What a round robin pays: returns by number of winning legs

In a round robin, only parlays whose every leg wins pay. If w of your n selections win, then C(w, k) of the parlays survive, and each pays the product of its legs' decimal prices. Five selections at -110 by 3s, with 10 a parlay, pays nothing at 2 winners, 69.58 at 3 winners and 278.32 at 4 winners, against a 100 outlay.

The round robin calculator works the returns for your own prices and number of winners.

The rule

Count the winning legs w. The number of winning parlays by k is w choose k. Each pays its stake times the product of the decimal prices of the legs inside it. With every leg at the same price d, the return is C(w, k) × stake × d^k. At -110, d = 1.9091, so a double pays 3.6446 and a three-leg parlay pays 6.9579.

Five selections at -110, by 2s, 10 a parlay (outlay 100)

• 5 winners: 10 doubles pay, 364.46
• 4 winners: 6 pay, 218.68
• 3 winners: 3 pay, 109.34
• 2 winners: 1 pays, 36.45
• 1 or 0 winners: 0

By 2s, three winners already return slightly more than the 100 outlay. By 3s, you need four. This is the standard trade: smaller groups survive more losses and pay less when everything lands, larger groups pay more and need more winners.

Against one five-leg parlay

A single parlay of the same five legs at 100 returns 100 × 1.9091^5 = 2,535.91 if all five win and nothing otherwise. The round robin by 3s returns 695.79 when all five win. The jackpot has shrunk to under a third of the single parlay, and in return you collect something on four winners and on three. That is the whole point of the structure, and the price of it is the second column: more slips, each with its own margin.

How many winners cover the outlay

Solve C(w, k) × stake × d^k ≥ total outlay. With five at -110: by 2s, w = 3 gives 109.34 against 100; by 3s, w = 4 gives 278.32 against 100 while w = 3 gives 69.58, a loss of 30.42. The break-even number of winners sits above half the selections, which matches the fact that each leg at -110 needs to win 52.38% of the time just to break even on a single bet. The needed rate for each price is in the break-even rate table.

When the prices differ

With legs at different prices, each parlay pays the product of the specific prices it holds, so one long-priced leg lifts every slip it appears in. The count by winners then depends on which legs won, not only how many. The calculator handles this by listing each combination.

How many slips each structure creates is in the counting article.

Try your own. Enter your selections, prices and stake into the round robin calculator to see the return for each number of winners.