The Kelly criterion for prediction markets

The Kelly criterion is the math behind every serious trader's sizing rule. It tells you what fraction of your bankroll to risk on a trade given your edge and the odds you're getting. Used correctly, it maximizes long-run growth. Used naively, it blows up accounts.

The formula

Kelly fraction = (p × b − q) / b

Where:

• p = your estimated probability that the trade wins
• q = 1 − p, your estimated probability that the trade loses
• b = the net odds you receive on a win (winnings ÷ stake)

The output is the fraction of your bankroll you should put on this trade.

Worked example: Polymarket YES contract

A YES contract is trading at $0.40. You estimate the true probability at 55%. If YES resolves, you make $0.60 per contract; if NO, you lose $0.40.

• p = 0.55
• q = 0.45
• b = 0.60 / 0.40 = 1.5
• Kelly fraction = (0.55 × 1.5 − 0.45) / 1.5 = (0.825 − 0.45) / 1.5 = 0.25

Full Kelly says risk 25% of your bankroll on this trade. That's enormous — and it's why nobody uses full Kelly in practice.

Why most pros use fractional Kelly

Full Kelly is mathematically optimal if your probability estimate is exact. It's not. You're guessing — informed, careful, calibrated — but still guessing. Full Kelly assumes perfect knowledge; any error in your estimate amplifies into devastating drawdowns.

Common practice:

• Half-Kelly: use 50% of the formula's output. Captures most of the long-run growth with much less variance.
• Quarter-Kelly: use 25%. The standard for traders who suspect their probability estimates are off by 5+ percentage points.
• Fixed fraction: always risk the same percentage of bankroll (e.g. 1% or 2%) regardless of edge. Simpler, leaves money on the table, but extremely robust.

The example above at half-Kelly: 12.5% of bankroll. At quarter-Kelly: 6.25%. These are real, livable sizes.

What happens if you use full Kelly with bad estimates

Suppose your true edge is half what you think it is. Full Kelly on the inflated estimate over-bets by roughly 2×. The optimal-growth curve falls off a cliff: instead of fast compounding, you get long drawdowns that take years to recover. A trader who runs 1% over Kelly grows; a trader who runs 2× over Kelly grinds toward ruin.

Sizing when probabilities are uncertain

One useful upgrade: instead of a point estimate for p, write down a range. "I think it's between 52% and 58%." Then run Kelly with the conservative end of the range. Half-Kelly on the conservative estimate is functionally equivalent to a confidence-adjusted sizing rule.

When not to use Kelly

• Tiny edges: if your edge is <1 percentage point, your probability estimate is almost certainly imprecise enough to drown the edge. Skip the trade.
• Correlated exposures: Kelly assumes independence. If you're already long YES on three related markets, treat them as one position and size accordingly.
• Illiquid markets: slippage erodes edge. If your size needs to be small enough to fit the order book, take the smaller size — don't pretend the edge is bigger to justify forcing a fill.
• Emotional trades: if you're sizing up because you're chasing a loss, the right Kelly fraction is zero.

Frequently asked questions

What if my Kelly fraction comes out negative?

It means you don't have edge — your estimated probability is below the market's implied probability. Either skip the trade or take the other side (sell YES, or buy NO).

How do I convert Kelly fraction into number of contracts on Polymarket or Kalshi?

Kelly fraction × bankroll = dollar size of the trade. Dollar size ÷ contract price = number of contracts.

Is the Kelly criterion the same for sports trading?

Yes. The formula is identical. The only difference is that in sports trading you typically convert American or decimal odds to b before applying Kelly. For decimal odds, b = decimal − 1.

What's a reasonable starting fraction for new traders?

Half-Kelly capped at 5% of bankroll per trade. The cap matters more than the formula in the first 100 trades — it forces you to survive the inevitable run of bad luck while you calibrate your estimates.

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