Kelly Criterion for Prediction Markets: A Fee-Aware Position Sizing Calculator for Polymarket and Kalshi
Turn a price, a probability, and a bankroll into an exact fee-aware stake, with fractional Kelly, a hard exposure cap, and a sensitivity ladder that keeps overconfidence honest.
Why does position sizing decide who survives in prediction markets?
Prediction-market shares are the cleanest instrument in trading: a share pays exactly $1 if the outcome happens and exactly $0 if it does not. That binary payoff makes the math of sizing unusually honest, and it makes sizing mistakes unusually fatal. A trader who is right 55 percent of the time at fair prices has a real edge, and that same trader goes broke anyway if they put 30 percent of their bankroll on each trade, because a routine four-loss streak, which happens constantly at those probabilities, removes most of the account. Being right and being solvent are separate skills, and the second one is the one traders skip.
Most people size by feel. A round number, a conviction vibe, whatever is left in the account. Feel fails in two directions at once: it oversizes thin edges, which converts ordinary variance into ruin, and it undersizes strong edges, which wastes the rare situations where the market is genuinely wrong. The Kelly criterion is the classical answer to both. It computes the fraction of bankroll that maximizes long-run compound growth for a given edge and payoff, more when the edge is fat, less when it is thin, and zero when it is not there at all.
The calculator at /bankroll operationalizes that math for Polymarket and Kalshi specifically. You give it three numbers, the market price, your own probability that the contract pays out, and your bankroll, and it returns a stake in dollars and in whole contracts, with venue fees already priced into the cost basis. The bankroll, the Kelly fraction, and the per-market cap are saved in your browser and shared with the arbitrage stake splitter on /divergence, so one set of risk settings governs every sizing tool on the site. None of it is financial advice, and none of it promises profit; it is arithmetic applied to your own estimate, and only trade money you can afford to lose.
What does a share actually cost after fees on Kalshi and Polymarket?
The single most common sizing error in these markets is computing edge off the sticker price. The number that matters is the all-in cost per share, and the two venues load it differently. Kalshi charges a trading fee of 0.07 × P × (1 − P) per contract, where P is the price you pay. The formula peaks in the middle of the range: a 50¢ contract carries about 1.75¢ of fee, a 40¢ contract about 1.7¢, while a 95¢ contract carries only about 0.3¢. Polymarket charges no trading fee, but settling on-chain is not free either; Polygon gas plus ordinary spread slippage runs roughly 0.2¢ per share in practice.
The calculator adds the venue fee to the price before doing anything else, so every downstream number, edge, breakeven, Kelly fraction, expected value, is computed from what the share actually costs you. The consequence is easy to state and easy to forget: a 40¢ share on Kalshi really costs about 41.7¢, which means your breakeven is not 40 percent, it is 41.7 percent. If your honest probability is 41 percent, the sticker price says you have an edge and the all-in cost says you do not. Fee-blind sizing systematically overtrades exactly the marginal situations where discipline matters most.
This is also why the same trade can be worth taking on one venue and not the other. Near the middle of the price range, Kalshi's fee is roughly eight times Polymarket's per-share cost, so a thin edge that survives on Polymarket can die on Kalshi. The calculator has a venue selector for precisely this comparison, and reading the fee line in its output before entering is the cheapest habit in trading: it costs nothing and it regularly deletes trades that were never profitable to begin with.
How does the Kelly formula work in plain language, with a worked example?
The formula is f* = (bq − (1 − q)) / b. In words: q is your probability that the contract pays $1, and b is the net payout multiple, the profit per dollar staked if it hits, which for a $1-payout share is (1 − cost) / cost. Multiply the payout multiple by your win probability, subtract your probability of losing, and divide by the payout multiple again. What is left is the fraction of your bankroll that maximizes long-run compound growth. The structure is intuitive: the more your probability exceeds the market's all-in price, the larger the surplus on top of the formula, and if your probability is below the cost, the formula goes negative, which means the growth-optimal stake is nothing.
A worked example on Kalshi. The contract trades at 40¢ and your honest estimate is 50 percent. The fee is 0.07 × 0.40 × 0.60, about 1.7¢, so the all-in cost is roughly 41.7¢ and the edge after fees is about 8.3¢ per share. The net payout multiple b is (1 − 0.417) / 0.417, about 1.40: each staked dollar returns about $1.40 of profit if the contract hits. Full Kelly is (1.40 × 0.50 − 0.50) / 1.40, which comes out near 14.3 percent of bankroll. Notice what the fee did: with no fee the same trade computes to 16.7 percent, so roughly two and a half points of optimal stake evaporated into cost before the market moved at all.
