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Poker Math That Matters

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135<br />

more than $24 from us when he hits his draw. We'll need to<br />

decide how we want to approach the hand. Larger SPRs make<br />

playing these spots difficult. But, as you can see, if we're willing<br />

to put the rest of the money in, and we wish to significantly cut<br />

down villain's implied odds, we may have to do something<br />

creative here. We may consider different ideas like overbetting<br />

the pot or even going for a check/raise if we can.<br />

As always, we need to consider the distribution of villain's range<br />

when we're betting. Here's an example of that.<br />

Hero: A♦K♥<br />

Villain: QJ, 5♣6♣, T♣9♣<br />

Board: A♠7♣ Q♣8♥<br />

We have raised in late position, and a tight player called in the<br />

big blind. The pot is $10, and we have $15 in the effective stack.<br />

We're ahead of villain's entire range; however, some of his draws<br />

have much more equity than others. He has 12 combinations of<br />

pair hands drawing to 5 outs. He has 2 combinations of an<br />

OESFD drawing to 15 outs. So, 86% of his range is drawing to<br />

only 5 outs. We could bet enough that the villain couldn't<br />

profitably call with 15 outs, but if that meant he would fold with<br />

his 5 out draws, we need to reconsider. We assume villain will<br />

call up to $5 with his whole range; however, he'll call all-in with<br />

his huge draws. He has 11% equity with the 5 out draw, and<br />

34% equity with his OESFD. If we bet pot, he'll need to be good<br />

33% and has a profitable call. We'll examine the EV of both<br />

shoving and betting $5. Let's start with the shove. Here is his<br />

EV when we shove.<br />

0.34($25) + 0.66($15) = EV<br />

$8.50 - $9.90 = (-$1.40)

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