Poker Math That Matters

150
Comparing these two bet sizes, we just answered our question
“How much should we bet?” The $80 bet is a more profitable
bet than $20 given our assumptions.
Now, let’s pretend that villain also has 50 combinations of
absolute trash. He’ll never call or raise with any of those hands.
He’ll simply fold to any bet we make. We’re not concerned
about those hands at all. They do not impact our betting
decision. However, if we want to know how much richer we
will bet after we make this wager, we will need to know the
villain’s entire range regardless of whether or not he calls. After
we’ve added 50 combinations to villain’s range, we now have 68
total combinations that represent villain’s entire range. We can
now find out how much richer we will be after making each
wager. The true EV of the $20 wager is:
0.26($20) = $5.20
The true EV of the $80 bet is:
.09($80) = $7.20
The actual results of doing an evaluative EV calculation mean
nothing in terms of what we’ll actually make. 15 It’s only useful
as a comparison to some other bet size to see which is best. We
do this because it’s easier than spelling out the entirety of
someone’s potential range. We only look at the parts of the
range that are relevant to our betting. When we’re value-betting,
we’re only interested in the loosest calling range given a small
bet we would consider making. When bluffing, we’re only
interested in the range of hands that beat us and what percent of
those hands we can get to fold. It’s just easier that way.
15
The exception would be if the range we’re concerned about actually
is his entire range.