Bettors see a contract trading at 45 cents on an exchange and the opposite outcome priced at plus money on a sportsbook, do the subtraction in their head, and assume the gap is locked profit. It usually isn’t, because exchanges charge a per-contract fee that eats into that gap before a single dollar moves.
This calculator adds the exchange’s effective probability (price plus fee) to the sportsbook’s implied probability on the other side. If the two numbers add up to less than 100%, it splits a stake across both legs and shows the guaranteed profit no matter which side wins.
Start with the total amount available to stake across both legs. Enter the exchange’s Yes price in cents, the price at which the contract can be bought right now. Select which exchange is being used (Kalshi, Polymarket, Robinhood, or no fee), since each charges a different per-contract cost that changes the effective price. Enter the sportsbook’s price on the opposite outcome, No.
The result opens by stating whether an arbitrage exists, based on whether the combined implied probability falls under 100% once the fee is added. If it does, the result shows how many contracts to buy on the exchange, the dollar amount that costs with the fee included, the amount to bet at the sportsbook, and the profit that’s locked in regardless of the outcome.
The exchange side’s effective probability is the listed price plus the per-contract fee, not just the price alone. A 45 cent Yes contract on Kalshi costs more than 45% once the fee is added. The sportsbook’s implied probability comes straight from its odds; +100 on No implies a 50% chance.
With the default inputs, those two numbers add up to an implied total of 97.00% with the fee included, under 100%, so an arbitrage exists. The calculator splits $1,000 in proportion to each side’s share of that total: 1,031 contracts on the exchange, costing about $484.54 with the fee, and $515.46 at the sportsbook. Whichever side wins, the payout comes back to $1,000 divided by 0.97, which is why the guaranteed profit lands at $30.93, or 3.09% of the stake.
This math matters most when a contract’s price and a sportsbook’s line look far enough apart to tempt a bettor into thinking the gap alone is the edge. The fee changes that gap, sometimes enough to erase it entirely. A price spread that looks wide before the fee can shrink to nothing after it, or turn a real arbitrage into a losing trade.
The common mistake is stopping at the raw prices and skipping the fee, or ignoring how many contracts the exchange’s order book can actually fill at the quoted price. A sharp bettor treats the combined implied probability, not the individual prices, as the number that decides whether to act. Once that number sits under 100%, the next question is depth: whether enough contracts trade at that price to place the full stake without moving the market against the position.
Why does the fee matter more on some exchanges than others? Each exchange charges its fee differently, and a higher per-contract cost pushes the effective price up more, which can turn a workable spread into one that no longer clears 100% combined.
What happens if the combined implied probability comes out above 100%? The calculator reports no arbitrage, since betting both sides in that case guarantees a loss rather than a profit, regardless of how the stake gets split.
Why split the stake unevenly between the two legs? The split is proportional to each side’s share of the combined probability, which is what makes the payout identical no matter which outcome hits. An even split across two legs with different effective prices would leave one outcome paying more than the other.
Does a wider gap between the exchange price and the sportsbook price always mean more profit? Not necessarily. The size of the locked profit depends on how far the combined implied probability falls under 100% after the fee, not on how far apart the two raw prices look before it.