This article explains a sizing formula and its failure modes. The worked numbers illustrate the mathematics under stated assumptions; they are not recommendations. Nothing here is investment advice. Decisions are yours.
The Kelly criterion is the bet size that maximizes long-run compounded growth: a formula taking your edge and odds and returning the exact fraction of capital to stake. It is mathematically correct and practically dangerous, because it assumes you know your edge. In crypto, where parameters drift by regime, full Kelly is a beautifully derived path to ruin.
The formula and what it optimizes
John Kelly derived the criterion at Bell Labs in 1956; Ed Thorp carried it from information theory to blackjack and then to markets. For a bet winning with probability p and paying b units per unit risked, the growth-optimal fraction is f* equals (bp minus q) over b, where q is the loss probability. Kelly maximizes the expected logarithm of wealth, which is the same thing as maximizing long-run compounded growth, the geometric quantity volatility drag punishes. Everything above f* buys extra variance that costs more growth than the extra exposure earns; everything below gives up growth for smoothness. In that one sentence, Kelly is the bridge between edge and sizing.
A worked crypto example
Take a breakout system with honest trend-following statistics: wins 40% of the time, and winners average 2.5 times the size of losers, the many-small-losses-few-big-wins shape from the breakout base rates. Kelly says f* equals (2.5 times 0.40 minus 0.60) over 2.5, which is 0.16: sixteen percent of the account on every signal. Any experienced operator reads that number and flinches, correctly. The formula answers a narrower question than the one that matters, growth-optimal IF these parameters are exactly true forever and IF you can tolerate the path. Neither IF holds here.
The violence of full Kelly
Even with perfect parameters, the full-Kelly path is brutal. Under the standard continuous approximation, a full-Kelly bettor has a one-in-two chance of at some point halving the bankroll, and in general a one-in-n chance of visiting one nth of it: a 10% chance of seeing 90% of the account gone, all while playing optimally. The overbetting cliff is sharper still: betting exactly twice Kelly drives long-run growth to zero, and beyond that, negative; the extra size does not merely add risk, it destroys the compounding it was meant to accelerate. Now add the recovery curve that drawdowns at crypto depth impose, and the behavioral evidence that operators abandon systems deep in the hole, which is how risk of ruin arrives in practice: a sizing rule that schedules 50/50 odds of a halving is not a rule most humans can actually follow, which makes its optimality theoretical in the least flattering sense.
Estimation error, the real enemy
The deeper problem is that p and b have to be estimated, never known, and crypto is the worst estimation environment in liquid markets: short histories, regime flips that reprice both parameters at once, backtests whose survivorship bias inflates the very edge being plugged in because the crypto graveyard is excluded from them, and fat-tailed returns violating the tidy win/lose structure entirely. The asymmetry of the error is what decides the policy: betting half of true Kelly costs only a quarter of the growth rate, while betting fifty percent over true Kelly, the inevitable outcome when an overfit backtest supplies the parameters, costs most of the growth and can cross into the negative zone. Under-betting is a mild tax; over-betting is a cliff, and parameter uncertainty means you cannot know which side of the line full Kelly puts you on. Fractional Kelly, a half or a quarter of the computed f*, is therefore not timidity, it is the mathematically correct response to not trusting your own inputs, the same shrinkage our own backtest audit applied to our own statistics.
Kelly in a correlated, levered market
Two final crypto corrections. Kelly's per-bet framing assumes bets resolve independently, and this market's one-factor stress behavior voids that: several concurrent positions are closer to one large bet than to several small ones, so naive per-position Kelly fractions sum to an aggregate far above portfolio Kelly. Total portfolio heat, not the per-trade fraction, is the number that binds. Our transplant experiment ran four concurrent 20% slots, an aggregate no defensible Kelly calculation would endorse under honest correlation inputs, and drew down 74%. And leverage does not change Kelly's answer, it only makes exceeding it easier: the formula already outputs the optimal exposure, and borrowing to exceed the optimum is definitionally growth-destroying. The synthesis is one line: compute Kelly to know where the cliff is, then stand well back from it. Decisions are yours.