Kelly Criterion
A formula for sizing bets that maximises long-run geometric bankroll growth. Used at TrapStats in a fractional, capped form to defend against probability mis-estimation.
The Kelly Criterion is a bet-sizing formula derived by John Kelly at Bell Labs in 1956. For a binary bet at decimal odds O with estimated win probability p:
f* = (b·p − q) / b
where b = O − 1 and q = 1 − p. The result f* is the optimal fraction of bankroll to stake.
Kelly maximises the long-run geometric growth rate of your bankroll — not your expected value on any single bet. With a correct p, full Kelly is mathematically optimal for compounding wealth.
The catch: Kelly assumes p is exactly right. Real probability estimates have noise; even small over-estimates make full Kelly catastrophically aggressive. The standard fix is fractional Kelly — stake α × f* where α is typically 0.25 (quarter-Kelly) or 0.5 (half-Kelly). Quarter-Kelly gives ~44% of full-Kelly's growth at ~1/16th the volatility.
TrapStats application: the Denis tracker uses a percentage-tiered staking scheme (1%/2%/3% of bankroll based on shrunk EV bucket) rather than pure Kelly, with explicit caps (denis_safety_max_ev=0.50, denis_safety_min_price=3.5) — a more conservative regime than even quarter-Kelly. See the Kelly blog post for a worked example.