Educational tool, not financial or betting advice.
What the Kelly criterion answers
Given a bet with a known edge, how much of your bankroll should you stake? Bet too little and you leave growth on the table; bet too much and variance eats you alive — or ruins you outright. The Kelly criterion finds the single fraction that maximizes the long-run growth rate of your bankroll, by maximizing the expected logarithm of wealth. For a bet that pays net odds b with win probability p:
f* = p − (1 − p) / b
Equivalently, f* = edge / odds. A coin-flip bet (b = 1) that you win 60% of the time gives f* = 0.6 − 0.4 = 0.2, so you stake 20% of your bankroll. If the edge is zero or negative, Kelly says stake nothing — and this calculator clamps to zero rather than suggesting a "small" losing bet.
Why almost everyone uses fractional Kelly
Full Kelly is the growth-maximizing bet, but it is wild: drawdowns of 50% or more are routine. The growth curve is also asymmetric — it rises gently to the peak and falls off a cliff beyond it. Betting half Kelly captures about three-quarters of the growth for roughly half the volatility, which is why it is the standard in practice. Betting twice Kelly, by contrast, has zero expected growth: you are as likely to shrink as to grow.
The catch: you never know p exactly
The formula is exact, but its inputs are estimates. Overestimating your win probability pushes you past the peak of the growth curve, where the penalty is severe and asymmetric — a reason beyond volatility that seasoned bettors and investors deliberately bet a fraction of Kelly. Treat the full-Kelly number as a ceiling you should stay well under, not a target.
Related tools: the Black-Scholes calculator values the options an edge might come from, and the APR/APY calculator covers compounding — the same exponential growth Kelly maximizes.