Expecting the Expected Value

Positive Expectation Poker

Poker EV"It's always hard to kill an actor." -- Raoul Walsh

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 Hold'em, 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 Hold'em 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 Hold'em 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. The blinds would cause you to 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 the actual statistical results by starting hand from 122 million Hold'em 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 assert 32 offsuit is somehow a "better" hand than 32 suited, the data shows players play the "better" hand worse -- and thus transform 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, Poker Variance, Good Variance vs. Bad Risk and Poker Odds and Gambler's Ruin