The optimal bet size, and why nobody uses all of it
Break-even needs 40.0%
Average win ÷ average loss
Only used to show dollar amounts
Full Kelly
25.0%
That is $2,500 of a $10,000 account at risk on one trade. Expectancy is +0.375R per trade. Growth turns negative above 49.0% — roughly twice this figure, not far above it.
And what you buy with it. The last two columns depend only on the Kelly multiple — not on your edge.
| Kelly multiple | Bet size | Growth kept | Ever −50% | Ever −75% |
|---|---|---|---|---|
| Quarter ×0.25 | 6.3% | 44% | 0.78% | <0.01% |
| Half ×0.5 | 12.5% | 75% | 12.5% | 1.6% |
| Three quarters ×0.75 | 18.8% | 94% | 31% | 9.9% |
| Full ×1 | 25.0% | 100% | 50% | 25% |
| Double ×2 | 50.0% | none | 100% | 100% |
Change the win rate or the reward ratio above and watch those two columns: they do not move. Under the standard approximation the chance of ever falling to a fraction α of your peak is α2/c − 1, where c is the Kelly multiple — the edge cancels out. A better strategy earns more, and gets you there faster, but it does not make full Kelly less violent. Bet size is what governs the ride.
Kelly assumes the win rate and the reward ratio are known exactly. In practice both are estimates from a limited number of trades, and the formula is asymmetric about that error: overstating your edge pushes the recommended size up, while the penalty for overbetting rises steeply. Since the zero-growth point sits at roughly twice full Kelly, an edge estimate that is off by half is enough to erase the growth the formula was maximising.
The model also treats trades as independent, which crypto does not respect. Losses arrive together because the conditions that caused one tend to persist, and a clustered run of losses cuts deeper than the independent case assumes. Sizing that is merely correct on paper leaves nothing in reserve for that.
The growth column is computed from the discrete formula, so it is exact for the win/loss model described. The two drawdown columns come from the continuous approximation, which is the standard treatment and is close for small bet sizes — but it is a lower bound on real risk, not a forecast.
The Kelly criterion answers a narrow question precisely: given a known edge, what fraction of capital maximises the long-run growth rate? The formula is (p·b − q) ÷ b, and betting more than it prescribes lowers growth rather than raising it. That much is settled mathematics, not opinion.
What the formula does not do is account for being wrong about the inputs. Every term in it is an estimate drawn from a finite record, and the cost of overestimating an edge is far larger than the reward for underestimating it — growth reaches zero at roughly twice the Kelly fraction, so the usable range is narrow on one side and forgiving on the other. Sizing below the optimum is the cheap mistake.
The volatility is the other objection, and it is the one people meet first. Betting the full fraction carries a one-in-two chance of the account halving at some point, and that figure holds regardless of how good the strategy is. Fractional Kelly exists because a strategy abandoned during a drawdown compounds at zero, whatever its theoretical growth rate was.
⚠️ Not investment advice. The output is a mathematical optimum under assumptions — a known and constant edge, independent trades, infinitely divisible bets — that real trading violates in every particular. Treat it as an upper bound on sensible size, never a recommendation. All decisions and risks are your own.
It is the bet size that maximises the long-run growth rate of capital given a known edge: (p·b − q) ÷ b, where p is the win rate, q is 1 − p, and b is the reward-to-risk ratio. Betting more than it prescribes lowers growth rather than raising it.
Two reasons. It assumes you know your edge exactly, and overstating it pushes the recommended size up while the penalty for overbetting rises steeply. It is also violent: full Kelly carries roughly a one-in-two chance of the account halving at some point.
About a quarter of the growth rate. Betting half of the Kelly fraction keeps roughly 75% of the long-run growth while cutting the chance of ever halving the account from one-in-two to one-in-eight. That asymmetry is the entire argument for fractional Kelly.
No, and this surprises people. Under the standard approximation the chance of ever falling to a fraction of your peak depends only on what multiple of Kelly you bet, not on the win rate or reward ratio. A stronger edge earns more and recovers faster, but the drawdown profile is set by bet size.
Growth falls, and it reaches zero at roughly twice the Kelly fraction — the same long-run result as never trading, after living through every drawdown on the way. Beyond that point capital declines even though every individual trade still has positive expectancy.
The formula returns a negative number, which means the correct bet is zero. No position size makes a negative-expectancy strategy profitable; reducing size only slows the loss.
Because win rate alone says nothing without the reward ratio. At 2:1 you break even at 33.3%, at 1:1 you need 50%. The break-even figure tells you which side of the line your inputs fall on before any sizing question arises.