Mark Gritter (markgritter) wrote,
Mark Gritter
markgritter

Nit-picking

Still working my way through The Mathematics of Poker, slowly. (Having a good Christmas, too, maybe some more on that once I get home.)

This gets technical very fast, so if you don't have the book, you probably won't be able to follow...

The authors pull a fast one on p. 119 where they solve the first non-trivial [0,1] game. They are calculating the indifference interval at x1* (the threshold between when X calls and X folds) they label one column "p(Y's hand)". But there are a couple strange things about this table:

1. They're either actually using conditional probabilities (what is the probability that Y has a hand in this range given that Y bet) or missing a row in their table. If the former, it still works out becuase the conditional probabilities differ from the absolute ones by just a constant factor. Because we're calculating p1 * EV1 + p2 * EV2 = 0, a constant factor in the p's cancels out. Still, it would be more rigorous to either admit we're using conditional probabilities, or show the row that is all zeroes (for the interval [y1,y0]) if using absolute probabilities.

2. They're not actually using ex-showdown equity here from Y's perspective. What they're calculating is the value to X under the assumption that Y has already "won the pot". So X can either lose one bet by calling or win P+1 bets by calling but folding costs him zero bets. This is clear if you remember how they defined their angle-bracket notation but I didn't find it entirely straightforward to follow after the introduction to the section in which they said they were interested in ex-showdown equity.

Neither of these changes the validity of the results--- they are just presentation issues. But since it is the first nontrivial [0,1] example I think more care should have been used in the presentation.
Tags: math, poker, rant, theory
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