Kelly Criterion Calculator
Calculate a stake from bankroll, odds, and an estimated probability, then compare full and fractional Kelly.
18+ where legal. Educational calculator only. Bet sizing outputs are not financial advice.
Kelly only grows a bankroll if you actually place the bets it sizes. 1Win's high limits let you bet the full fraction without getting capped.
You found the edge — now get the price.
The calculators do the math; these are the books readers use to put it to work. Each bonus adds bankroll, so a real edge compounds faster.
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How the Kelly Criterion Calculator Works
The Kelly Criterion is a mathematical formula derived by John L. Kelly Jr. in 1956 while working at Bell Labs. Originally designed for signal transmission, it was quickly adopted by gamblers and investors as the mathematically optimal staking strategy. The core insight: bet proportionally to your edge, not a fixed amount.
The formula: f* = (bp − q) / b, where b = decimal odds minus 1, p = your estimated win probability, and q = 1 − p. The result is the fraction of your bankroll to bet. If Kelly returns 8%, you should bet 8% of your current bankroll — not 8% of your starting bankroll.
The critical caveat: Kelly requires accurate probability estimates. If you overestimate your win probability by even 3%, the formula tells you to overbet, increasing drawdown risk dramatically. This is why professional bettors use half Kelly (50% of the Kelly output) as their default. Half Kelly sacrifices roughly 25% of long-run growth but cuts variance nearly in half — a trade-off almost every professional accepts.
Quarter Kelly (25% of output) is appropriate for bettors who are less confident in their probability estimates or who are betting in highly variable markets like player props or live betting. The mathematical relationship: as you scale down from full Kelly, variance decreases faster than expected growth, making fractional Kelly a highly efficient risk management tool.
The Kelly Formula
f* = (b × p − q) / b Where: b = Decimal Odds − 1 (net profit per unit) p = Win Probability (0 to 1) q = 1 − p (loss probability) f* = Fraction of bankroll to bet Half Kelly = f* × 0.5 (recommended default) Quarter Kelly = f* × 0.25 (conservative)
Kelly Staking Examples
b=1, p=0.55, q=0.45 → f* = (0.55 − 0.45)/1 = 10% full Kelly. Half Kelly = 5%. On $1,000 bankroll: bet $50 to $100.
b=0.90, p=0.52, q=0.48 → f* = (0.90×0.52 − 0.48)/0.90 = 1.3% full Kelly. Half Kelly = 0.65%. Tiny edge = tiny bet.
Frequently Asked Questions
What is the Kelly Criterion?
The Kelly Criterion is a mathematical formula that calculates the optimal fraction of your bankroll to bet. It maximizes long-run expected log wealth — meaning it grows your bankroll faster than any other staking strategy given accurate probability estimates.
Should I use full Kelly or half Kelly?
Most professional bettors use half Kelly (50% of the full Kelly output). It reduces variance by ~50% while sacrificing only ~25% of long-run growth. Full Kelly is mathematically optimal but requires perfectly accurate probability estimates — rarely achievable in practice.
What does a negative Kelly value mean?
A negative Kelly value means the bet has no positive expected value at those odds. The calculator shows 0%, meaning you should not bet. This happens when bp − q < 0, i.e., the offered odds are lower than the true fair odds given your probability estimate.
How accurate does my probability estimate need to be?
Very accurate. The Kelly formula is highly sensitive to probability input. A 3% overestimate on a coin flip (53% instead of 50%) produces the same Kelly as a 3% overestimate on a 70% shot — but with very different real-world consequences. When uncertain, use quarter Kelly as a safeguard.
What's the difference between flat staking and percentage staking?
Flat staking risks the same dollar amount on every bet — always $20, say — no matter how the bankroll moves. Percentage staking risks a fixed share of the current bankroll (e.g., 2%), so the dollar stake shrinks automatically after losses and grows after wins. Percentage staking self-corrects toward zero if you're losing; flat staking does not.
Should I use fixed staking or Kelly staking?
Fixed and percentage staking are simpler, lower-variance, and don't require a precise probability estimate — a reasonable default for most bettors. Kelly staking sizes the bet to your actual edge and compounds a bankroll faster when your probability estimates are accurate, but it punishes bad estimates hard. A common compromise: use Kelly as a ceiling and bet the smaller of your fixed stake and your Kelly stake — exactly what the calculator above computes as 'Recommended Stake'.
What does 'Max Bets at Stake' mean?
It's the number of consecutive losing bets, at the recommended stake, that would take your bankroll to zero — a rough ruin-resilience metric. Above 50 is comfortable; under 20 means a single bad losing streak could end your bankroll.
Bet sizing: fixed stake, percentage and Kelly compared
Bet sizing determines whether an edge turns into long-run profit or into variance-induced ruin. Two bettors with an identical 55% true win probability can end up with opposite outcomes purely because of how they size their stakes — one flat-betting a conservative 1–2% of bankroll, the other overbetting a full Kelly fraction straight into a losing streak.
Flat staking (level staking) risks a fixed dollar amount on every bet, unchanged until you top up the bankroll. Percentage staking risks a fixed share of your current bankroll, so the dollar stake shrinks after losses and grows after wins. Both are simpler and lower-variance than Kelly, and neither adjusts for the size of your edge — a 51% edge and a 65% edge get the same stake.
Kelly staking, covered above, sizes the bet to the edge itself. The trade-off is that Kelly needs an accurate probability estimate, and full Kelly is aggressive enough that most professionals scale it down. The calculator below lets you compare a flat or percentage stake against your Kelly output on the same bankroll.
Fixed Stake & Bet Sizing Calculator
The Sizing Formula
Fixed Stake = Bankroll × (Risk% / 100) Kelly Stake = Bankroll × Kelly_fraction Recommended = if Kelly > 0: min(Fixed, Kelly) else Fixed Max Bets = floor(Bankroll / Recommended)
Flat vs Percentage vs Full vs Fractional Kelly on a $1,000 Bankroll
Same bankroll, same 55% win probability at 2.00 odds (full Kelly = 10%, from the strong-edge example above). Here's what each staking method actually risks per bet.
| Method | Formula | Stake on $1,000 | Behavior |
|---|---|---|---|
| Flat staking | Fixed $ amount, e.g. $20 | $20 | Never changes — same $20 whether the bankroll is $500 or $5,000 |
| Percentage staking (2%) | Bankroll × 2% | $20 | Recalculated every bet — shrinks after losses, grows after wins |
| Full Kelly | f* = (bp − q)/b = 10% | $100 | Maximizes long-run growth; largest bankroll swings |
| Half Kelly | Full Kelly × 0.5 = 5% | $50 | ~75% of the growth, roughly half the variance |
| Quarter Kelly | Full Kelly × 0.25 = 2.5% | $25 | Conservative — for lower-confidence edges |