Poker Math That Matters

101
We can minraise or shove and every amount in between. This
aggression will give us more than one way to win the hand. We
can make the best hand for showdown, or he can fold. Let's look
at shoving.
First, let's make some assumptions about how he'll respond to a
shove with his range. Let's say he'll call with AK and TT, but
will fold 88 and 89s. There are 15 combinations he calls with,
and 9 combinations he folds. So, he folds 37% of the time.
We have about $87 left in our stack, but our stack doesn't matter
here because the big blind has less money than we do. He had
$27 left in his stack on the turn and then bet $12. So, he now has
$15 left. There is currently $39 in the pot. We can move all-in,
which will risk $27 to win the current $39 pot. Going back to
the reward to risk table (See Table 8), we know when risking x
to win about 1.4x, we need to him to fold about 40% of the time.
He's only folding 37% of the time. Does that mean raising is not
good? No. In the bluffing section, we were always looking at a
straight bluff with no chance of improvement. Here we have
showdown equity in the hand to go along with our fold equity.
Let’s look at a detailed way to figure out how often he needs to
fold when we shove. If this look complicated, do not be
concerned. At the end of this section, I’m going to show you a
shortcut to do this at the table.
Fold%(pot won when he folds) + Call%(amount we win/lose
when he calls)
Here we’re going to let x equal the percentage of times he folds.
x($39) + (1-x)(0.24($54) + 0.76(-$27)) > 0
39x + (1-x)($12.96 – $20.52) > 0
39x + (1-x)(-7.56) > 0