Nobody sane trades full Kelly, for reasons the next section covers, so the calculator applies your chosen fraction and cap. At quarter Kelly the stake is about 3.6 percent of bankroll: on a $1,000 account that is roughly $36, which buys 85 whole contracts at the 41.7¢ all-in cost, with an expected value of about $7 on the position. Every one of those numbers is conditional on your 50 percent estimate being right, and that conditional is the entire game. The calculator sizes your opinion; it cannot verify it, and past performance of any sizing method does not guarantee future results.
Why use fractional Kelly and a hard exposure cap instead of full Kelly?
Full Kelly is optimal only in a world where your probability estimate is exactly correct, and it is violently volatile even there, with drawdowns that most humans abandon strategies over. The asymmetry that matters is what happens when you are wrong about your edge. Staking below the true Kelly fraction costs you some growth. Staking above it, which is what happens every time you overestimate your probability and size to it, costs growth much faster, and far enough past the optimum, expected compound growth goes negative: you can hold a genuine edge and still grind an account to zero purely through oversizing.
Since your probability is always an estimate, fractional Kelly is insurance against your own inputs. The growth curve is nearly flat around its peak, so half Kelly keeps roughly three quarters of the optimal growth rate at about half the variance, and quarter Kelly, the calculator's default, gives up more growth for a ride most traders can actually hold through a cold streak. The right way to read a Kelly number is as a ceiling, never a target: the formula tells you the most that could be justified, and the fraction is your standing admission that your estimate carries error.
The exposure cap, the max-percent-per-market setting with a 5 percent default, is a second brake that binds independently of the math, and the calculator flags when it, rather than Kelly, set your stake. It exists because Kelly's assumptions are cleaner than real books. The formula prices one trade in isolation, but real portfolios hold several positions that resolve on the same news, and five markets that all hinge on the same election night are closer to one large position than five small ones. A hard per-market cap keeps any single estimate, or any single correlated theme, from ever being the whole account.
How does the sensitivity ladder catch overconfidence?
Below the headline numbers, the calculator prints a ladder: your probability estimate shifted by two, four, and six points in each direction, with the edge, the stake, and the expected value recomputed at every rung. Your own estimate sits highlighted in the middle. It is a small table doing a serious job, showing you what happens to the trade if your number is a little wrong, which it always is.
The reading that matters most is the flip. If shifting your estimate down by just two points turns the row into a no-trade, the entire position lives inside your estimate's error bar, and the edge is thinner than it feels. Probability calibration research is humbling on this point: very few people can consistently estimate real-world event probabilities to within five points, so a trade that dies at minus two is, for most traders, indistinguishable from no trade at all. The ladder converts that abstract humility into a number you can see before committing.
Used as a pre-commit ritual, the ladder sorts trades into three piles. If the stake stays positive across the whole ladder, the edge is robust to your own imprecision and the Kelly number means something. If it flips at the far rungs, size at the small end of your range. If it flips at minus two, the honest move is usually to pass, and this is exactly the situation where fractional Kelly earns its keep, because whatever residual edge exists is too fragile to press. Overconfidence is the standing tax on traders in these markets; the ladder is the cheapest audit of it available.
When is the correct stake zero, and what are the limits of Kelly sizing?
When your probability is at or below the all-in cost, the Kelly formula goes negative, and the calculator does not soften the answer: it returns a stake of $0 and states the breakeven you failed to clear. This no-trade rule is the tool's most valuable output. A negative-edge position sized small is not prudent, it is a slow donation, and the discipline of passing, dozens of times for every trade taken, is what separates traders who compound from traders who churn. A sizing tool that regularly tells you not to trade is working exactly as intended.
The limits deserve equal billing. Kelly is garbage-in, garbage-out: it sizes your probability, it cannot check it, and a confidently wrong estimate produces a confidently wrong stake. The fee model covers Kalshi's published trading fee and a realistic per-share cost on Polymarket, but it is not an order book: thin markets, crossed spreads, and partial fills all worsen your real cost basis beyond what the calculator sees, and the correlation between positions in your broader book is outside the model entirely. Rows elsewhere on the site can deep-link a price and probability straight into the calculator, but the probability you finally size to should be one you can defend, not one you inherited.
This is an educational tool, not financial advice, and nothing about it promises profit. Expected value is an average over futures you will only live once, past performance does not guarantee future results, and prediction-market shares can and do settle at zero. Set the bankroll number to money you can genuinely afford to lose, keep the fraction conservative and the cap on, and let the calculator do the one thing math can actually do for a trader: keep the size of every position proportional to the evidence behind it.
WhaleTracks is informational analytics, not financial advice. Past performance does not guarantee future results.