always hard to kill an actor." -- Raoul Walsh
No matter how much some people want to pretend otherwise, all poker decisions are mathematical. When playing for money, all poker
situations and decisions have a value. Sometimes this value will be absolutely known. For example, your sole opponent bets all-in into
you when you hold the nut hand. You will precisely know what your expectation of calling is simply by counting the pot. Of course,
such obvious situations are rare. More often you have think in terms of generalities, like what your expectation is if you are dealt
AA on the dealer button while playing Holdem, or more specific estimation, like when you are dealt AA on the button playing $20/40 and
John Smith raises first to act and everyone else folds to you and you have two tight players in the blinds behind you.
In most situations we won't know the exact math of each of the decisions facing us. The math still exists though. It's always there.
We can influence it, change it to be more (or less) in our favor, but it never goes away. Successful poker results from having the
math on our side. The ironic thing is a player doesn't even need to know the math is on his side for this to be true. This is why
looking at the results of individual hands is seldom helpful in determining proper play. In poker, it is very easy to do the right
action for the wrong reasons. But just because it was "right" doesn't mean it was really "right".
The action that is really correct is the one that has the best expectation. If you reraise two players with 72 offsuit before the flop,
and you happen to win a huge pot from A2 and KK when the flop comes 227, you still did the wrong thing. You did not have the best of it.
Reraising with 72 has a negative expectation. It has a negative value. Winning poker is playing when the positives are on your side.
Expectation isn't at all constant though. Your expectation for when you have KK first to act in Holdem in New Jersey is different than
mine in California. They may be close, but they are still different. The fine lines of expectation are the tactical "stuff" of poker.
If you wanted to, when playing raked-game Holdem you could guarantee
to play with a positive expectation every hand outside the blinds merely by only playing AA when you get it. Of course, this would be silly.
You would lose your shirt. Other situations have positive expectations too, so not playing those hands is poor poker. Our challenge as
players is to find the situations of positive expectation, expand that group of situations, and minimize our situations of negative expectation.
Some things have a no-brainer
positive expectation -- like fishing through your pants pockets before doing the laundry. Every human will find some amount of money
this way over the course of his or her lifetime, but the amount will be different for everyone due to a lot of factors, including level
of forgetfulness and level of wealth. Here we have a situation of pure positive expectation for everyone, but one that is still variable.
In poker, it is very common that poor play can turn a positive expectation situation into a negative one. Even more interesting, poor
play can lead to expectations that have no apparent rational reason to occur.
One online cardroom posted on their site the actual statistical results by starting hand from six million Holdem hands dealt at
their cardroom. Remember, results don't tell the whole story, but some things are clear from the data. The hand that performed the
worst, losing .17 big bets each time it was dealt, was 32 suited. In comparison, 32 offsuit lost .15 per instance. A2 offsuit lost
.16 per instance, also more than 32 offsuit!
While no one will argue that 32 offsuit is somehow a "better" hand than 32 suited, what we can easily see is that people
play the "better" hand worse -- and thus make the expectation of the better hand to be worse than the worse hand.
While that sounds like a bit of circular gibberish, it's a crucial poker concept to grasp. How you play affects the expectation of your
hands. If you are smart enough to commonly fold 32 offsuit, but for some reason always raise and reraise with 32 suited, you are going to
have a better expectation with the offsuit hand than the suited one. They will both be negative, but money not lost spends as well as money
won. Making a negative expectation situation less of a negative situation is a positive expectation situation unto itself.
Also: Changing the Poker Math,
Good Variance vs. Bad Risk and
Poker Odds and Gambler's Ruin