Poker Math That Matters

Appendix B
When Villain is +EV
We've learned that when our opponent has a -EV call, we profit.
However, what if he has a +EV call? Does that mean we're
losing money by betting? If so, should we bet at all? Let's look
at an example.
Hero: A♣A♠
Villain: 5♦6♦
Board: 3♠4♠K♥Q♥
The pot is $10, and we have $2 left in our stack. Villain has
18% equity. Let's look at villain's EV if we shove.
0.18($12) + .88(-$2) = EV
$2.16 - $1.76 = $0.40
Villain makes money with his call. That means we're losing
money. Does that mean we shouldn't bet? Let's work it out.
We'll look at two options: checking and shoving.
If we check, we're giving villain a free chance at the $10 pot.
We win the $10 pot 82% of the time.
0.82($10) = $8.20
If we bet, we own 82% of a $14 pot that costs us $2 to create.
0.82($14) - $2 = $9.48
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