The Kelly formula for a $1 contract
A standard Kalshi contract pays $1 if the market settles your way and $0 if it does not. Buy one at price c (in dollars). It gains 1 - c when it wins and loses c when it loses. If p is your probability of a win, full Kelly says to spend this share of your bankroll on the trade:
The numerator is your edge per contract. The denominator is what the contract can still gain. Suppose you put a contract at 62% and it trades at 55c. Full Kelly is (0.62 - 0.55) / 0.45, which is 15.6% of bankroll. On a $2,000 bankroll that is $311, or 565 contracts at 55c, before fees. If your probability is at or below the price, the formula gives zero or a negative number. That means no trade.
Kelly turns an edge into a position size, so the inputs matter. The expected value guide shows how to work out the edge on a contract. The odds converter turns a price into an implied probability.
The idea comes from J. L. Kelly Jr., a Bell Labs researcher who published it in the Bell System Technical Journal in 1956. Kelly sizing picks the bet that maximizes the expected logarithm of your bankroll. Over many bets, that is the size with the fastest long-run growth. The Kelly and EV calculator runs the numbers for any price, side and fee type.
Where the formula comes from
The textbook version is for a bet that pays b for every 1 you stake. It says to bet f = (bp - q) / b of bankroll, where q = 1 - p is the chance of losing. Edward Thorp gives it in this form in his 2006 survey of the Kelly criterion.
A $1 contract bought at c pays 1 - c of profit for every c you put in. So b = (1 - c) / c. Put that into the textbook formula and it becomes p - (1 - p) × c / (1 - c). Over one denominator, the pc terms cancel and you are left with the short form:
Here f is the share of bankroll you spend on contracts. A losing contract settles at $0, so f is also what you lose if the market goes against you.
Worked numbers, before and after the fee
Kalshi's fee schedule, effective July 7, 2026, sets the general taker fee with this formula:
C is the number of contracts, P is the price in dollars and M is the series multiplier. M is 1 on most series, and every example here uses M = 1. Per contract the fee is then 0.07 × P × (1 - P) before rounding. Add it to the price to get the all-in cost. That is the c that belongs in the formula. Kalshi charges no settlement fee, so a contract held to the end costs only its entry fee.
The four rows below use hypothetical estimates.
| Your estimate | Price | Edge | Full Kelly | All-in cost | Full Kelly after fee |
|---|---|---|---|---|---|
| 62% | 55c | 7c | 15.6% | 56.73c | 12.2% |
| 80% | 75c | 5c | 20.0% | 76.31c | 15.6% |
| 92% | 90c | 2c | 20.0% | 90.63c | 14.6% |
| 30% | 25c | 5c | 6.7% | 26.31c | 5.0% |
On the first row the fee is about 1.73c a contract, and it cuts full Kelly from 15.6% to 12.2%. On the third row the fee is only 0.63c. But that is almost a third of a 2c edge, so full Kelly drops from 20.0% to 14.6%. The fee rounds up, so a one-contract order pays a little more per contract than the table shows. The Kalshi fees guide covers rounding in detail. The fee calculator gives the exact fee for any order.
A resting order that fills as a maker pays no fee on most series. Kalshi lists the series that do charge makers. The standard maker fee is 0.0175 × C × P × (1 - P), a quarter of the taker rate. A few combo series charge makers half the taker rate. On a maker fill without a fee, the raw price is the right c.
Why a 2c edge at 90c sizes like a 5c edge at 75c
Look at the second and third rows before fees. Both come out at 20%. The formula divides the edge by what the contract can still gain. At 90c the contract can gain 10c, and 2 / 10 is 0.2. At 75c it can gain 25c, and 5 / 25 is also 0.2.
The 90c contract loses rarely, so Kelly will commit a lot of bankroll to it. When it does lose, you lose 90c on every contract. That makes the size very sensitive to your estimate. If the true chance is 90% instead of 92%, the edge and the Kelly size are both zero. The same 2-point miss at 75c still leaves a 3c edge and a 12% Kelly fraction.
Kelly on the NO side
The formula works on whichever side you buy. Use the NO price and your probability that the market settles NO. Kalshi treats buying NO and selling YES as the same trade.
Kalshi's API returns the order book as bids only. Its documentation explains that a YES bid at X is the same as a NO ask at $1 minus X. So the NO ask you pay is $1 minus the best YES bid.
