Bet Sizing

Core Concepts

Kelly Criterion (Discrete)

For a binary bet with payoff odds b, win probability p, and loss probability q = 1-p:

f* = (b*p - q) / b

where f* is the optimal fraction of wealth to wager. The Kelly criterion maximizes the expected logarithm of wealth (geometric growth rate) over repeated bets.

Properties:

• f* = 0 when edge = 0 (no bet when there is no advantage)
• f* < 0 when negative edge (the formula tells you to bet the other side)
• f* > 0 only when b*p > q (positive expected value)

Note: the reference script's discrete_kelly clamps negative Kelly fractions to 0 (no bet) rather than returning a negative value — it does not recommend taking the other side.