You found positive expected value on a mispriced YES. The next question is not whether to trade but how much: one oversized bet can wipe a bankroll even when your model is right on average. The Kelly criterion sizes for long-run growth when you reinvest and face repeated opportunities—while prediction markets remind you that p is uncertain, events correlate, and platforms charge friction.
What Kelly optimizes
Kelly maximizes the long-run growth rate of wealth. Classic derivations maximize expected log wealth. For a binary YES bought at price c (0–1) with subjective probability p, a frictionless Kelly fraction of bankroll on the YES leg is f = (p − c) / (1 − c)* when p > c. If p ≤ c, Kelly says do not bet—same as zero EV.
Intuition: edge (p − c) relative to what you win on success (1 − c). Module 01’s price is the crowd’s c; Kelly needs your p unless you have no edge.
For even-money style binaries where you risk $1 to win $1, a simplified form is f = 2p − 1* when p > 0.5—only positive when you have more than half chance on a fair-paying contract.
Worked sizing in prose
YES at 40¢, you believe 55%: f* = (0.55 − 0.40) / (1 − 0.40) = 0.25—a quarter of bankroll on one binary is aggressive in practice. Half-Kelly → 12.5% → about $1,250 notional on a $10,000 bankroll before fees. Election headlines can move c from 40¢ to 52¢ while you scale; Kelly assumes many independent trials; politics clusters.
Market YES 68¢, you believe 58%: buying NO risks 32¢ to win 68¢ if NO resolves. Edge on NO is c − p = 0.10; symmetric sketch f* ≈ 0.10 / 0.68 ≈ 14.7% on the NO leg. Plug effective c from simulated fills, not banner mid.
Tiny edge: c = 62¢, p = 64%, f* ≈ 0.02 / 0.38 ≈ 5.3%; half-Kelly ≈ 2.6% → about $260 risk on $10,000—right scale for a two-point disagreement, not a career plunge.
Kelly versus gut sizing
Flat dollar tickets ignore edge and bankroll. All-in “conviction” invites ruin. Full Kelly is theoretically optimal for log growth but produces violent drawdowns; fractional Kelly (¼–½) is standard because p is misspecified and markets correlate. Over-Kelly drives negative growth.
Even with correct p, full Kelly can drop 20–40% before psychology breaks. The better response to drawdown is halve Kelly and review calibration—not revenge size. Regulated caps and liquidity caps mean practical f* = minimum of Kelly, legal max, and what the book can absorb.
Subtract fees from (p − c) before sizing. Spread on CLOBs and AMM curvature act like hidden fees. Rough break-even: if round-trip costs 2¢ on a 50¢ contract, you need more than ~4¢ of edge before Kelly matters.
Drawdowns and psychology
Over 200 trials, law of large numbers becomes visible; over 10, variance still feels like luck. After −20% bankroll, doubling size to “recover” is anti-Kelly. After +50%, feeling invincible and raising fraction without recalibrating p is the same mistake on the upside.
Portfolios and modules
When politics contracts move together, treat them as one draw and cap cluster exposure (e.g. 5% bankroll) even if per-contract Kelly sums higher. Locked arb has low variance—Kelly for risky binaries overstates safe arb size; capital and fees still bind.
Module 02: wide spreads and slippage shrink effective payoff. Module 03: a pump to 75% on thin liquidity is not your p; trade your model, not the manipulated print. Chapters on EV and variance: positive EV with tiny edge → tiny Kelly; high variance argues for fractions.
Forecasting tournaments reward Brier; live P&L scales with log wealth. Researchers estimate p, traders map p and c to fractional Kelly, risk officers enforce cluster caps. On play-money platforms, oversized bets teach variance without ruin; on regulated venues with deposit limits, Kelly is a guide, not a mandate.
Common mistakes
Using market price as p—Kelly becomes trend-chase. Ignoring path risk on 55% edge at 25% Kelly. Double-counting structural arb as independent binary bets. Stacking correlated events as implicit over-Kelly.
Kelly and log utility
Kelly’s link to log wealth is why it pairs with the logarithmic scoring chapter. Over-betting shrinks log wealth even when arithmetic EV is positive; fractional Kelly is the pragmatic admission that p is an estimate, not a truth. If your confidence interval on p is wide, treat full Kelly as an upper bound, not a target.
Role split on a desk
Researchers publish f and defend likelihoods; traders map f and c to fractional Kelly; risk caps cluster exposure. That split exists because the same person often overstates p after clicking. Process beats hero trades.
When Kelly says zero
p ≤ c after fees ⇒ f = 0*. That includes “I agree with the market” and “I disagree but not enough to overcome spread.” Sitting out is a sizing decision, not a failure. The hardest discipline is passing +2¢ EV when variance and correlation make the bet a portfolio duplicate.
Simulation intuition
Imagine 100 independent 55% bets at half Kelly on a frictionless 50¢ contract—variance is still painful over a season. Now imagine ten contracts that all lose on one bad election night because ρ > 0. Kelly on each leg overstated safety. Fractional Kelly plus cluster caps is how practitioners approximate a portfolio Kelly without building a covariance matrix every morning.
Deposits and position limits
Regulated venues cap notional regardless of formula output. Your displayed Kelly might be 18% while compliance allows 5%—the binding constraint wins. Treat Kelly as an upper bound scaled by law, liquidity, and sleep.
NO leg Kelly in words
For NO bought at price c_NO with belief q = 1 − p on NO, frictionless Kelly resembles (q − c_NO) / (1 − c_NO) when q > c_NO. Symmetric logic to YES—pick the side with better edge per dollar locked. Many tickets are clearer on NO when YES is rich above 70¢.
Growth versus utility
Kelly optimizes long-run growth, not your happiness. A forecaster maximizing Brier might trade smaller than Kelly on the same edge because calibration error dominates. Use Kelly as a ceiling, Brier as the audit, and variance as the gut check—three different optimizers, one bankroll.
Edge uncertainty
If true p might be 53–57% and c = 54¢, Kelly on 55% is fragile. Many desks use min(p) in the Kelly numerator for sizing, or quarter-Kelly by default, to respect model error. The formula is not wrong; the input is.
Manipulation and Kelly
A spiked mid to 80% on thin liquidity implies huge Kelly if you naively use price as p. Correct response: estimate p from fundamentals, get Kelly near zero, and let arbitrage chapters handle the gap—or fade with limits if rules allow.
Closing habit
Before submit: compute f*, halve it, compare to cluster cap, compare to venue max, then click or pass. Kelly is one line of arithmetic; discipline is the rest.
What comes next
Next: Brier score—measuring whether your p was any good after the event resolves.