The Kelly Criterion

The problem
biased coin · P(H) = 60% · heads doubles, tails losesH×2 · P = 0.6T×0 · P = 0.4bankroll $100 · repeat indefinitelywhat fraction f of bankroll should you bet each round?

A biased coin lands heads with probability p=0.6p = 0.6, tails with probability 0.40.4.

Each round, you choose a fraction ff of your bankroll to bet:

  • Heads: your bet doubles (you get 2f2f times your stake back).
  • Tails: you lose your bet.

You play indefinitely. What fraction ff maximizes your long-term wealth growth?