From edge to bet size with Kelly

Question

A market offers decimal odds of 3.00 on an outcome you believe wins 40\% of the time. Solve in your head. What is your expected value per \1, and what fraction of your bankroll does the Kelly criterion say to bet? Aim: under 30 seconds.

Accepted Answer

Expected value first: EV = 0.40 	imes 3.00 - 1 = 1.20 - 1 = 0.20 \approx +20 	ext{ cents per dollar.} Kelly fraction. With net odds b = d - 1 = 2 (you win \2 profit per \1 risked), win probability p = 0.40, lose probability q = 0.60: f^ = \frac{bp - q}{b} = \frac{2(0.40) - 0.60}{2} = \frac{0.80 - 0.60}{2} = \frac{0.20}{2} = 0.10. So stake 10\% of your bankroll. A tidy shortcut: f^ = EV / b = 0.20 / 2 = 0.10, the expected value per dollar divided by the net odds. Sanity note. Full Kelly is aggressive; many traders bet a fraction of it (half-Kelly here would be 5\%) to cut volatility for a sm…

From edge to bet size with Kelly

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