What is the Kelly criterion?

Kelly is the bet-sizing formula that maximises long-run logarithmic bankroll growth. Formula: f* = (bp - q) / b, where b = payout-1, p = win probability, q = 1-p. The result is the fraction of bankroll to stake per bet.

Why cap at quarter-Kelly?

Full Kelly is mathematically optimal but extremely volatile — bankroll swings of 50%+ are routine. Quarter-Kelly (25% of the suggested fraction) reduces variance dramatically with only modest growth-rate penalty.

What if the Kelly fraction is negative?

Negative Kelly means the bet has negative EV — you should not bet. The calculator caps at $0 (no negative stakes).

Bankroll & Kelly Criterion Calculator | Optimal Stake Sizing

Bankroll & Kelly criterion calculator

Kelly-criterion bet-sizing calculator for any positive-edge bet. Enter bankroll + win probability + payout multiplier, get the EV-optimal stake (quarter-Kelly capped for variance sanity) and the expected number of rounds to lose half your bankroll if EV is negative.

Bankroll ($)Win probability (0-1)Win multiplier (per $1)

Suggested stake (Kelly-capped): $0.00
EV per $1 bet: $0.960
Expected rounds to half bankroll: 17

Raw Kelly: -4.0%. Capped at 25% (quarter-Kelly) for variance sanity. Negative Kelly = the bet has negative expected value; suggested stake is $0.

How to use this

For any gambling game with known win probability and win multiplier (Coinflip 50% × 2x; Crash 48% × 2x; Plinko 16-row high outermost 0.0015% × 935.5x; etc.) enter the values and the calculator returns the EV-optimal stake size.

For most casino games (any house-edge game), Kelly will be negative — the calculator caps at $0. The correct “optimal stake” on a negative-EV game is $0; everything else is entertainment spend, not an investment.

Frequently asked questions

What is the Kelly criterion?: Kelly is the bet-sizing formula that maximises long-run logarithmic bankroll growth. Formula: f* = (bp - q) / b, where b = payout-1, p = win probability, q = 1-p. The result is the fraction of bankroll to stake per bet.
Why cap at quarter-Kelly?: Full Kelly is mathematically optimal but extremely volatile — bankroll swings of 50%+ are routine. Quarter-Kelly (25% of the suggested fraction) reduces variance dramatically with only modest growth-rate penalty.
What if the Kelly fraction is negative?: Negative Kelly means the bet has negative EV — you should not bet. The calculator caps at $0 (no negative stakes).

Ready to play?

See how provably fair works

Bankroll ($)Win probability (0-1)Win multiplier (per $1)

Suggested stake (Kelly-capped): $0.00
EV per $1 bet: $0.960
Expected rounds to half bankroll: 17

Raw Kelly: -4.0%. Capped at 25% (quarter-Kelly) for variance sanity. Negative Kelly = the bet has negative expected value; suggested stake is $0.

How to use this

Frequently asked questions

What is the Kelly criterion?: Kelly is the bet-sizing formula that maximises long-run logarithmic bankroll growth. Formula: f* = (bp - q) / b, where b = payout-1, p = win probability, q = 1-p. The result is the fraction of bankroll to stake per bet.
Why cap at quarter-Kelly?: Full Kelly is mathematically optimal but extremely volatile — bankroll swings of 50%+ are routine. Quarter-Kelly (25% of the suggested fraction) reduces variance dramatically with only modest growth-rate penalty.
What if the Kelly fraction is negative?: Negative Kelly means the bet has negative EV — you should not bet. The calculator caps at $0 (no negative stakes).

Bankroll & Kelly criterion calculator

How to use this

Related

Frequently asked questions

Ready to play?

Bankroll & Kelly criterion calculator

How to use this

Related

Frequently asked questions

Ready to play?