Poker Math That Matters

Determining how much to bluff is tricky business. Some have
said you want to bet just enough to get the job done. While that
makes sense, what that job is needs to be defined. Let's look at
an example.
Hero: A♠4♠
Villain: TT, JT, QJ, KJ, AJ, KQ, AK
Board: 2♠5♠9♥J♦K♣
The pot is $100. You have $180 left, and your opponent has you
covered. You're thinking about bluffing with your A high since
you don’t feel it's ever good here. You're thinking about making
a pot-size bet. When you make a pot-size bet, you need your
opponent to fold 50% of the time to break even. You have the
following assumptions. To a pot-size bet, you'll feel he'll fold
TT, JT, QJ and AJ, but he'll call with his KJ, KQ and AK. What
percent of his range is he folding?
TT, JT, QJ and AJ total 39 combinations. KJ, KQ and AK total
30 combinations. His folding range consists of 39 out of 69
combinations.
39 / 69 = 0.565
95
That's about 56% of his total range. Your bluff is +EV given
these assumptions. Looking at our chart and not changing his
folding range, you could even bluff $125 on the river. But, you
do not need to bluff that much. We realize that, in general, as we
lower our bet size, his calling range increases. As we raise our
bet size, his calling range decreases. When we're trying to fold
out those Js, we need to make assumptions about what bet size
he starts to call with them and keep our bet just over that hump.
Obviously if he'd fold his Js to a $33 bet (1/3 pot), we'd rather