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Poker Math That Matters

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Determining how much to bluff is tricky business. Some have<br />

said you want to bet just enough to get the job done. While that<br />

makes sense, what that job is needs to be defined. Let's look at<br />

an example.<br />

Hero: A♠4♠<br />

Villain: TT, JT, QJ, KJ, AJ, KQ, AK<br />

Board: 2♠5♠9♥J♦K♣<br />

The pot is $100. You have $180 left, and your opponent has you<br />

covered. You're thinking about bluffing with your A high since<br />

you don’t feel it's ever good here. You're thinking about making<br />

a pot-size bet. When you make a pot-size bet, you need your<br />

opponent to fold 50% of the time to break even. You have the<br />

following assumptions. To a pot-size bet, you'll feel he'll fold<br />

TT, JT, QJ and AJ, but he'll call with his KJ, KQ and AK. What<br />

percent of his range is he folding?<br />

TT, JT, QJ and AJ total 39 combinations. KJ, KQ and AK total<br />

30 combinations. His folding range consists of 39 out of 69<br />

combinations.<br />

39 / 69 = 0.565<br />

95<br />

<strong>That</strong>'s about 56% of his total range. Your bluff is +EV given<br />

these assumptions. Looking at our chart and not changing his<br />

folding range, you could even bluff $125 on the river. But, you<br />

do not need to bluff that much. We realize that, in general, as we<br />

lower our bet size, his calling range increases. As we raise our<br />

bet size, his calling range decreases. When we're trying to fold<br />

out those Js, we need to make assumptions about what bet size<br />

he starts to call with them and keep our bet just over that hump.<br />

Obviously if he'd fold his Js to a $33 bet (1/3 pot), we'd rather

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