Kelly Criterion Bet Size Calculator
Calculate the mathematically optimal stake size using the Kelly Criterion to maximize long-term bankroll growth. Use it whenever you have a genuine edge and want disciplined stake sizing.
About this calculator
The Kelly Criterion determines the fraction of your bankroll to wager when you have a positive expected edge. The core formula is: f = (p × b − q) / b, where p is your estimated win probability, q = 1 − p is the loss probability, and b = odds − 1 (the net odds received). Multiplying f by your bankroll gives the optimal dollar amount to stake. In this calculator the formula is: betSize = bankroll × max(0, (p × odds − q) / (odds − 1)) / 100, capped at a user-defined maximum percentage of bankroll. The division by 100 converts the probability from percentage form. If the result is negative or zero, the Kelly formula indicates no edge and you should not bet. The cap prevents over-betting in high-variance situations.
How to use
Your bankroll is $2,000, the decimal odds are 2.50, and you estimate a 50% win probability with a 25% maximum bet cap. First compute p = 50/100 = 0.50, q = 0.50, b = 2.50 − 1 = 1.50. Kelly fraction = (0.50 × 1.50 − 0.50) / 1.50 = (0.75 − 0.50) / 1.50 = 0.25/1.50 = 0.1667 (16.67%). Optimal stake = $2,000 × 0.1667 = $333.33. The cap is 25% of $2,000 = $500, which is higher, so the uncapped Kelly stake of $333.33 is returned as your recommended bet.
Frequently asked questions
What does it mean when the Kelly Criterion calculator returns zero or a negative value?
A zero or negative Kelly output means the bet has no positive expected value based on the inputs provided. This occurs when your estimated win probability is too low relative to the implied probability embedded in the bookmaker's odds. For example, if the odds imply a 55% chance of winning but you only estimate 50%, the Kelly formula outputs a negative number, signaling you should not place the bet. Never force a stake when Kelly returns zero — it is the formula's way of protecting your bankroll.
Why do professional bettors often use half Kelly or fractional Kelly instead of full Kelly?
Full Kelly maximizes long-term geometric growth but produces very large drawdowns in the short run, which can be psychologically and financially damaging. Fractional Kelly — typically 25–50% of the full Kelly recommendation — sacrifices some growth rate in exchange for significantly lower variance and smoother bankroll curves. Research shows that half Kelly achieves roughly 75% of the full Kelly growth rate with far less risk of ruin. Many professionals use the maximum bet percentage cap, as included in this calculator, to achieve a similar effect.
How accurate does my win probability estimate need to be for the Kelly Criterion to work?
The Kelly Criterion is highly sensitive to errors in your probability estimate — a condition known as estimation risk. Overestimating your edge leads to over-betting, which can destroy a bankroll faster than flat staking. Even a few percentage points of error can meaningfully change the recommended stake. This is why many practitioners use conservative (low) probability estimates and apply fractional Kelly as a buffer. The formula is most reliable when your probability estimates are derived from large historical datasets or robust predictive models rather than intuition alone.