Kelly: The Mathematically Correct Bet Size
Updated
The Kelly criterion answers one question exactly: given an edge, what bet size maximises long-run growth? For blackjack the answer is your edge divided by the variance — and almost everyone who uses it in practice bets half that much.
- Kelly bet = edge ÷ variance. Our variance is 1.2819.
- At a 1% edge that is 0.78% of your bankroll per hand.
- Full Kelly means enormous swings. Half Kelly is the practical standard.
- Betting more than Kelly reduces growth and raises ruin. There is no upside.
The formula and what it gives
For a bet with edge e and variance v, the growth-maximising fraction of bankroll is e ÷ v. Blackjack’s variance is 1.2819, which we computed rather than looked up.
| Your edge | Full Kelly bet | Bankroll needed for a $25 unit |
|---|---|---|
| 0.5% | 0.39% of bankroll | $6409 |
| 1.0% | 0.78% of bankroll | $3205 |
| 1.5% | 1.17% of bankroll | $2136 |
| 2.0% | 1.56% of bankroll | $1602 |
Read the last column carefully. To bet $25 a hand at full Kelly with a 1% edge, you need $3205 behind it. That is the reality check most Kelly explanations skip.
Why almost nobody bets full Kelly
Full Kelly maximises growth and produces swings most people cannot tolerate. Drawdowns of half your bankroll are routine rather than exceptional.
Half Kelly gives about three quarters of the growth with roughly a quarter of the variance. That trade is so favorable that betting half is the practical standard among people who do this seriously.
The asymmetry is worth understanding: betting less than Kelly costs you growth slowly. Betting more costs you growth and increases ruin — past twice Kelly, expected growth turns negative even with a genuine edge.
How it is actually used at a table
Nobody recalculates a fraction of bankroll each hand. In practice you set a unit from your total bankroll, then use a bet spread tied to the true count, which approximates Kelly closely enough.
And if you have no edge, Kelly returns zero. There is no bet size that makes a negative-expectation game grow — which is the mathematically formal version of the point on why betting systems fail.
Keep reading
By Martin Kosek · every number on this site is computed by us, not copied.
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