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Poker Math That Matters

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133<br />

opponent cannot call profitably, we prefer they call. Let's look at<br />

an example.<br />

Hero: A♣A♠<br />

Villain: 5♦6♦<br />

Board: 3♠4♠K♥Q♥<br />

The pot is $10, and we have $10 left in our stack. The villain<br />

has eight outs with one card to come. His equity is about 16%.<br />

If we bet 1/4 pot, he would have about a neutral EV call since he<br />

would need about 16% equity. Since he's not losing any money,<br />

we're not making any money. However, this is still better than<br />

checking. If we check, we're giving away 16% of the current<br />

pot. If we bet $5, then villain would need to have 25% equity.<br />

He does not have that much, so his call is -EV. Let's look at the<br />

EV of his call.<br />

0.16($15) + 0.84(-$5) = EV<br />

$2.40 - $4.20 = (-$1.80)<br />

On average, he loses $1.80 if he calls. 13 Where does that money<br />

go? It goes to us. If he calls, we will own 84% of a $20 pot.<br />

<strong>That</strong>'s $16.80. If he folds, we get the $10 pot and our $5 back.<br />

The difference is $1.80. Yes, sometimes your opponent will<br />

draw out on you, and that will cost you the pot. But, we make<br />

more money when we bet and he makes an unprofitable call. So,<br />

we're not trying to blow our opponent off a draw when he cannot<br />

call profitably. Obviously, if we could bet the whole $10, and he<br />

would call, that would be even better for us. When he cannot<br />

call profitably, we want to bet as much as he will call. Even if<br />

13<br />

This is assuming we can play perfectly on the river so he has no<br />

implied odds.

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