KELLY CRITERION CALCULATOR
Enter your bankroll, your win probability, and the net odds you are getting. The tool returns the Kelly-optimal stake, the raw Kelly fraction, and the safer half-Kelly bet. It is built for positive-edge (+EV) situations — and it will honestly tell you not to bet when the math shows you have no edge.
Independent, data-led tool — see our methodology · Last updated
f* = (b·p − q) / b, where q = 1 − p. The recommended stake is f* × bankroll. If the edge (b·p − q) is zero or negative you have no advantage, Kelly returns 0, and the correct bet size is nothing. Half-Kelly simply halves f* to cut variance.
Illustrative examples computed with f* = (b·p − q) / b. Change the inputs above for your own numbers.
| Scenario | Win prob (p) | Net odds (b) | Edge (b·p−q) | Kelly f* | Half-Kelly |
|---|---|---|---|---|---|
| Small edge, even money | 55% | 1.00 | +0.10 | 10.0% | 5.0% |
| Strong edge, even money | 60% | 1.00 | +0.20 | 20.0% | 10.0% |
| Underdog value bet | 40% | 2.00 | +0.20 | 10.0% | 5.0% |
| Coin flip, priced at 2.10 | 50% | 1.10 | +0.05 | 4.5% | 2.3% |
| No edge (typical house game) | 49% | 1.00 | −0.02 | 0% — no bet | 0% |
What the Kelly Criterion actually tells you
The Kelly Criterion answers one narrow but important question: given a bet you already believe is profitable, what fraction of your bankroll should you stake to grow your money fastest over the long run? It was derived by John L. Kelly Jr. in 1956 and is widely used by professional gamblers and investors. The formula is f* = (b·p − q) / b, where p is your probability of winning, q = 1 − p is the probability of losing, and b is the net odds — the profit you collect per unit staked when the bet wins. The output f* is the share of your bankroll to put at risk; the calculator above multiplies it by your bankroll to give a dollar stake, and also shows the half-Kelly figure.
The key input is honesty about p. Kelly does not estimate your edge for you — it takes the win probability you supply and sizes the bet accordingly. Feed it an inflated probability and it will confidently tell you to over-bet, which is the fastest route to ruin. The numerator b·p − q is your edge: it is positive only when the reward-weighted chance of winning beats the chance of losing. When that number is zero or below, you have no advantage and Kelly correctly returns zero.
Why Kelly usually says “don’t bet” in a casino
Here is the honest part most bet-sizing pages skip. In ordinary casino games you do not have a positive edge — the house does. A 1% house edge means your expected value on each wager is negative, so when you plug realistic numbers into Kelly, the edge term b·p − q comes out negative and the optimal Kelly stake is nothing. That is not a bug; it is the formula working exactly as intended. Kelly is a tool for positive-expectation situations, and negative-edge games such as slots, roulette, dice and crash are not among them, no matter how you size the bets. You can confirm the edge on any game with our house edge & RTP calculator.
So where is Kelly useful? In the genuine +EV situations that do occasionally exist around gambling: advantage play (like card counting where the count is in your favour), value bets in sports where you believe the true probability beats the bookmaker’s implied odds, prediction-market or arbitrage positions, and sometimes a casino bonus whose expected value is positive after wagering requirements. In all of those, the hard part is estimating p and b accurately; Kelly is just the sizing step that follows. For pure bankroll survival on games you play for entertainment, a flat, small percentage-of-bankroll approach — see our bankroll calculator — is the more appropriate tool.
Full Kelly vs half-Kelly
Full Kelly is growth-optimal in theory, but in practice it is aggressive. It maximises the long-run compound growth rate, yet it accepts brutal short-term swings to do so, and it assumes your probability estimate is perfect. Because no real estimate is perfect, betting the full fraction risks systematic over-betting. The standard remedy is fractional Kelly: stake a fixed fraction of f*, most commonly one-half. Half-Kelly retains roughly three-quarters of the theoretical growth rate while cutting the variance and the depth of drawdowns by far more than half. Many disciplined bettors go further to quarter-Kelly. The calculator shows both the full and half figures so you can see the trade-off directly.
Worked example
Suppose you have identified a value bet you believe wins 55% of the time at even money (b = 1), and your bankroll is $1,000. Then p = 0.55, q = 0.45, and the edge is b·p − q = 0.55 − 0.45 = 0.10. The Kelly fraction is f* = 0.10 / 1 = 0.10, or 10% of bankroll — a $100 full-Kelly stake, or $50 at half-Kelly. Now change the win probability to 49% with the same even-money odds: the edge becomes 0.49 − 0.51 = −0.02, Kelly returns a negative fraction, and the tool reports 0% — do not bet. That single flip — from a real edge to a house edge — is the whole story of why Kelly is a sizing tool for advantage situations and not a system for beating the casino.
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f* = (b·p − q) / b, where q = 1 − p. Multiply that fraction by your bankroll to get the recommended stake. It answers how much to bet, not which bet to make — and it only helps when you already hold a positive edge.f* = (b·p − q) / b, where p is your probability of winning, q = 1 − p is the probability of losing, and b is the net odds (profit per unit staked on a win). Example: with a 55% win chance at even money (b = 1), f* = (1 × 0.55 − 0.45) / 1 = 0.10, so Kelly recommends staking 10% of your bankroll. On a $1,000 bankroll that is a $100 full-Kelly bet, or $50 at half-Kelly.