# kelly criterion

Tags: statistics


• 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