Poker Math That Matters

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2. Hero: J♠A♠
Villain: QQ, KK, 55, 44
Board: 5♦4♠T♠
What is hero's equity assuming we're all-in?
Answer: These hands fit well into two groups. We have
a lot of outs against his big pairs, but we're crushed by
his sets. Against the big pairs, we have about 45%
equity (remember against half of the pair hands, you'll
only have 8 flush outs instead of 9). Against the sets, we
have about 25% equity. There are 12 combinations of
big pairs, and 6 combinations of the sets. So, the big
pairs are two times more likely than the sets. We have
to find 2/3 of the way from 25 up to 45. That middle of
25 and 45 is 35. But, we have to slide it more towards
45. I'd estimate the equity to be in the upper 30s. If you
Pokerstove it, you'll find our equity to be 39%.
3. Hero: 3♠3♥
Villain: KT, TT, 55, A♦K♦
Board: 5♦3♦T♠
What is hero's equity assuming we're all-in?
Answer: Villain’s range divides into three categories.
KT is in terrible shape with 6% equity. TT and 55 have
us in terrible shape by having 96% equity. Then A♦K♦
has about 25% equity. There are 12 combinations of