How to use the Kelly criterion for prediction markets

The Kelly criterion is a formula John L. Kelly Jr. developed at Bell Labs in 1956. It gives the fraction of your bankroll to stake on a bet with positive expected value so that the bankroll compounds fastest over many bets.

Bet too little and the bankroll grows slower than it could. Bet too much and a losing streak wipes you out. The chart above shows both: growth peaks at the Kelly fraction and turns negative at about twice it.

Kelly assumes you know the true probability better than the market does. If the price already reflects the true probability, Kelly says bet nothing. Plenty of traders run the calculation and find their edge does not justify the size they had in mind.

For a binary market the formula is f = (p - c) / (1 - c). f is the fraction of your bankroll to bet, p is your estimate of the true probability, and c is the cost of the share. It is your edge divided by the potential payout. If p equals c, it returns zero.

Example: you put an event at 70% and Yes costs 55¢. Your edge is 0.15. The Kelly fraction is (0.70 - 0.55) / (1 - 0.55) = 0.15 / 0.45 = 0.333, so Kelly says bet 33.3% of your bankroll. On a $10,000 account that is $3,333 of shares.

No shares work the same way. If you put the event at only 30% and Yes is 55¢, you buy No at 45¢. Your probability for No is 70%, so the fraction is (0.70 - 0.45) / (1 - 0.45) = 0.25 / 0.55 = 0.455.

A binary market suits Kelly because the payoff is simple: $1 a share or $0. With an honest probability estimate you can calculate the bet for any market in seconds. The chart above shows the fraction at each price for a fixed edge.

Write down your probability before you look at the market price. That prevents anchoring, where the price drags your estimate toward it. Then compare. If your estimate is at least 5 to 10 percentage points from the price, calculate the fraction. If the gap is small, the Kelly bet comes out tiny, which is the formula saying the edge may not be worth the risk.

Kelly also assumes your estimate is correct, and it never is exactly. If you say 70%, your confidence in that 70% is itself uncertain. That is the main reason most practitioners use a fraction of Kelly.

Full Kelly is optimal only if your estimates are perfectly calibrated, and it swings hard. A trader on full Kelly might bet 30% or more of the bankroll on one market, and a wrong probability can take months to recover from.

Half-Kelly halves the bet and keeps roughly 75% of the growth rate with much less volatility and drawdown. Quarter-Kelly keeps about 50% of the growth rate with a smooth equity curve and minimal risk of ruin. The right fraction depends on your risk tolerance, the accuracy of your estimates, and how many positions you hold at once.

Half-Kelly is the sensible default. If your estimate is off by a few points, the damage stays manageable, where full Kelly turns the same error into an overbet. If you are new to Kelly sizing, start at quarter-Kelly and move up as you validate your calibration.

Your edge is your estimated probability minus the market price. Estimate 65% against a market at 55% and your perceived edge is 10 points. If you are unsure of the 65%, your effective edge is smaller and the bet should shrink to match.

Keep a prediction journal. Before each trade, write down your estimate, the market price, your reasoning and the Kelly bet. After 50 to 100 resolved markets you can measure your calibration: if events you rated at 70% happened 70% of the time, you are well calibrated. If they happened 55% of the time, you are systematically overconfident and should use a smaller Kelly fraction.

Benchmark against the track records on 0xinsider.com/leaderboard. If the highest-rated traders are positioned against your trade, re-examine your estimate. You do not have to follow them, but you need a specific reason for disagreeing with traders who have shown consistent skill.

Overestimating your edge is the most dangerous. If you think the edge is 15 points and it is 5, full Kelly on the perceived edge is a massive overbet against the real one. Use fractional Kelly and track your calibration. With fewer than 30 resolved markets you do not have enough data to know how good your estimates are.

Sizing each position alone is the second. 10 open positions at half-Kelly each can add up to an extremely high total allocation. Kelly assumes independent bets, and prediction markets are often correlated: political markets move together, crypto markets move together, and macro events hit several markets at once. Cut individual sizes when total portfolio risk crosses your target.

Betting when Kelly says not to is the third. If the market is more accurate than your estimate, the formula returns a negative number, which means do not bet. Traders who bet anyway because the opportunity feels too good lose steadily.

Example 1: a market on a central bank rate rise prices Yes at 40¢ and you estimate 55%. Kelly fraction: (0.55 - 0.40) / (1 - 0.40) = 0.15 / 0.60 = 0.25. Half-Kelly is 12.5%. On a $20,000 account you buy $2,500 of Yes, about 6,250 shares at 40¢. If the rate rise happens you collect $6,250, a $3,750 profit.

Example 2: an election market prices a candidate at 72¢ and you estimate 80%. Kelly fraction: (0.80 - 0.72) / (1 - 0.72) = 0.08 / 0.28 = 0.286. Half-Kelly is 14.3%. On a $15,000 account that is $2,143 of Yes, about 2,976 shares at 72¢. The edge is 8 points against 15 in Example 1, and the fraction is similar, because the formula divides the edge by the payout and a 72¢ share pays 28¢.

Example 3: a crypto market prices Yes at 50¢ and you estimate 52%. Kelly fraction: (0.52 - 0.50) / (1 - 0.50) = 0.02 / 0.50 = 0.04. Full Kelly is 4% of your bankroll and half-Kelly is 2%. A 2-point edge is not worth a big bet: the expected value is slightly positive and the variance is enormous against it. Skip this one and keep the capital for a wider edge.