The bankroll-growth-optimal stake for a bet with an edge — and the fractional versions serious bettors actually use.
For decimal odds d and win probability p, the Kelly fraction of bankroll is:
f* = (d × p − 1) ÷ (d − 1)
The numerator is your edge; the denominator is the net odds. When d × p ≤ 1 the bet is −EV and Kelly says stake nothing.
You're 55% on a bet at +100 (d = 2.00): f* = (2 × 0.55 − 1) ÷ 1 = 10% of bankroll. On $1,000 that's $100 full Kelly, $50 half Kelly, $25 quarter Kelly.
Full Kelly assumes your probability is exactly right — it never is. Overestimating your edge with full Kelly overbets, and overbetting destroys bankrolls faster than underbetting slows growth. Half or quarter Kelly gives up a little growth for a lot less variance, which is why most professionals size at 0.25–0.5× Kelly.
Deep dive: Kelly bankroll management →
The bet is negative EV at that price — the correct stake is zero. Kelly only ever bets when the price beats your probability.
Full Kelly is optimal only if your probability estimate is exact. Since estimates carry error, full Kelly systematically overbets; fractional Kelly (¼–½) protects the bankroll from your own overconfidence.
Correlated or simultaneous bets share bankroll risk, so the naive per-bet Kelly overbets. A common practical fix is dividing each stake by the number of concurrent bets, or capping total exposure.
Expected value of a bet from your fair win probability and the offered price.
Strip the bookmaker margin from two- or three-way odds to reveal the fair price.
Check two or three prices for a guaranteed profit and split your stake exactly.