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Foundations · Lesson 7 of 8

Bankroll and Bet Sizing

Given an edge estimate, how big should a stake be — and what happens if the estimate is wrong?

Beginner9 min read

Sizing decides whether you survive the variance

Two people with the same edge can end in very different places depending on stake size. Too large and ordinary losing runs wipe out the bankroll before the edge shows up. Too small and the bankroll is safe but grows slowly. Bet sizing is about surviving uncertainty, not maximising any single result.

$0$467$933$1400$1866400 bets
A 55% win rate at −110 (a real edge) staking a flat 2% of the starting bankroll. Even with the edge, a meaningful share of paths is below the start after 400 bets.

Flat staking

Stake the same amount each time — typically 1–2% of the starting bankroll. Flat staking is simple, easy to audit and forgiving of edge estimates that are too optimistic. It is the default for anyone whose probabilities are not rigorously calibrated.

The Kelly criterion

f* = (p × b − q) / b      // b = decimal − 1, q = 1 − p
32% at +280: f* = (0.32 × 2.8 − 0.68) / 2.8 = 7.7%

Kelly maximises long-run growth if p is exactly right. It never is. Overestimating p by a few points can more than double the Kelly stake while the true edge is small or negative.

Fraction of KellyLong-run growth vs fullVariance vs full
Full100%100%
Half75%25%
Quarter44%6%
Why fractional Kelly

Half Kelly keeps about three-quarters of the growth with a quarter of the variance, and it builds in a safety margin for an overstated edge. That trade is why fractional Kelly is the common choice among people who use Kelly at all.

Limitations

Kelly assumes independent bets, a known probability, and no simultaneous exposure. Correlated bets on the same game, or several bets at once, need smaller stakes than the single-bet formula suggests. Never size from a probability you cannot defend.