What Kelly is — and what it isn't
Kelly maximizes the expected logarithm of your bankroll. Over many bets, no other constant bet-sizing rule grows wealth faster. But Kelly is also extremely volatile: full-Kelly play has a 50% chance of halving your bankroll at some point. Most disciplined practitioners use half-Kelly or quarter-Kelly to keep drawdowns survivable.
The formula
For a game with edge e (as a decimal) and per-unit standard deviation σ, the full-Kelly fraction of bankroll to bet per unit is:
f* = e / σ²
For blackjack at a 1% true count edge and σ = 1.14 per unit, f* ≈ 0.0077, or 0.77% of bankroll per unit. With a $10,000 bankroll, that's about $77 per unit. Half-Kelly cuts this to about $38.
When Kelly fails you
Three real-world traps:
- Edge mis-estimation: a 0.5% edge you thought was 1% means you are betting twice the right size. Kelly is brutal under overestimation.
- Bet caps: if the table maxes you out before you reach the Kelly bet, your true growth rate falls below the formula's prediction.
- Wonging penalties: if your edge depends on entering the count favorably and you can't always get a seat, your effective edge per hour is lower than your edge per round.
Practical advice
Most advantage players use a fixed unit size and a bet spread (e.g., 1-12 spread on a 6-deck shoe) rather than recomputing Kelly on every hand. That spread is itself derived from a Kelly calculation done once for an average true count. The calculator above gives you the per-bet anchor; the spread converts it to a workable in-shoe rule.