Poker Math That Matters

3. Hero: A♣Q♦
Villain: 8♥9♦
Board: 2♣5♦8♣A♥
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The pot is $20. How much money are we giving away if
we check, letting the villain see the river for free?
Answer: We give villain a free chance to draw with
about 10% equity. So, we’re giving him 10% of a $20
pot, which is $2.
4. Hero: Q♣Q♦
Villain: 8♣7♣
Board: 2♣5♦9♣K♥
The pot is $20. You have $40 in the effective stack.
The villain is passive and never folds a flush draw.
What is the best bet size?
Answer: This is a very common situation in micro-stakes
games. Opponents do not like to fold a flush draw. In
this case, we can just go all-in. We get the money in
now while he’s drawing for his flush instead of letting
him keep some after he’s missed on the river. We’re not
trying to blow the villain off a hand; we’re getting the
maximum value. If the villain were an aggressive
bluffer and could fold if we shoved the turn, we may
consider betting less on the turn and letting him bluff the
river.