Kelly Criterion For Prediction Markets: How Much To Put On A Contract
I spend more time talking traders out of oversized positions than I spend helping them find edges. Finding a mispriced contract is the fun part; deciding how much of your bankroll to put on it is the part that decides whether you are still trading in six months. The Kelly criterion is the cleanest answer to that question I know, and prediction markets are the friendliest home it has ever had, because a contract price already is a probability. There is no odds conversion and no payout table. If you can subtract two numbers and divide, you can run Kelly on a Kalshi contract in your head before the order screen loads. Here is the formula, the derivation, worked examples at real prices, and the reason I still cut the answer to a quarter before I size anything.
In Summary
- The Formula Is Two Numbers. For a contract at price p with your estimated win probability q, Kelly says stake f* = (q - p) / (1 - p) of your bankroll. A 50-cent contract you make 60% to win is (0.60 - 0.50) / 0.50, a 20% full-Kelly stake.
- Quarter Kelly Is The Real Recommendation. Full Kelly assumes your q is exactly right. Overestimate by a few points and full Kelly quietly becomes oversizing, which destroys growth instead of maximizing it.
- The Same Stake Requires Less Edge At Higher Prices. A 7-point edge at 30 cents, a 5-point edge at 50 cents, and a 3-point edge at 70 cents all produce the same 10% Kelly stake. That is exactly why expensive favorites are where overconfidence hurts most.
- Fees Change The Price You Plug In. The taker fee raises your effective cost per contract, so fold it into p before you size. At 50 cents it trims a 20% Kelly stake to about 17.1%.
- A Flat 2-5% Cap Is A Fine Alternative. If you do not trust your probability estimates enough to size off them, the community's flat-cap heuristic keeps you in the same safe neighborhood as fractional Kelly.
Why Contract Prices Make Kelly Easy
The Kelly criterion answers one question: what fraction of your bankroll maximizes long-run growth on a repeated favorable position? The classic formula is written for odds:
f* = (b x q - (1 - q)) / b
where q is your probability of winning and b is the net odds you are paid per dollar risked. At a sportsbook you have to convert an American price into b before you can use it. On an exchange the conversion is already done for you. A Yes contract at price p (in dollars) risks p to win (1 - p), so the net odds are simply:
b = (1 - p) / p
Substitute that into the classic formula and simplify:
f* = q - (1 - q) x p / (1 - p)
= (q x (1 - p) - p x (1 - q)) / (1 - p)
= (q - p) / (1 - p)
That is the whole thing. Your probability minus the price, divided by one minus the price. The numerator is your edge in probability points. The denominator scales the stake to how much the contract pays when it wins. Since the price in cents reads directly as an implied probability (our Kalshi odds guide covers the cents-to-American conversion if you want the bridge back to sportsbook prices), both inputs are sitting on the screen in the same units. One is the market's number. The other is yours.
One boundary case worth stating plainly: if q is less than or equal to p, the formula returns zero or a negative number, and the answer is no position. Kelly does not size bad trades smaller. It refuses them.
Worked Examples At 30, 50, And 70 Cents
Three positions, all run through f* = (q - p) / (1 - p), all on a $1,000 bankroll.
A longshot at 30 cents. You price the outcome at 37%. Kelly: (0.37 - 0.30) / (1 - 0.30) = 0.07 / 0.70 = 10%. Full Kelly stakes $100; quarter Kelly stakes $25. Notice you needed a 7-point edge to get there.
A coin flip at 50 cents. You price it at 60%. Kelly: (0.60 - 0.50) / 0.50 = 20%. Full Kelly stakes $200 of the $1,000, which should already feel uncomfortable. Quarter Kelly stakes $50.
A favorite at 70 cents. You price it at 76%. Kelly: (0.76 - 0.70) / 0.30 = 20%. The same 20% stake as the coin flip, from an edge of only 6 points instead of 10.
