The Kelly criterion tells you what share of your bankroll to stake on a bet. It assumes you know your true probability of winning.
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1 Game time
The formula, term by term
The Kelly criterion works out the stake that grows your bankroll fastest over a large number of bets. It comes with one condition: your estimated probability has to be right.
Share of the bankroll Stake = (b × p − q) ÷ b
- b: the net win per $1 staked, which is the decimal odds minus 1. At -110 (1.91), b is 0.91.
- p: the probability you give the bet, 0.55 for 55%.
- q: the probability of losing, 1 − p, here 0.45.
- b × p − q: the average profit per dollar staked. Zero or negative means no bet.
- ÷ b: divides that average profit by the possible win, which gives a share of the bankroll.
2 The box score
A worked example
A $1,000 bankroll, a bet at -110 (1.91), an estimated probability of 55%.
- 1 The terms: b = 1.91 − 1 = 0.91 and q = 1 − 0.55 = 0.45.
- 2 The average profit: 0.91 × 0.55 − 0.45 = 0.0505, or about 5 cents per dollar staked.
- 3 The stake: 0.0505 ÷ 0.91 = 0.055, or 5.5% of the bankroll: $55.
The break-even rate is the implied probability, 1 ÷ decimal odds: 52.4% at -110. Below it, the formula gives no bet.
The Kelly stake for five bets
- -110 (1.91), estimated at 50%
- Break-even
- 52.4%
- Kelly
- 0%
- Half Kelly
- 0%
- -110 (1.91), estimated at 55%
- Break-even
- 52.4%
- Kelly
- 5.5%
- Half Kelly
- 2.8%
- -110 (1.91), estimated at 57%
- Break-even
- 52.4%
- Kelly
- 9.7%
- Half Kelly
- 4.9%
- +180 (2.80), estimated at 40%
- Break-even
- 35.7%
- Kelly
- 6.7%
- Half Kelly
- 3.3%
- -200 (1.50), estimated at 70%
- Break-even
- 66.7%
- Kelly
- 10.0%
- Half Kelly
- 5.0%
3 The stat sheet
Why bettors stake a fraction of Kelly
p is an estimate. Over 100 bets, a bettor who truly wins 55% has 50 wins or fewer 18.3% of the time, and 60 or more just as often. Estimated on those records, p would be 50% or 60%: the formula would give 0% or 16.0%.
Full Kelly means deep drawdowns. Take that 55% bettor at -110 (1.91), with $1,000 and 500 bets. Each stake is a share of the current bankroll.
Bettor who truly wins 55% at -110 (1.91), 500 bets, $1,000 start. Exact calculation over every possible sequence.
The median bankroll, the one that half of all runs finish above, is $2,018 at full Kelly, $1,698 at half Kelly and $1,362 at quarter Kelly. Half Kelly keeps most of the growth for a fifth of the risk. The bankroll management guide puts numbers on losing streaks too.
How the median is worked out
A win multiplies the bankroll by 1 + 0.91 × stake, a loss by 1 − stake. The median run has 275 wins out of 500, or 55%. At 5.5%: $1,000 × 1.05005^275 × 0.945^225 = $2,018.
Share of runs that finish above $1,000: 84.9% at quarter Kelly, 80.4% at half Kelly, 72.1% at full Kelly.
4 The replay
When you overestimate your edge
The same bettor estimates 57% instead of 55%. The stake becomes 9.7% instead of 5.5%, nearly double. The median, $1,356, falls to the quarter Kelly level, yet the bettor drops below $500 in 68.4% of runs, versus 0.1% at quarter Kelly.
At twice the Kelly stake, 11.1%, the median falls to $990, below the starting point, despite a true return of 5%. At an estimated 60%, the stake climbs to 16.0% and the median falls to $157. The expected value guide shows how to estimate p.
Two points of probability too many are enough to nearly double the stake. Bet half Kelly, or a quarter.
Size your own stake with the Kelly criterion calculator.
Switching sides
A small stake needs time
Kelly aims for the fastest growth. A challenge asks a different question: reach +35% before you lose 20%. On the steady profile, between 2% and 5%, a 2% stake then gives the best chance, as long as you have the time.
Put a 30-day clock on it, 90 bets at most at three a day, and the 2% stake hits the target only about one time in nine: the clock forces a bigger stake.
55% of bets won at -110 (1.91), flat stake as a share of the starting bankroll. Rounded to the nearest point. 30 days: 90 bets at most.
