kelly criterion

Tags: statistics

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• http://www.herrold.com/brokerage/kelly.pdf

• Criterion: \( f^* = p - \frac{q}{b} = \frac{bp-q}{b} = \frac{bp-(1-p)}{b} = \frac{p(b+1) - 1}{b}\)

  • \(f^*\) 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
  • \(q = 1-p\) is the probability of loss

• 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_criterion#Proof

• Usage in blackjack: https://wayback.archive-it.org/all/20090320125959/http://www.edwardothorp.com/sitebuildercontent/sitebuilderfiles/KellyCriterion2007.pdf

• https://www.amazon.com/dp/B000SBTWNC/ref=dp-kindle-redirect?_encoding=UTF8&btkr=1