Here is the full grid, with every row computed from the formula:
| Price p | Your q | Edge | Full Kelly f* | Quarter Kelly | Quarter Stake On $1,000 |
|---|---|---|---|---|---|
| 30c | 37% | 7 pts | 10.0% | 2.5% | $25 |
| 30c | 44% | 14 pts | 20.0% | 5.0% | $50 |
| 50c | 55% | 5 pts | 10.0% | 2.5% | $25 |
| 50c | 60% | 10 pts | 20.0% | 5.0% | $50 |
| 70c | 73% | 3 pts | 10.0% | 2.5% | $25 |
| 70c | 76% | 6 pts | 20.0% | 5.0% | $50 |
Read down the Full Kelly column and the pattern jumps out: the divisor (1 - p) shrinks as the price rises, so the same stake requires less and less edge. At 30 cents you need 7 points of edge to justify a 10% position. At 70 cents you need 3. That is mathematically correct and practically dangerous, because a 3-point edge on an expensive favorite is precisely the kind of number that is most likely to be estimation error rather than real. The formula trusts your q completely. The next section is about why you should not.
Why Full Kelly Punishes An Overconfident Q
Kelly's growth curve is not symmetric, and this asymmetry is the single most important thing to understand before you use the formula with real money.
Plot long-run growth against the fraction you stake and you get a hill. Growth rises as your stake approaches the true Kelly fraction, peaks there, then falls. But the two sides of the hill are not alike. Stake half of true Kelly and you still capture roughly three quarters of the maximum growth rate with far smaller drawdowns. Stake roughly double the true Kelly and long-run growth falls back to approximately zero. Push past double and it goes negative: you can hold a real edge on every single trade and still grind your bankroll down, purely from oversizing.
Now connect that to the only input you control. Suppose you make a contract 60% at a price of 50 cents. Full Kelly says 20%. Consider what happens as your estimate degrades:
- Your q was right (true 60%). You are at the peak. Best case.
- You were 5 points optimistic (true 55%). The true Kelly stake was (0.55 - 0.50) / 0.50 = 10%, and you staked 20%. You are staking double the correct fraction, which lands you near zero long-run growth while riding 20% swings.
- You were 10 points optimistic (true 50%). There was no edge at all. You are cycling a fifth of your bankroll through coin flips and paying the taker fee on every one.
Being 5 points optimistic about a sports outcome is not a rare failure. It is a Tuesday. That is the case for fractional Kelly in one sentence: quarter Kelly at your believed edge stays below the true full Kelly even when your estimate was meaningfully wrong. In the example above, quarter Kelly stakes 5%, safely under the true 10% peak even after a 5-point misjudgment. You give up some theoretical growth in the good case to stay off the wrong side of the hill in the realistic one.
Quarter Kelly, Half Kelly, Or A Flat Cap
My default recommendation for anyone trading event contracts part time is quarter Kelly, and it is not a timid choice. It is the setting that acknowledges your q comes from a model, a projection, or a read, not from an answer key. Half Kelly is defensible if you have a long, tracked record showing your probabilities are calibrated, meaning your 60%s actually win about 60% of the time. Full Kelly is for people whose estimates are exactly right, a group that does not include me and, statistically, does not include you.
There is also a simpler scheme that skips the formula entirely: cap every position at a flat 2-5% of bankroll, a heuristic you will see repeated constantly in prediction market communities, and for good reason. Look back at the table above and notice that quarter Kelly on realistic edges lands between 2.5% and 5% anyway. The flat cap is fractional Kelly with the arithmetic pre-done for typical edges. What it costs you is proportionality: it will not tell you to pass when you have no edge, and it will not scale down for a marginal one. If you use the cap, you still have to do the honest part, which is asking whether q really beats p at all. For where a defensible q comes from in the first place, our Kalshi strategy guide walks through the edge-finding side of the workflow.
The formula is only as good as the q you feed it. The live odds screen prices every sports market at no-vig fair odds across DraftKings, FanDuel, and every other major book: the tool surfaces a market-grade probability to hold against a contract price instead of a gut number. Compare the fair price to the cents, and the (q - p) numerator stops being a guess.
