The Kelly criterion sizes a bet so your bankroll grows fastest over time, given your edge. For a prediction market contract it needs only two numbers: the price you pay and the chance you think it wins.
Kelly fraction
Enter 0 for no fee.
Most prop firms cap one position. Leave empty for no cap.
Suggested stake
$1,250
The position limit is smaller than the Kelly stake, so the limit sets the size. Kelly assumes your probability is right. If it is even slightly too high, full Kelly bets too much, which is why most traders use half or less.
A contract costs c (in dollars, including the fee) and pays $1 if it wins. If you think it wins with probability q, the share of your bankroll Kelly says to stake is:
f = (q − c) ÷ (1 − c)
Example: at 40¢ with no fee, if you think the chance is 50%, f = (0.50 − 0.40) ÷ 0.60 = 16.7% of your bankroll. On $25,000 that is $4,167, or 10,416 contracts. Half Kelly is $2,083. A fee at rate 0.07 raises the cost to 41.68¢ and cuts full Kelly to 14.3%.
Kelly is only optimal if your probability is right. Overbetting hurts far more than underbetting: staking about twice the Kelly amount wipes out the expected growth, and more than that shrinks the bankroll over time. Because estimates are noisy and usually too confident, half or quarter Kelly is the practical choice.
Prop firm rules change the math in two ways. First, most firms cap a single position: at Lenium it is 5% of the account. In the example, even half Kelly with the fee ($1,783) is above the cap, so the cap sets the size ($1,250). Second, the account ends at a drawdown floor (10% below the start in a Lenium evaluation), not at zero. Kelly assumes you can lose almost everything and keep going; with a floor 10% away, a few full-Kelly losses in a row end the account. Size well below Kelly and check your room with the drawdown calculator.
Read the full position limits on the rules page.
Put it to work on live prices
Lenium is a prediction market prop firm: trade an evaluation on live market prices and earn a share of the profits. All accounts are simulated, evaluation, funded and Instant accounts alike: they trade virtual balances on live market prices. No real money is traded and no orders are sent to any exchange.
Lenium is not affiliated with, endorsed by, or sponsored by any exchange or prediction market operator.