When EV doesn't work

Most of the time people think that expected value is the basis for all poker decisions. But that's just a misconception.

Not all expected values are alike.

Expected value is the sum of the product x*p(x) where x is the value of a state of nature and p(x) is the probability of that state of nature. It's useful to think of this as a payoff function and a probability distribution.

Whether or not expected value is a useful metric depends on the complexity characteristics of the payoff function and the probability distribution.

Think of the characteristics of the payoff function and probability distribution as lying in a four quadrant matrix -- simple payoff function with simple probability distribution, simple payoff and complex probability, complex payoff and simple probability and complex payoff with complex probability.

If you're in a situation in that fourth quadrent -- complexkity in both the payoff function and the probability distribution then you're in a world where you aren't likely to come up with good outcomes resulting from investing much into estimating expected values -- the complexities will combine in a way that makes your estimates highly unreliable.

An example of a payoff function simplicity or complexity is when you're drawing to a flush and trying to estimate whether your opponent will call a bet if your flush comes in (implied odds). Probability distribution complexity comes in to play when you need to estimate whether the flush will be any good if it makes (drawing to a K high flush, for example).

Usually the best thing to do when you're in that fourth quadrant is to just give it up early, don't play the hand.