Poker Math That Matters

140
decision may be a totally different decision. Referring to
balanced play by saying "optimal poker" may easily be taken to
mean that playing a balanced strategy is superior to playing an
exploitive play. This isn't always the case. Taking a look at a
maximally exploitive strategy will get us closer to thinking
properly about playing balanced poker.
Playing a maximally exploitive strategy has us making drastic
changes in our play. Here’s an example to show this in action.
Let’s say we get to a river, and our opponent bets the pot. We
have a bluff catcher, and we’re left with a decision of whether or
not to call. When someone bets the pot, we need to be good
better than 33% of the time in order to make a +EV call. This
means our opponent must be bluffing more than 33% of the time
in order for us to have a +EV call. Now, let’s say we know our
opponent has only bluffs. How often do we call? We obviously
call 100% of the time. Let’s say we know our opponent is never
bluffing. How often do we call? We obviously never call.
However, what is the maximally exploitive play if our opponent
bluffs 50% of the time? Some people feel that we should now
call a bit more frequently; however, this would not be the
maximally exploitive strategy. The maximally exploitive
strategy is to call 100% of the time. When playing a maximally
exploitive strategy, we call 100% of the time whether the
opponent is bluffing 34% of the time or 100% of the time.
Anytime his bluffing frequency is over 33%, we call 100%.
Each time we fold a bluff catcher, we lose some expectation
value. The same is true if the opponent were only bluffing 25%
of the time. Some may feel we should now fold sometimes.
However, this is not maximally exploiting the weakness in our
opponent’s strategy. The maximally exploitive decision is to
always fold. This is true whether he’s bluffing 32% of the time
or never bluffing. Each time we call with a bluff catcher, we
lose some EV. So, you see that a maximally exploitive strategy