Suppose the best YES bid is 40c, which puts the NO ask at 60c. You estimate YES at 33%, so NO is 67%. Full Kelly on NO is (0.67 - 0.60) / 0.40, or 17.5% of bankroll. The taker fee at 60c is 1.68c. That makes the all-in cost 61.68c, and full Kelly after the fee 13.9%.
Two slips are common here. One is plugging your YES probability into the NO price. The other is taking 1 minus the YES ask as the NO price. That number is the best NO bid, which is where you could sell NO.
Half Kelly and quarter Kelly in numbers
Fractional Kelly means betting a fixed share of the full Kelly amount. Half Kelly on the 62% at 55c example is 7.8% of bankroll before fees. Quarter Kelly is 3.9%.
Thorp works out the trade-off with a continuous approximation. Betting k times the Kelly amount earns k × (2 - k) of the full Kelly growth rate. The chance that the bankroll ever falls to a fraction x of where it started is x raised to the power (2 / k - 1). The table applies both formulas with x = 0.5: a halving of the bankroll.
| Bet size | Growth kept (approximation) | Growth kept (62% at 55c, exact) | Chance of ever halving |
|---|---|---|---|
| Quarter Kelly | 43.8% | 43.4% | 0.8% |
| Half Kelly | 75.0% | 74.6% | 12.5% |
| Full Kelly | 100% | 100% | 50.0% |
| 2x Kelly | 0% | -10.1% | 100% |
Half Kelly keeps about three quarters of the growth. It cuts the chance of ever losing half the bankroll from one in two to one in eight. Quarter Kelly keeps a bit under half the growth, and a halving becomes a rare event. Thorp writes that most people strongly prefer half Kelly or something near it, for the added safety. He bases this on his own experience and on reports from blackjack players and teams. A simulation of the 62% at 55c bet over 3,000 trades comes in slightly under the table's halving odds: about 47% for full Kelly and 11% for half Kelly.
Betting above Kelly earns no extra growth and adds a lot of risk. In the approximation, 1.5x Kelly keeps the same 75% of growth as half Kelly, with a 79% chance of halving instead of 12.5%. Growth hits zero at 2x Kelly and turns negative past it. For a single binary contract the exact crossing moves with the price. Across the four rows in the first table, it falls between 1.87x and 2.07x Kelly.
When your probability is wrong
Kelly treats p as a known number. In practice p is an estimate, and any error in it flows straight into the size.
Suppose you estimate 62% on the 55c contract, but the true chance is 58.5%. Your full Kelly is 15.6%. Full Kelly on the true number is 7.8%. You are betting exactly twice the right amount, and the expected growth rate sits just below zero. A 3.5-point miss is easy to make. At full Kelly it erases all of the growth the edge had to offer.
Now size at quarter Kelly on your 62% estimate: 3.9%. That equals half Kelly on the true 58.5%, which keeps about 75% of the best growth available. Half Kelly on your estimate lands exactly on the true full Kelly. Either fraction still grows the bankroll after a 3.5-point miss, where full Kelly grows nothing.
Fees, fills and the order book
- Cost is price plus fee. On Kalshi's general schedule, 100 contracts taken at 50c pay $1.75 in fees, so the all-in cost is 51.75c a contract.
- Depth caps the size. Kelly gives a dollar amount. The order book shows how many contracts wait at your price. If Kelly says 400 contracts and 120 rest at 55c, the trade at 55c is 120 contracts.
- Each price level is a new calculation. The next contracts fill at a higher price, such as 56c. The edge is smaller there, so the Kelly fraction is smaller too.
- Kelly applies to the whole position. If you already hold contracts in the market, the next order is the gap between the Kelly target and what you hold.
The order book guide shows how to read depth from Kalshi's bids-only book. The limit orders guide covers resting an order at your price instead of crossing the spread.
Correlated strikes and several bets at once
The single-bet formula assumes one bet at a time. Many Kalshi events list several markets on the same number, such as a ladder of strikes on an economic release. Those markets move together. Sizing each one alone can add up to a far bigger bet than either size suggests.
Take two hypothetical strikes on one monthly figure. "Above 2.0" trades at 60c and you put it at 70%. "Above 2.5" trades at 30c and you put it at 40%. Single-bet Kelly says 25.0% on the first and 14.3% on the second. That is 39.3% in total. Both lose together whenever the figure comes in at 2.0 or below, which you put at 30%.