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6 Overtime
In a challenge, the stake range overrides the formula
In a challenge, the stake is not entirely yours to choose. At Prime Sports Funded, it runs from 2% to 5% of the starting bankroll, or 100 to 250 on the 5,000 challenge. The 5.5% Kelly stake of the example is above that cap. Half Kelly, 2.8%, fits. Quarter Kelly, 1.4%, falls below the minimum.
Take a fraction of the Kelly stake, then bring it inside the limits. The standings below count what a funded account really costs: the challenge price divided by the chance of passing, on the steady profile.
Steady profile: 55% of bets won at -110 (1.91), 3 bets a day
- 1
Prime Sports Funded Challenge
€114 real cost
72% chance of getting funded. €81.75 with code PROMO25 (€109 without).
See the No. 1 
MySportsFunding Instant Funding
€499 real cost
€499.
Priced in pounds
GetBet Funded Standard plan
£225 real cost
34% chance: 54%, then 63%. 90 bets at most in 30 days. £76 price shown with the operator's 20% discount, no published end date.
Priced in US dollars
Bankroll U Combine
$292 real cost
$245. Based on: Combine only.
Fan Funded 3 Step
$435 real cost
14% chance: 52% per phase, 3 times in a row. 90 bets at most in 30 days. $59.99.
Not ranked: Playvo (bankroll size not published), OddsON (stake limits not published; accounts of 5,000 and up not yet on sale).
Real cost: challenge price ÷ chance of getting funded. Flat stakes, average odds of -110 (1.91).
How we calculate
- Three profiles: 54% of bets won and 2 bets a day; 55% and 3; 57% and 4.
- Each operator is modeled at the stake that gives it the best chance, within its allowed range.
- Time-limited challenge: the number of bets is capped by the profile's pace.
- Several phases: the chances multiply.
- Not simulated: daily loss limits, minimum number of bets, activity targets, consistency rules.
- Bankroll U is taken at its Combine, the lowest real cost among the offers considered for this matchup, on the steady profile. Five levels: not ranked (higher real cost on the steady profile).
- Bankroll U: Combine only, which opens the Rookie level at 10% of profits.
- Fan Funded is taken at its 3 Step, the lowest real cost among the offers considered for this matchup, on the steady profile. 2 Step: not ranked (higher real cost on the steady profile). Blitz: not ranked (too close to call: the gap depends on the exchange rate).
- GetBet Funded: price shown with the operator's 20% discount, no published end date.
- Prime Sports Funded price with code PROMO25.
- Amounts are shown in each operator's own currency, with no conversion. Operators are not ranked across currencies.
- The math holds for these profiles, not for every bettor.
Frequently asked questions
What is the Kelly criterion?
A formula that gives the share of your bankroll to stake on a bet: (b × p − q) ÷ b, where b is the decimal odds minus 1, p the probability of winning and q the probability of losing. If p is right, it is the stake that grows the bankroll fastest over a large number of bets.
How do you calculate a Kelly bet?
For a bet at -110 (1.91) that you put at 55%: b = 0.91 and q = 0.45. Then b × p − q = 0.0505. Divided by b, that gives 0.055: 5.5% of the bankroll, or $55 on $1,000. If p is at or below 1 ÷ decimal odds (52.4% at -110), no bet.
What is half Kelly?
Half of the Kelly stake: 2.8% instead of 5.5% in the example. Over 500 bets won 55% of the time at -110 (1.91), from $1,000, the median bankroll is $1,698 versus $2,018 at full Kelly. The risk of falling below $500 along the way drops from 35.2% to 6.7%.
What happens if you overestimate your edge?
You stake too much. Estimate 57% when you truly win 55% at -110 (1.91), and the stake goes from 5.5% to 9.7%. Over 500 bets, the median bankroll falls from $2,018 to $1,356 and the risk of dropping below $500 climbs from 35.2% to 68.4%.
Can you use the Kelly criterion in a prop firm challenge?
Only inside the operator's stake range. At Prime Sports Funded, a stake runs from 2% to 5% of the starting bankroll: the 5.5% Kelly stake of the example is above the cap, while half Kelly at 2.8% fits. With no time limit, a small stake has all the time it needs to work toward the +35% target.
The verdict
Fractional Kelly, no clock
One step at +35%, no time limit: a small stake has room to play out. The 5,000 challenge costs €81.75 with code PROMO25, down from €109.
Prime Sports Funded No. 1 in our standings
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