Polymarket Kelly criterion bet sizing — the math for variance-adjusted stakes

Knowing a Polymarket bet has positive expected value is necessary but not sufficient. You also need to know how much of your bankroll to put on it. Too small and you compound too slowly. Too large and a string of unlucky losses ruins you even with positive EV. The Kelly criterion gives the answer — and the version most retail traders learn from poker is dangerously over-sized for prediction markets. Here's the right adaptation.

What Kelly actually computes

The classic Kelly criterion answers one question: given a positive-EV bet with probability P of winning and net odds B (you win B dollars per $1 staked on a win, lose $1 on a loss), what fraction of your bankroll should you stake?

f* = (P × B − (1 − P)) / B

Where f* is the optimal fraction. Wagering more than f* is over-Kelly and reduces your long-term geometric growth. Wagering less than f* is under-Kelly and grows your bankroll more slowly than optimal.

Kelly maximises long-term geometric growth of capital. It does NOT minimise variance, drawdown, or risk of ruin. Those are separate considerations that require fractional Kelly adjustments.

Why full Kelly is dangerous

Two reasons:

First, full Kelly assumes you know P exactly. In practice, your AI's probability estimate has error. If you wager full Kelly based on P = 0.40 when the true probability is 0.30, you are catastrophically over-sized. The penalty for over-sizing is non-linear: even small errors in P estimation produce large reductions in expected growth.

Second, full Kelly produces drawdowns that most traders cannot psychologically endure. Even with positive long-term EV, the median Kelly bettor sees their bankroll drawn down by 50% at some point during a 100-bet sequence. Most retail traders quit at 30-40% drawdowns, which means they exit the strategy during the inevitable bad run and lock in the loss instead of recovering.

Practical recommendation: never bet more than half-Kelly. Most professional bettors use quarter-Kelly or even tenth-Kelly to control drawdown variance.

Worked example: full Kelly on a Polymarket bet

AI scores a Polymarket question at 0.38 probability YES. Market YES price is 0.12. You're considering BUY YES.

Your variables:

• P = 0.38 (your AI's probability estimate)
• You buy YES at $0.12. If YES wins, you get $1, profit $0.88. If NO wins, you lose $0.12.
• Net odds B per $1 staked: you stake $0.12 to win $0.88, so B = $0.88 / $0.12 = 7.33

Full Kelly fraction:

f* = (0.38 × 7.33 − 0.62) / 7.33 = (2.79 − 0.62) / 7.33 = 0.296

Full Kelly says to stake 29.6% of your bankroll on this bet. That is a lot. Even quarter-Kelly (which is what most professional bettors use) would be 7.4% of bankroll — still a large bet by retail standards.

The reason: when EV is high (and edge is 26pp here), Kelly wants you to size up aggressively because the compounded long-term growth from getting these bets right is enormous. The price you pay is variance: you might lose this particular bet, and you'll feel that loss hard.

Why this is the wrong sizing for almost everyone

Even quarter-Kelly at 7.4% of bankroll per bet is too aggressive for most retail traders. Three reasons:

Reason 1: Your AI probability estimate is not perfectly calibrated

Your AI might be slightly miscalibrated — actual long-run probability when AI says 38% might be 35% or 40%, not exactly 38%. Kelly is extremely sensitive to this error. If actual P is 0.30 instead of 0.38, you should not have bet at all (negative EV), but Kelly told you to stake 29.6% based on the wrong P.

The standard correction: estimate the variance of your AI probability estimate. Apply Kelly only on the lower-bound probability (e.g., 95% confidence lower bound). This dramatically shrinks position sizes but protects against P-estimation error.

Reason 2: Repeated bets compound the variance

If you have 50 bets per month at quarter-Kelly, the variance compounds. Even with positive long-term EV, you can experience 60%+ peak-to-trough drawdowns. Most retail traders cannot psychologically tolerate this.

Reason 3: Single-bet sizing should leave room for portfolio

You usually want to be running multiple bets simultaneously. Kelly's optimal sizing assumes this is the only bet you have. If you have 10 concurrent bets, the per-bet Kelly fraction needs to be divided down to keep total exposure manageable.

The practical framework: tenth-Kelly with caps

For most retail prediction market traders, the right framework is:

• Compute full Kelly using your AI's probability estimate.
• Apply tenth-Kelly (1/10 of the computed fraction). This dramatically reduces drawdown variance while preserving most of the long-run growth.
• Apply a hard cap of 2% of bankroll per single bet, regardless of what Kelly says. No matter how good the EV looks, never bet more than 2% on any single market.
• Apply a portfolio cap of 10% of bankroll total open exposure. If you have 5 concurrent bets at 2% each, you're full. Skip the next signal until one resolves.

This framework produces meaningfully positive long-term returns from positive-EV bets while keeping individual drawdowns survivable. Most retail traders who fail at prediction markets fail at sizing, not at picking. The Kelly framework above is what separates the two.

Applied to the worked example

Back to the AI=0.38, market=0.12 bet:

• Full Kelly: 29.6%
• Tenth-Kelly: 2.96%
• Capped at 2%: bet 2% of bankroll

On a $10,000 bankroll, you'd stake $200 on this bet. Win: profit +$1,467 (which is +14.7% on bankroll — material but not life-changing). Loss: −$200 (−2% on bankroll — survivable, especially with portfolio caps spreading risk).

Compared to full Kelly's 29.6% ($2,960 stake), this is 15× smaller. You give up some upside growth in exchange for keeping the strategy runnable through drawdowns.

What our service does

PREDICT publishes signals with edge magnitude, AI probability, and market price. We do not place bets on subscribers' behalf — the sizing decision is yours to make based on your own risk tolerance and bankroll.

What we do provide: enough metadata that the Kelly computation above takes 30 seconds to verify per signal. If you want to do half-Kelly or tenth-Kelly or flat $1 stakes, the math is right there in the signal. You stake what you want, where you want, when you want.

For traders who want bet-sizing automation, our roadmap includes a "smart stake" mode that computes recommended Kelly fraction inside the signal itself based on your bankroll input. That feature lands later in 2026; for now, the math above is the right approach.