Glossary · Staking

Kelly Criterion

The mathematically optimal stake size given your edge and the odds — maximises long-run bankroll growth.

The Kelly Criterion tells you the fraction of your bankroll to stake on a bet so that, over the long run, your bankroll grows as fast as possible without going broke.

It rewards edge and punishes uncertainty. If you have no edge, Kelly stakes zero. If your edge is huge, Kelly stakes aggressively. Most professional bettors stake a fraction of full Kelly — commonly half-Kelly or quarter-Kelly — because real-world probability estimates are imperfect and full Kelly is brutally volatile.

Formula
f* = (bp - q) / b

where:
  f* = fraction of bankroll to stake
  b  = decimal odds - 1  (the net amount won per 1 unit staked)
  p  = your estimated probability the bet wins
  q  = 1 - p  (probability the bet loses)

Equivalent form using decimal odds (d):
  f* = (p · d - 1) / (d - 1)

Fractional Kelly:
  stake = bankroll · f* · k
  where k is your Kelly fraction (e.g. 0.5 for half-Kelly).
Worked example
Bankroll: $1,000. Decimal odds: 2.10. Your model probability: 52%.

  b = 2.10 - 1 = 1.10
  p = 0.52
  q = 0.48
  f* = (1.10 · 0.52 - 0.48) / 1.10
     = (0.572 - 0.48) / 1.10
     = 0.0836  → 8.36% of bankroll on full Kelly

Full-Kelly stake: $83.60
Half-Kelly stake: $41.80  (recommended in practice)