The Kelly Criterion Explained (and Why Most People Use Half)

For a bet at decimal odds o that wins with probability p, let b = o - 1 (the profit per unit staked) and q = 1 - p. The Kelly fraction is: f* = (b x p - q) / b.

With a 4% edge at even money (o = 2.00, so b = 1) and p = 0.52, f* = (1 x 0.52 - 0.48) / 1 = 0.04 — stake 4% of your bankroll. The fraction scales up with your edge and shrinks as the odds get shorter. If the formula returns zero or negative, the bet has no edge at that price and Kelly says stake nothing.

Full Kelly maximises the long-run growth rate, but it assumes your probability estimate is exactly right. It almost never is. If you overestimate your edge even slightly, full Kelly overbets, and the drawdowns become brutal: a full-Kelly bettor should expect to lose half their bankroll at some point with near-certainty, and spends a lot of time well below their peak.

It also has high short-term variance by design. The growth-optimal path is a wild ride, and most people abandon it — and their edge — during a deep drawdown.

The standard fix is to bet a fixed fraction of the Kelly stake. Half-Kelly keeps roughly three-quarters of the growth rate while cutting the variance and the expected drawdown substantially. Quarter-Kelly is more conservative still.

Fractional Kelly also gives you a margin of safety against estimation error: if your true edge is smaller than you think, a half-Kelly bet is closer to the correct full-Kelly bet for that smaller edge than a full-Kelly bet would be.

Treat Kelly as an upper bound on sensible stake size, not a target. Size to a fraction of it, cap any single bet at a hard percentage of bankroll regardless of what the formula says, and recompute as your edge estimate and bankroll change. Pair it with a risk-of-ruin check so you know the downside you are accepting.