Break-even win rate for a parlay: the whole ticket and each leg

A parlay breaks even when it wins 1 ÷ its decimal price of the time. Two legs at -110 pay +264, decimal 3.645, so the ticket must win 27.4% of the time. Each leg must still win 52.38%, because the ticket wins only when both do. The per-leg figure is the ticket rate raised to the power 1 ÷ the number of legs.

The break-even calculator gives both numbers for any price and any number of legs.

The ticket and the leg are two different numbers

The ticket rate is what the whole slip needs: 1 ÷ 3.645 = 27.44%. The leg rate is the square root of that for two legs: √0.2744 = 52.38%. For three legs it is the cube root, for four the fourth root. When every leg is priced at -110 and the parlay pays the exact product of the leg prices, the per-leg rate is 52.38% at any number of legs. That is why a parlay at fair product pricing gives no leg an easier job than a straight bet.

The ticket rates at -110

• 1 leg: decimal 1.909, break-even 52.38%
• 2 legs: decimal 3.645 (+264), break-even 27.44%
• 3 legs: decimal 6.958 (+596), break-even 14.37%
• 4 legs: decimal 13.283 (+1228), break-even 7.53%

The ticket threshold falls fast with extra legs, and that makes long parlays look easier than they are. A 7.5% target sounds modest. It is the product of four 52.38% chances.

When the payout is smaller than the product

Some slips pay less than the legs would multiply to. Take three legs at -110 on a ticket that pays +550 (decimal 6.5) instead of +596. The ticket break-even is 1 ÷ 6.5 = 15.38%. The per-leg rate is the cube root, 53.58%. The same three legs now need 1.2 points more from each. Boosted payouts do the reverse and lower the per-leg bar, so it is worth running the figures on any parlay whose price you did not see computed.

The margin that builds up in a standard parlay is explained in why a parlay's margin compounds. The per-leg view makes the same point from the other side: you do not escape the price on any leg by joining them.

Legs that are not independent

The multiplication above assumes the legs are independent. When two legs are linked, as with a team to win and a total on the same game, the ticket's real chance differs from the product of the two. Many places refuse to combine them for that reason, and where they allow it, they price the correlation in. The correlation article covers it.

How to use the number

Write down the per-leg rate the ticket needs. Compare it with the rate you have grounds to expect for each leg, remembering that your own estimates carry error. If a leg's rate is below the break-even for the ticket's price, the ticket loses in the long run however many legs are added. If the legs are above it, the parlay still needs every one to land on the day.

Run your parlay. Put the number of legs and the ticket price into the break-even calculator and read off the ticket and per-leg rates.