Arbitrage Calculator

Worked example: +110 at one book, +105 at another

Suppose one sportsbook prices Team A at +110 and another prices Team B, the only other outcome, at +105. Convert each to implied probability: +110 is 1 ÷ 2.10 = 47.62%, and +105 is 1 ÷ 2.05 = 48.78%. Together they sum to 96.40%. Any total under 100% means the two prices disagree enough to cover both outcomes at a profit.

To make the payout the same whichever side wins, stake each side in proportion to its implied probability. On $100 total that is $49.40 on +110 and $50.60 on +105. Either winner returns about $103.73, a $3.73 profit, or 3.73% of the money staked.

Rounding the stake split to whole dollars

On $1,000 the exact split is $493.98 and $506.02, returning $1,037.35 either way. Few bettors place cents, and a book may reject odd amounts. Round to $494 and $506 and the profit becomes $37.40 if +110 wins or $37.30 if +105 wins, almost unchanged. Round further to $490 and $510 and the outcomes spread out to $29.00 and $45.50. A flat $500/$500 still profits on both sides, $50.00 or $25.00, because the margin here is wide; on a thinner arb, loose rounding can turn one side into a loss.

How thin real arbitrage margins are

Most arbs are smaller than the example. +110 against -105 sums to 98.84% for a 1.18% profit. +120 against -110 sums to 97.84% for 2.21%. +105 against +102 sums to 98.29% for 1.74%. Two standard -110/-110 quotes sum to 104.76%; splitting $100 across them returns $95.45 either way, a guaranteed loss of $4.55, which is the vig you pay when there is no price disagreement to exploit.

Why the guaranteed profit is only guaranteed on paper

The math assumes both bets are accepted at the quoted prices. If you place $494 at +110 and the +105 disappears before your second bet goes in, you are holding an ordinary single bet: +$543.40 if it wins, -$494 if it loses. Place the harder-to-get side first, and expect prices that disagree this much to move quickly.

Settlement rules can also differ between books. One book may void a player prop when the player does not take the field while the other grades it as a loss; baseball bets can depend on listed pitchers; some markets include overtime and others do not. Books may also cancel bets on an obvious pricing error and limit accounts that bet arbs regularly. Confirm the two markets settle identically before treating the profit as locked.