Kelly is the bet-sizing rule used by professional blackjack counters, sports bettors, and quantitative traders. It maximizes the long-run growth rate of a bankroll given a known edge and known variance. It is not what most beginning counters use, because most beginning counters haven't read about Kelly. By the second or third year, they've read about it twice and switched to it twice.
The formula
Kelly fraction = edge / variance.
For blackjack counting, edge per hand is your true count's expected return (typically 0.5-1.5%) and variance is the per-unit-bet variance, which is roughly σ² where σ ≈ 1.4-1.6 for typical spreads.
Example: 1% edge, σ=1.4 → Kelly fraction = 0.01 / 1.96 = 0.51% of bankroll per unit bet. With $20,000 bankroll, that's $102 per unit. At a 1-12 spread, your average bet is roughly 4-5 units, or $400-$500.
Why nobody bets full Kelly
Full Kelly maximizes the expected log of your bankroll. That's a great property mathematically. Practically, full-Kelly play has a 50% chance of halving your bankroll at some point along the way to that growth-maximizing path. The drawdowns are brutal.
Most working APs use half-Kelly:
- Half-Kelly captures ~75% of the long-run growth rate of full Kelly
- Variance drops to roughly 25% of full Kelly's variance
- RoR (risk of ruin) drops from 13.5% to ~1.8%
- Drawdowns become survivable
The math works out: you give up about a quarter of the growth rate but get a much smoother ride. For a real human with bills to pay, that trade is overwhelmingly correct.
Quarter-Kelly: the conservative default
Some pros go even further — quarter-Kelly. You give up another quarter of the growth rate but RoR drops to almost zero. New counters often start at quarter-Kelly while they verify their edge estimate is correct.
Reason: edge estimation errors are brutal under Kelly. If you think your edge is 1% but it's actually 0.5%, you've been over-betting by 2x relative to your true Kelly. Full Kelly under that overestimate is suddenly RoR ~30%. Half-Kelly with the same error is RoR ~5%. Quarter-Kelly with the same error is RoR ~1%. The conservative fraction protects you from your own optimism.
Spread vs flat-bet Kelly
Pure Kelly says: bet the Kelly fraction of bankroll on every hand, scaled by your edge. In blackjack counting, edge varies hand-to-hand by true count. A pure-Kelly counter would adjust bet size on every hand. In practice, that's:
- Mathematically optimal
- Operationally insane — you'd need to recompute Kelly bet on every hand
- Maximally suspicious — pit bosses notice precise count-based betting
Working solution: derive a bet spread (e.g., 1 unit at TC≤1, 2 units at TC=2, 4 at TC=3, etc.) by averaging Kelly across the count distribution. Bet the spread. You're not optimal Kelly on each hand, but you're optimal-on-average across the shoe.
What changes Kelly's math
Three variables you should track:
- Penetration — how far into the shoe before reshuffle. Better penetration = higher edge per shoe = more bet ramp warranted.
- Cover plays — give back some edge for stealth. Adjust your edge estimate downward.
- Heat — if you're getting watched, your effective edge drops because you can't extract full count-based bets.
Most counters track these three variables and adjust their Kelly fraction or their bet spread to match. There's no published formula for this — it's experience.
When to recompute Kelly
Recompute on bankroll change of ±20% or so. Bankroll up 20% = bet up 20% (same Kelly fraction). Bankroll down 20% = bet down 20%. This is dynamic bet sizing, and it's what makes Kelly self-correcting: you bet bigger when you can afford it, smaller when you can't.
The catch: if you're playing in a casino that recognizes your face, your bet size shouldn't visibly drop after a losing trip. Cover requires consistent betting patterns. Reality requires shrinking bets after losses. Pick your poison.
Bottom line
Use the /calc/kelly calculator to find your unit bet. Use half-Kelly unless you have a specific reason to deviate. Never use full Kelly without acknowledging the 50% drawdown probability that comes with it. Recompute every 20% bankroll move. Stay disciplined when the variance is brutal — and it will be brutal at some point.