Fold The Fee Into The Price Before You Size
There is one adjustment left before the formula is honest: Kalshi's taker fee. A standard market order costs round up(0.07 x C x P x (1 - P)), where C is contracts and P is the price in dollars, a curve that peaks at 50 cents and is covered in full in our Kalshi fees breakdown. The fee does not change your payout; it changes your cost. So the fix is simple: compute the fee per contract, add it to the price, and run Kelly on the effective price.
At 50 cents: 100 contracts cost $50.00 plus the maximum fee, 0.07 x 100 x 0.50 x 0.50 = $1.75. Effective price: 51.75 cents. With q = 60%, Kelly becomes (0.60 - 0.5175) / (1 - 0.5175) = 0.0825 / 0.4825, about 17.1% instead of 20%. Quarter Kelly drops from $50 to about $43 on a $1,000 bankroll.
At 30 cents: 100 contracts cost $30.00 plus 0.07 x 100 x 0.30 x 0.70 = $1.47. Effective price: 31.47 cents. With q = 37%, Kelly becomes (0.37 - 0.3147) / (1 - 0.3147) = 0.0553 / 0.6853, about 8.1% instead of 10%.
Two practical notes fall out of this. First, the fee haircut peaks near 50 cents, where the table above already produces some of the largest stakes, so the correction matters most on exactly the positions you were about to size biggest. Second, resting limit orders pay no fee on most markets, so patience does not just get you a better fill price; it hands the fee haircut back and restores the sharper Kelly number.
What Kelly Will Not Do For You
A quick honesty section, because sizing formulas attract more faith than they deserve. Kelly assumes each position is independent, so if you hold five contracts that all win when the same team covers, you do not have five separately sized positions; you have one big one wearing five tickets. It assumes you can actually get your size filled at the quoted price, which thin order books routinely refuse. And it says nothing about whether your q is any good, which is the input that decides everything. The formula is the last step of a process, not a substitute for one. Kalshi operates as a CFTC-regulated event-contract exchange, availability varies by state and over time, and no sizing scheme changes the fact that a bad probability estimate loses money at any stake.
FAQ
What is the Kelly criterion formula for prediction markets? For a contract at price p (in dollars) with your estimated win probability q, the Kelly fraction is f* = (q - p) / (1 - p) of your bankroll. A contract at 50 cents that you believe wins 60% of the time gives (0.60 - 0.50) / 0.50, a 20% full-Kelly stake.
How much of my bankroll should I put on one Kalshi contract position? Run the Kelly formula, then take a quarter of the answer. Full Kelly assumes your probability estimate is exactly right, and overestimating pushes you into oversizing territory fast. If you would rather skip the math, the common 2-5% flat cap per position is a defensible simple alternative.
Why is full Kelly considered risky? Because the penalty for oversizing is much worse than the penalty for undersizing. Staking less than Kelly costs you a little growth. Staking roughly double the true Kelly wipes out long-run growth entirely, and your estimate only has to be a few points optimistic for that to happen.
Do Kalshi fees change Kelly sizing? Yes. The taker fee raises your true cost per contract, so add the per-contract fee to the price before you run the formula. At 50 cents on a standard market, the maximum fee of $1.75 per 100 contracts turns a 50-cent price into an effective 51.75 cents, which cuts a 20% Kelly stake to about 17.1%.
What does it mean if the Kelly formula gives zero or a negative number? It means your estimated probability is at or below the market price, so you have no edge at that number. Kelly's answer is to pass. No sizing scheme can turn a contract priced above your probability into a good position.
Size The Next One Like A Trader
The whole discipline compresses into four steps I run before any order: build a q I can defend, fold the fee into the price, run (q - p) / (1 - p), then stake a quarter of the answer or my flat cap, whichever is smaller. It takes about fifteen seconds, and it is the difference between a bankroll that compounds and one that donates its edge back through variance. The hard part is never the division. It is being honest about q.
Get a q worth sizing on. The odds comparison converts any price into an implied probability in one step, and the live odds screen shows the no-vig fair probability on every sports market, so you can hold a de-vigged market number against the contract price before the Kelly math ever runs.
Event contracts involve risk and are not appropriate for everyone. Any probabilities discussed here are model estimates, not predictions of fact and not financial or trading advice. 18+. Availability varies by state. Trade responsibly.
