = d
(150- 0.08 x 550) / [(3/4 - 0.08)550] = d
0.29 = d
So if the villain is semi-bluffing more than 29% of the time, then a call is better than a fold.
If the villain is drawing a bit more than half the time, then it becomes better to raise than call.
Fixed numerous mistakes in this post.