Sizing them together means maximizing expected log growth across the three outcomes at once. Before fees, the answer is 15% on the first strike and 10% on the second. That is 25% in total.
| Outcome | Your probability | Bankroll change, each sized alone | Bankroll change, sized together |
|---|---|---|---|
| At or below 2.0 | 30% | -39.3% | -25.0% |
| Above 2.0, at or below 2.5 | 30% | +2.4% | 0.0% |
| Above 2.5 | 40% | +50.0% | +33.3% |
The joint sizing loses less in the worst case and has an expected growth rate about 47% higher. The stacked sizes were over-betting the shared outcome.
Mutually exclusive markets work the same way. Kalshi's API marks an event as mutually exclusive when at most one of its markets can resolve YES, as with candidates in one election. If you buy YES on two candidates, at most one pays. Joint Kelly sizes all of the candidates together as one position.
Unrelated bets still share one bankroll. Five independent bets like the 62% at 55c example come out at about 14.2% each when sized together, against 15.6% alone. The total is about 71% of bankroll in play at once.
Capital that waits for settlement
Kelly measures growth per bet. It assumes the next bet comes soon after the last one settles. A contract that settles in nine months holds its stake for nine months.
Take two trades with the same hypothetical edge: 80% on a 75c contract, before fees. At full Kelly, each grows the bankroll by about 0.70% per trade in the log terms Kelly uses. One settles in 3 days and the other in 270. Per day of capital, the first grows about 0.23% and the second about 0.003%. The short trade compounds about 90 times faster, as long as another trade like it follows.
You can end the lock early by selling before settlement. The exit costs the spread and, if you cross it, another taker fee. The guide to selling a Kalshi contract early walks through that math. Kalshi also pays a variable interest rate to eligible users in the US and its territories. It applies to cash and to open positions, valued at the last traded price. The rate was 3.50% on Oct 19, 2026, with a $250 average monthly balance minimum. Because it accrues on cash and positions alike, it does little to change the Kelly size.
Questions traders ask
What is the Kelly criterion in one sentence?
It is the bet size that maximizes the long-run growth rate of a bankroll. For a Kalshi contract that pays $1, the size is (p - c) / (1 - c) of bankroll, where p is your probability and c is the all-in price. If p is at or below c, the size is zero.
Is full Kelly too aggressive for prediction markets?
Full Kelly is volatile even when your probability is right. In Thorp's approximation it carries a 50% chance that the bankroll halves at some point. Half Kelly cuts that to 12.5% and keeps about 75% of the growth. If your estimate runs high, full Kelly on it over-bets the true edge.
What is half Kelly?
Half Kelly is a bet of half the full Kelly fraction. With a 62% estimate on a 55c contract, full Kelly is 15.6% of bankroll before fees, so half Kelly is 7.8%. It keeps about three quarters of the growth rate and leaves a margin if your probability is too high.
Does Kelly include Kalshi's fees?
Only if you put them in. Add the per-contract fee to the price and use the total as c. On Kalshi's general schedule the taker fee is 0.07 × P × (1 - P) per contract, rounded up. On the 62% at 55c example, that turns 15.6% into 12.2%.
What if the order book holds fewer contracts than Kelly says?
Then depth sets the size at that price. The contracts resting at your price are the trade. The next price level is a separate trade with a smaller edge and a smaller Kelly fraction. A resting limit order at your price can fill more later, with no guarantee that it fills at all.
Sources
- Kalshi, Fee Schedule, last updated and effective July 7, 2026 (accessed Oct 19, 2026)
- Kalshi API documentation, Fee Rounding (accessed Oct 19, 2026)
- Kalshi API documentation, Orderbook Responses (accessed Oct 19, 2026)
- Kalshi API documentation, Get Event (mutually_exclusive field) (accessed Oct 19, 2026)
- Kalshi Help Center, Portfolio: Balances and Positions (accessed Oct 19, 2026)
- Kalshi Help Center, Buying Yes vs Selling No (accessed Oct 19, 2026)
- Kalshi Help Center, Limit Order Sale (accessed Oct 19, 2026)
- Kalshi Help Center, APY on Kalshi (accessed Oct 19, 2026)
- J. L. Kelly Jr., "A New Interpretation of Information Rate," Bell System Technical Journal 35(4), pp. 917-926, 1956 (accessed Oct 19, 2026)
- E. O. Thorp, "The Kelly Criterion in Blackjack Sports Betting, and the Stock Market," Chapter 9 in Handbook of Asset and Liability Management, Vol. 1, pp. 385-428, Elsevier, 2006 (accessed Oct 19, 2026)