Knowing a bet is in your favour doesn't tell you how much to put on it — stake too little and you leave growth on the table, too much and a bad run wipes you out. The Kelly criterionA formula from John Kelly (1956) for the bet size that maximises the long-run growth rate of a bankroll: edge ÷ odds. It grows a bankroll faster than any other constant fraction — and famously underpins how some investors size positions, not just gamblers. finds the stake that grows your bankroll fastest over the long run: edge ÷ odds. Expected value picks the bet; Kelly sizes it.
The bet
I win% of the time. A win paysto 1Net odds: a win returns this many times your stake in profit, plus the stake back. ‘2 to 1’ means risk 1 to win 2. Even money is 1 to 1., and a loss costs× the stakeHow much of the stake a loss takes. 1× loses the whole stake (a classic bet); set it below 1 for a position you'd cut at a stop-loss, e.g. 0.5 to lose half..
MybankrollThe total pool you bet from. Kelly stakes a fraction of it, and that fraction is what compounds, win after win.is€.
20% edge per unit staked · you win 60% against a 50% break-even
How much to stake
BetStake a fixed fraction of full Kelly. Half- or quarter-Kelly keeps most of the growth for a fraction of the swings, which is why few stake the full amount in practice.1.00×
€2 000to stake · 20% of bankroll
20%Full KellyThe bet size that maximises long-run growth: edge ÷ (loss × odds). The full-Kelly stake, before any fractional dialing-down.
2.03%Growth / betThe bankroll's expected compound growth per bet at this stake — the geometric mean of a win and a loss, not the arithmetic average. This is the quantity Kelly maximises.
34Bets to doubleRoughly how many bets it takes to double the bankroll at this growth rate: ln 2 ÷ growth. A long-run average, not a guarantee on any single run.
€400EV / betExpected profit on a single bet at this stake: edge × the amount staked. The average payoff per bet — what the Expected Value trinket sums across a whole decision.
Full KellyStake 20% of your bankroll — €2 000 — to compound about 2.03% per bet, doubling roughly every 34 bets. Full Kelly grows fastest but rides the wildest swings — many stake a half or quarter of it for a far smoother ride.
The growth curve
break-evenfull Kelly · 20%
0%38.9% · ruin line50.6% of bankroll
The hump is the whole story. Growth peaks at full Kelly — stake more and you take wilder swings for less growth, not more. Bet past 38.9% (about twice Kelly) and growth turns negative: the bankroll grinds down over time even though every bet is in your favour. Overbetting is punished harder than underbetting, which is why most stake a half or quarter of Kelly — keeping the bulk of the growth for a fraction of the volatility.
Kelly fraction = edge ÷ odds · maximises long-run growth, not any single bet · see the Kelly criterion