Poker Math That Matters

102
39x – 7.56 + 7.56x > 0
46.56x > 7.56
x > 0.1624
He has to fold more than 16% of the time in order for our shove
to be +EV. I often like to test my work to make sure I did it
correctly. Here we can plug in the percentages.
0.1624($39) + 0.8376(0.24($54) + 0.76(-$27)) > 0
$6.33 + 0.8376($12.96 – $20.52) > 0
$6.33 + 0.8376(-$7.56) > 0
$6.33 – $6.33 > 0
Our work checks out. Notice he is folding 37% of the time, and
we only needed him to fold 16%. So, obviously the shove is
+EV. Let’s look at the EV of this shove.
0.37($39) + 0.63(0.24($54) + 0.76(-$27)) = EV
$14.43 + 0.63(-$7.56) = EV
$14.43 – $4.76 = $9.67
Let’s compare this to the EV of the calling.
0.28($39) + 0.72(-$12) = EV
$10.92 – $8.64 = $2.28
So, we can see the power of the semi-bluff here. We often win
the whole pot uncontested, and when we do win on the river if he
calls, we win a bigger pot.