Poker Math That Matters

100
Let's do a quick exercise to estimate our equity against that
range. We’ll analyze his hand range: 9 combinations of AK, 12
total combinations of 88 and TT, and 3 combinations of 89s.
These hands divide well into two groups.
Group 1: Against 88, TT, and 89s, we have roughly 15 outs with
1 card to come for an estimated 30% equity. 9
Group 2: Against AK, we only have roughly the 9 flush outs for
a total of 18% equity.
So, the 2 groups are 30% equity and 18% equity. Notice the
30% equity group contains 15 combinations, and the 18% equity
group contains 9 combinations. So, the 30% group "weighs"
quite a bit more than the 18% group. I'd use the MS Method
here to find about 2/3 the way up from 18 to 30. The exact
middle I know is 24, so I'd slide it a bit higher than that and
estimate about 27% equity against this range. If you put this in
Pokerstove, you'll find it gives us 28% equity. We're close, and
close will do just fine.
Remember we needed 23% to call his bet, so we have the
immediate odds to call his turn bet. Against his AK, it's likely
we even make more money on the river as well, so there are
some implied odds to consider. But, we can call without even
considering implied odds.
However, we always need to make sure we consider all our
options. We can fold. The EV of folding is always 0, so we
know that's already worse than calling and out of the question.
We can call, and we already explored that briefly. But, we can
also raise. We can even raise to different amounts. Remember,
only through aggression can we take advantage of fold equity.
9 I say "roughly" because against some of the TT and 88 hands, he has
a diamond which reduce our flush outs by one.