Prediction markets and sportsbooks price the same events with different customers, different fee structures and different speeds. When they disagree by more than their combined margins, buying one side on the market and backing the other at the sportsbook locks in a profit. This guide converts the two into a common language, applies the arbitrage test, sizes the position, and lists what can go wrong.
Convert both sides to decimal odds
A Polymarket share at price p pays $1.00, so its decimal odds are 1/p. A sportsbook price is already odds. Put both in decimal, after fees on the market side:
market YES at p, fee f: effective = 1 + (1/p − 1) × (1 − f) sportsbook price: decimal as displayed
(margin already inside)
64¢ YES with a 2% fee
1/0.64 = 1.5625; effective 1 + 0.5625 × 0.98 = 1.551. The market is offering 1.551 on YES.
Apply the test
Two outcomes, one on each venue. Sum the implied probabilities of the effective prices; below 100% is an arbitrage.
Market YES at 64¢, sportsbook on the opposite outcome at +200
Market: 1.551 → 64.5% implied. Sportsbook: 3.00 → 33.3%. Sum: 97.8%. Arbitrage of 1/0.978 − 1 = 2.2%. Stakes on 100 total: 100 × 0.645/0.978 = 65.9 on the market (buying 65.9 / 0.64 = 103 shares), 34.1 at the sportsbook. If YES resolves: 103 shares × $1 × (1 − 2% on the $37 profit) ≈ 102.2, minus the 34.1 lost at the book, net +2.2. If it does not: sportsbook pays 34.1 × 2.00 = 68.2 profit, minus 65.9 lost on the shares, net +2.2. The
arbitrage calculator
takes the market price in cents on one leg and the sportsbook price on the other, with the fee applied to the market leg.
Typing "64" with the Polymarket format selected, or "64¢" in any mode, is enough; the calculator converts to odds before solving. Sportsbook prices can be typed as +200 or 3.00.
Which side to buy
Prediction markets and sportsbooks tend to disagree in a consistent direction on certain events. Markets often price political and news outcomes with more information than sportsbooks, while sportsbooks price sports with more information than markets. Check both directions: sometimes the arbitrage is buying YES on the market and backing the other side at the book, sometimes buying NO on the market and backing the outcome at the book. The NO share at 1 − p is the mirror; a 38¢ NO is 2.63 decimal before fees.
Sizing with shares, not stakes
A sportsbook bet is a stake at fixed odds. A market position is a number of shares at a price, and the price can move as you buy. The calculator's "stake" on a market leg is dollars spent; divide by the price for the share count, and check the order book has that many shares at that price. If the ask has 50 shares at 64¢ and then 100 at 65¢, a 103-share order fills at a blended price and the arbitrage shrinks. Size to the liquidity available, not to the headline price.
Fees and costs
Fees on the market side are applied to profit in the calculators. The actual fee depends on the market category and can change; treat the preset as a placeholder and enter the rate from the market's own fee page. Beyond the fee, a position carries gas and withdrawal costs that are fixed rather than proportional, which makes small arbitrages uneconomic. As a rule of thumb, an arbitrage under 2% rarely survives real costs on a market leg.
Timing and resolution risk
Two risks are specific to this pairing.
Resolution rules differ. A sportsbook settles on the official result under its own rules; a market resolves according to its written criteria, which might reference a specific source, a date, or a definition that differs from the sportsbook's. A match postponed past the market's resolution date can resolve NO on the market while the sportsbook voids the bet. Read both sets of rules before treating the two as opposite sides of the same coin.
Prices move at different speeds. Markets trade continuously and react to news within seconds; sportsbooks may suspend and reprice. Place the leg more likely to move first, and confirm the other before committing.
Group markets
Events with several outcomes are usually split into one binary market per outcome. Two arbitrage structures exist:
- Within the market group. If the YES prices sum to less than $1.00, buying every YES pays $1.00 per share on exactly one of them. The group arbitrage calculator sizes each basket.
