Poker Math That Matters

110
and we’ll give him a $500 stack again. Let’s examine our
choices again.
The EV of the $500 bet is still the same. He’s calling 3.5% of
the time, and the EV is $17.50. However, let’s examine the $8
bet.
$8(0.965) + $500(.035) = EV
$7.72 + $17.50 = $25.22
So, we get action with our $8 bet 100% of the time, and we still
get the benefit of the big payoff 3.5% of the time. Notice our EV
is $25.22. This is obviously better than the $17.50 EV of the
$500 bet. If we wanted to, we could figure out how often he
needs to raise with his flush in order for the $8 bet to be better
than the $500 bet. We can let x equal the percentage of time he
raises with his flush. We will solve for x where the result is
greater than $17.50.
$8(1-x) + $500(x) > $17.5
8 – 8x + 500x > 17.5
8 + 492x > 17.5
492x > 9.5
x > .0193
He has the flush 3.5% of the time. We can find out how often he
must raise with his flush by dividing .0193 by .035.
.0193 / .035 = 0.551
So, if he’ll raise with his flush a bit over 55% of the time, we’re
better off just betting the $8.