Kelly Criterion
A formula for sizing bets to maximize long-run bankroll growth based on estimated win probability and payout odds.
Definition
The Kelly Criterion calculates the optimal fraction of bankroll to wager on a bet. For a binary market with probability p of winning and payout odds b (net profit per unit staked), the Kelly fraction is f* = (bp − q) / b where q = 1 − p. Betting this fraction maximizes the expected logarithm of wealth, which corresponds to maximum long-run growth without ruin.
In practice
For a Polymarket position where the bot estimates p = 0.60 of YES winning and the market offers odds of approximately 1:1 (buying at $0.50, paying out $1.00), Kelly suggests f* = (1 × 0.60 − 0.40) / 1 = 0.20, or 20% of bankroll. In practice bots use half-Kelly or quarter-Kelly to reduce variance. Fees must be subtracted from the expected payout before applying the formula. Position sizing based on Kelly ensures the bot scales up naturally on high-edge signals and sizes down on low-confidence trades, compounding growth without blowing up.