Calculators
Kelly Criterion Calculator
Find the bet size that grows your bankroll fastest, and see exactly why betting more than that quietly destroys it.
Growth rate vs. bet size
The Kelly criterion tells you the bet size that grows your money the fastest over many repeated bets. Growth peaks right at f*, bet more than that and you don't grow faster, you actually grow slower and edge toward ruin (the drop to the right of the peak). Because that curve is steep on the downside and a wrong probability guess pushes you into it, many pros deliberately bet a fraction such as half-Kelly, giving up a little growth for a much smoother, safer ride.
Educational tool. Assumes a repeated, independent bet with fixed win probability and odds. Not investment advice.
Learn how it works
Five worked examples. Read a couple before you dive in, try to answer first, then reveal the solution.
Small edge on an even-money bet
You win 55% of the time (p = 0.55) and a win pays the same as you stake (odds b = 1, i.e. +$1 per $1 risked). What fraction of your bankroll does full Kelly say to bet?
Formula: f* = (b·p − q) ÷ b, where q = 1 − p.
Show solution
q = 1 − 0.55 = 0.45. f* = (1 × 0.55 − 0.45) ÷ 1 = 0.10 = 10%.
A thin 55/45 edge says risk about a tenth of your bankroll per bet. Wager much more and the swings (and the risk of going broke) grow faster than the extra growth is worth.
A bigger edge means a bigger bet
Win probability p = 0.60, even-money odds b = 1. What is the full Kelly fraction?
Show solution
q = 0.40. f* = (1 × 0.60 − 0.40) ÷ 1 = 0.20 = 20%.
A stronger 60/40 edge doubles the recommended stake versus the 55% case (20% vs 10%). More edge → more to bet, but notice how fast the number climbs as the edge grows.
A coin flip with a 2-to-1 payoff
You win only half the time (p = 0.50), but a win pays 2-to-1 (b = 2, i.e. +$2 per $1 risked); a loss costs your $1. What is the Kelly fraction?
Show solution
q = 0.50. f* = (2 × 0.50 − 0.50) ÷ 2 = (1.0 − 0.50) ÷ 2 = 0.50 ÷ 2 = 0.25 = 25%.
Even with a coin-flip win rate, the fat 2-to-1 payoff creates a real edge, and Kelly says stake a quarter of the bankroll. The size of the payoff matters just as much as how often you win.
No edge, Kelly says don't bet
Win probability p = 0.40, even-money odds b = 1. What is the Kelly fraction?
Show solution
q = 0.60. f* = (1 × 0.40 − 0.60) ÷ 1 = −0.20 = −20%.
A negative Kelly fraction means you have no edge, the bet is a long-run loser. The only winning move is not to play (or, if you could, to take the other side). Never stake a negative-edge game.
Half-Kelly for a smoother ride
You computed full Kelly = 10% (the 55%, even-money case). Many traders bet only half of Kelly. How much do they stake, and why?
Show solution
Half-Kelly = 10% ÷ 2 = 5%.
Betting half the Kelly amount keeps most of the long-run growth (theory says roughly three-quarters of it) while cutting the wildness of your bankroll dramatically. Because real-world probabilities are only estimates, over-betting is brutal, so fractional Kelly (half, or even a quarter) is the practical default for most people.
What you'll learn
How much to bet when you have an edge, the maths of bankroll growth, why full Kelly is aggressive, and why over-betting is ruin.