(originally posted here∞)


When you want to calculate the Expected Value of a play, all you have is past information. Use whatever Bayesian inference algorithm you like, but you can't use future actions. This sounds like a nitpick -- obviously you didn't mean to imply that you can predict the future -- but when I read this paragraph it doesn't sound like you really, truly understand EV.

It's this precise: given an exact situation, every move is +EV, 0EV, or -EV. Every move has an expected SD. Frankly, every move has a complete probability distribution, just nobody cares enough to graph it. If the EV gain of a mathematically correct move is too low relative to its ESD and your Kelly criteria, so be it, but you then must reject all situations with similar statistical profiles in order to be logically consistent, even if Situation #2 occurs 10x more (or less) frequently.

In case you don't believe me yet, consider a trivial argument by contradiction:

Case 1 - being dealt A4 UTG. If you play live full-ring poker 40 hours a week, this will happen twice a year. Limping has a EV of X1 and a variance of Y1.

Case 2 - being dealt A3-A5s in the first two seats. Playing the same amount of poker, this will happen every week. Limping has an EV of X2 and a variance of Y2.

The important facts here are that X1 == X2 and Y1 == Y2.* It doesn't matter in the slightest that case 1 is very rare. Given my clever choice of cards, enjoying case 2's profit while refusing that from case 1 actually demonstrates reductio ad absurdum.

*ok, maybe not a good C operator to use with floating-point values. Point to take home is that if there's a difference, it's several orders of magnitude under the radar of any mortal being.


Back to CollectedWritings