Poker Math That Matters

5. Hero: A♦J♦
Villain has $60 left:
Call up to $20 – A9, AT, AK, AQ, J9, JT, QJ
Shove $60 as bluff after your $20 bet (you’ll
call) – 78
Call all-in for $60 – AK, J9, JT, QJ
Board: 6♣5♦J♥A♥J♠
Which bet is more profitable?
195
Answer: The scenario is the same as question four;
however, there’s a little twist. The smaller bet will
induce a bluff shove from your opponent’s missed
OESD. This adds a tremendous amount of value to your
smaller bet. Nothing in his range will fold; however, 16
of the 60 combinations will give you $60. This is our
EV for the $20 bet.
0.73($20) + 0.27($60) = EV
$14.6 + $16.2 = $30.80
Now, let’s examine the EV of the $60 bet.
0.33($60) = $19.80
Obviously the EV of the $20 bet is better and highlights
the power of inducing bluffs. The astute student may
have noticed the EV of the $60 bet is less now than it
was in question four even though the bet size and
number of combinations calling are both the same. If
you're curious, see Appendix A.