- Against a sportsbook. Back one outcome at the sportsbook and buy NO on that outcome's market, or buy YES on the market and back the field at the book. Each pairing is a two-way arbitrage as above.
Worked example, both directions
Election market: YES 58¢ / NO 44¢; sportsbook: candidate 1.60, other 2.40
Direction A: market YES at 58¢ (1.724 before fees; 1.710 at 2%) versus sportsbook other at 2.40. Implied: 58.5% + 41.7% = 100.2%. Not an arbitrage.
Direction B: market NO at 44¢ (2.273 before fees; 2.247 at 2%) versus sportsbook candidate at 1.60. Implied: 44.5% + 62.5% = 107%. Not an arbitrage either; the market is more confident in the candidate than the sportsbook on one side and less on the other, but not by enough to beat the spread plus the sportsbook margin.
The check took thirty seconds in the calculator. Most pairs look like this; the ones that do not are worth the effort.
Hedging a market position with a sportsbook bet
The same arithmetic runs in reverse. Suppose you hold 200 YES shares bought at 40¢ (cost 80) and the market has moved to 60¢; the shares are worth 120 and pay 200 on YES. You can sell them, or you can lock the position with a sportsbook bet on the opposite outcome. Treat the shares as a back bet at 1/0.40 = 2.50 with stake 80, and the sportsbook's price on the other side as the second leg. If the book offers 2.80 on NO, the equal-profit stake is 80 × 2.50 / 2.80 = 71.4: on YES you collect 200 − 80 − 71.4 = +48.6; on NO you collect 71.4 × 1.80 − 80 = +48.6. Selling the shares at 60¢ would bank 40 today; the hedge locks 48.6 at settlement because the sportsbook is offering a better price than the market's own NO side implies. Fixed-leg mode in the arbitrage calculator does this with the share cost locked as the first leg.
Adding up the costs
Three costs sit between a nominal arbitrage and a real profit. The spread is paid on entry (you buy at the ask) and again if you exit early. The fee, where one applies, comes off profit and behaves like exchange commission; at 2% it costs about a cent on a 50¢ share. The sportsbook margin is already in its price and cannot be removed. Add them up for the pairing you have in mind: a 2¢ spread on a 60¢ market is 3.3% of the price; a 2% fee is worth about 0.8 points of implied probability at that price; and a -110 sportsbook line carries 2.4 points of margin on its side. An apparent 4% arbitrage can be a 0.5% one after all three, which is why the practical threshold is around 2% and why a wider spread kills a position faster than a fee does.
A capital plan
Market positions need capital on the venue, sportsbook bets need capital at the book, and neither can be moved quickly. Keep enough at each to take the size you want, treat the market balance as slow money (withdrawals cost time and gas), and size positions to what the order book can absorb rather than to the bankroll. A useful discipline is to write down, before placing anything, the expected profit after spread, fee and margin, the resolution rule on both venues, and the leg you will place first. If any of the three is uncertain, the position is not an arbitrage yet.
Finding candidates
Arbitrages between a market and a sportsbook cluster in a few places. Political and macro events, where markets carry more information than sportsbooks; sports events with a market that has gone stale while the sportsbook reprices on news; and any market with a wide spread, where a limit order inside the spread can be filled by a trader who does not check the sportsbook. Watching both venues on the same list of events, converting the market ask to decimal after fees, and comparing with the best sportsbook price on the opposite side is the whole search. The comparison is a subtraction of implied probabilities, and the calculator does it for any pair of prices you type; the work is in keeping the list current and acting quickly when the sum drops below 100%.
Checklist
- Convert the market price to decimal after fees; take the sportsbook price as shown.
- Sum the implied probabilities across the two venues; below 100% is an arbitrage.
- Size dollars in proportion to implied probability; convert market dollars to shares and check the order book.
- Confirm resolution rules match.
- Place the faster leg first.
- Expect costs to eat anything under 2%.
- Write down the expected profit after spread, fee and margin before placing either leg, and walk away if the number is not there.