kelly criterion
Tags: statistics
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Criterion: \( f^* = p  \frac{q}{b} = \frac{bpq}{b} = \frac{bp(1p)}{b} = \frac{p(b+1)  1}{b}\)
 \(f^*\) is the fraction of the current bankroll to wager
 how much to bet
 \(b\) is the net odds received on the wager
 betting $10, on win, rewards $4 > \(b = 0.4\)
 \(p\) is the probability of a win
 \(q = 1p\) is the probability of loss
 \(f^*\) is the fraction of the current bankroll to wager

Maximize the expected log of wealth
 sometimes known as the “geometric mean maximizing portfolio strategy”, maximimizing logarithmic utility, etc
 derived from Shannon  A Mathematical Theory of Communication

relatively simple proof: https://en.wikipedia.org/wiki/Kelly%5Fcriterion#Proof

Usage in blackjack: https://wayback.archiveit.org/all/20090320125959/http://www.edwardothorp.com/sitebuildercontent/sitebuilderfiles/KellyCriterion2007.pdf

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