Quote:
Originally Posted by Yadoula8
We have QQ
Villains range - AA, KK, JJ and AK
He has gone all in, we have to call 75 to win 200
Against AA - We win about 20% of the time so 40 is ours, cost of the play is 75, so we lose 35
Against KK - We win about 20% of the time, so we lose 35
Against JJ - We win about 80% of the time so 160 is ours, we win 85
Against AK - We win 55% of the time so 110 is ours, we win 35.
- 35 - 35 + 85 + (3x35) = 120.
120 / 6 = 20
Average Profit 20
This math is wrong because it is assuming that we lose our $75 call even when we win the pot. If you want to do it this way, then:
-Against AA - We win about 20% of the time. When we call the pot is $275, so we get back $55 from the pot. We had to call $75. So it is a $20 loss.
-Against KK - Same as against AA.
-Against JJ - We win about 80% of the time. When we call the pot is $275, so we get back $220 from the pot. We had to call $75. So it is a $145 profit.
-Against AK - We win about 55% of the time. When we call the pot is $275, so we get back $151.25 from the pot. We had to call $75. So it is a $76.25 profit.
-20 - 20 + 145 + 76.25*3 (presumably because AK is more likely than the other hands, but it is less than 3x) = 333.75.
333.75/6 = 55.63
$55.63 profit.
Now, let us see how close that is:
Rather than doing each hand in the villain's range individually with an estimated equity and then applying multipliers to certain hands based on the number of combinations of each hand relative to one another, I would just put the range into an equity calculator and see what the actual equity vs. the range is (I'll also note that it is weird that villain can have JJ,KK,AA, but not QQ). The following equity numbers is the output from Equilab:
........Equity
........Win
.............Tie
MP2
...47.29%
......47.07%
.......0.22%
......... QQ
MP3
...52.71%
......52.49%
.......0.22%
......... KK+, JJ, AKs, AKo
So our equity is 47.29%. If we call, the pot will be $275, so we get back $131.94 from the pot. We had to call $75. 131.94 - 75 = 56.94
So $56.94 profit.
So, pretty close. Probably easier to do it the second way though.