Kelly Criterion Calculator
Enter your bankroll, your probability estimate, and the contract's price or odds to get the full Kelly stake, half and quarter Kelly, and how the expected growth rate changes as you bet more or less than that.
Your bet
Full Kelly: stake 16.00% of bankroll ($1,600.00)
Net odds b = 1.000. Half Kelly stakes $800.00, quarter Kelly stakes $400.00.
Full Kelly (f*)
16.00%
Half Kelly
$800.00
8.00%
Quarter Kelly
$400.00
4.00%
Growth rate across stake fractions
Expected log-growth per bet at multiples of full Kelly. Growth rises to a peak exactly at 1x Kelly, then falls -- overbetting past full Kelly costs you growth, not just adds risk.
| Kelly multiple | Fraction staked | Stake | Expected log-growth |
|---|---|---|---|
| 0x | 0.00% | $0.00 | 0.00000 |
| 0.25x | 4.00% | $400.00 | 0.00560 |
| 0.5x | 8.00% | $800.00 | 0.00962 |
| 0.75x | 12.00% | $1,200.00 | 0.01204 |
| 1x | 16.00% | $1,600.00 | 0.01286 |
| 1.5x | 24.00% | $2,400.00 | 0.00950 |
| 2x | 32.00% | $3,200.00 | -0.00095 |
How this is calculated
Net odds b = (1 / price) − 1 -- how much you win per dollar staked. At the default 50¢ price, b = 1.00 exactly (even money). Kelly's formula is then f* = (b·p − q) / b, where q = 1 − p is the probability of losing. At p = 58%, that's f* = 16.00% of bankroll -- $1,600.00 on a $10,000 bankroll.
When f* is zero or negative, the formula is telling you something specific: at this price, your stated edge (b·p vs q) doesn't clear the bar needed to grow your bankroll by betting at all. The honest answer at that point is to stake nothing, not a small amount -- Kelly sizing doesn't have a graceful way to express "a little bit of a bad bet."
Full Kelly is a ceiling, not a target. It maximizes long-run growth only if your probability estimate is exactly correct every time -- a fragile assumption. Fractional Kelly (half or quarter) trades some of that theoretical growth for a lot less sensitivity to being wrong, which is why most practitioners size well under full Kelly rather than at it.
Frequently Asked Questions
What does the Kelly criterion actually optimize for?
The long-run growth rate of your bankroll if you make this same kind of bet over and over, not the size of any single win. It answers 'what fraction of my bankroll maximizes how fast it compounds' -- which is a different question from 'what fraction minimizes my risk of losing' or 'what fraction maximizes my expected profit on this one bet' (that second one, taken alone, always says bet everything, which is obviously reckless).
Why does a stake this big feel too aggressive?
It usually is, for real money. Full Kelly assumes your probability estimate is exactly right, which it never is in practice -- overestimate your edge even a little and full Kelly overbets, sometimes badly. That's why half Kelly ($800.00 on the default example) is the common real-world default: it gives up some long-run growth for meaningfully less volatility and much less damage from a probability estimate that turns out to be wrong.
What happens if I bet more than full Kelly?
Growth gets worse, not better -- and can turn negative. On the default example, doubling full Kelly's stake to 2x doesn't double your growth rate; it actually produces an expected log-growth of -0.00095, which is worse than staking nothing at all. Kelly's peak really is a peak -- betting past it is provably a mistake, not just a matter of taste.
Why is the formula b·p − q, not just p − price?
Because Kelly sizing needs to know the actual payout ratio, not just whether there's an edge. b is the net odds -- how many dollars you win per dollar staked if you're right -- and q is the probability you lose. At a 50¢ price, b works out to exactly 1 (a $1 payout on a 50¢ stake is a $0.50 net win per $0.50 risked, i.e. even money), which is why this page's 50¢ examples have particularly clean numbers.
Does this account for fees?
No -- this page uses the contract price as the only cost. A real fee (see the payout calculator) effectively raises your entry price, which lowers b and therefore lowers f* -- sometimes past zero, turning a marginal edge into a no-bet. Run the payout calculator's fee-inclusive cost through this page's price field if fees matter to your situation.
SidebySideCalc's prediction-market calculators apply standard odds, probability, and bankroll-sizing math to the numbers you enter -- they are not trading advice. Prediction markets carry real risk of loss and may be restricted or unavailable in some jurisdictions; nothing here names or endorses a specific trading venue.