Round Robin Calculator: Every Parlay, Every Payout

How many parlays a round robin makes

The count is a combination: how many ways you can choose k picks out of n, written C(n, k) and equal to n! ÷ (k! × (n − k)!). Order does not matter, so the Chiefs with the Lakers is the same parlay as the Lakers with the Chiefs.

The cost grows faster than the number of picks. Six picks by 2s and 3s at $10 a parlay is $350 of action, so it pays to check the bet count before you check the payout. With three picks, 3s is the full three-leg parlay itself, which is why the calculator only offers 2s at that size.

The payout formula

Each parlay is settled on its own. Convert every price to decimal: a plus price of +X becomes 1 + X ÷ 100, a minus price of −Y becomes 1 + 100 ÷ Y. A parlay pays its stake multiplied by the decimal odds of every leg in it. If any leg loses, that parlay pays nothing. A pushed or void leg counts as 1.00, so the parlay pays on the legs that remain. A dead heat divides that leg's odds by the number tied. The payout of the round robin is the sum of all its parlays; profit is the payout minus the total stake. That is the whole sum the round robin calculator runs, once per parlay.

Worked example: four picks by 2s, three winners

Four picks, $10 on each two-leg parlay:

C(4,2) gives six parlays, so the total stake is $60. Say A, B and D win and C loses. Every parlay with C in it (A+C, B+C, C+D) pays nothing. The three that pay:

• A + B: $10 × 1.9091 × 2.20 = $42.00
• A + D: $10 × 1.9091 × 3.00 = $57.27
• B + D: $10 × 2.20 × 3.00 = $66.00

Payout: $165.27. Profit: $105.27 on the $60 staked. In exact fractions, −110 is 21/11 in decimal, so A + D is $10 × 63/11 = $57.2727, which rounds to $57.27.

Now the same slip with C pushing instead of losing. The three parlays with C become straight bets on the other leg: A pays $19.09, B pays $22.00 and D pays $30.00. Add the $165.27 from the other three and the payout is $236.36.

Round robin versus a single parlay

Put the same $60 on one four-leg parlay and the decimal odds multiply to 1.9091 × 2.20 × 1.6667 × 3.00 = 21.00, or +2000. If all four win it pays $1,260. In the example above, C lost, so it pays $0.

The round robin by 2s, with all four winning, pays $283.76 on the same $60. That is the trade. The single parlay pays far more when everything lands and nothing when one leg fails. The round robin spreads the stake so that three winners out of four still return a profit. Two winners out of four by 2s leave one paying parlay, and whether that covers the $60 depends on which two: A + B alone returns $42, a loss, while B + D returns $66.

Our view: a round robin suits a slate where you like several picks and expect one to miss. Prices decide how much room you have. Four favourites at −150 by 2s pay $27.78 per winning parlay on $10: one miss still returns $83.33 on $60, but two misses return $27.78. At plus prices a single paying parlay can cover the whole stake. The parlay maths on its own is set out on the parlay calculator, which uses the same pricing.

Round robin versus the Yankee and other full-cover bets

UK bookmakers sell the same idea under fixed names. The difference is that a full-cover bet always includes every size up to the full accumulator, and some add singles.

Take the four picks above as a Yankee at $10 a bet. The four three-leg parlays cost $40; with C losing only A + B + D pays, $10 × 1.9091 × 2.20 × 3.00 = $126.00. The four-fold loses. So the Yankee costs $110 and pays $165.27 + $126.00 = $291.27. A round robin by 2s and 3s costs $100 and pays the same $291.27, because the one bet it leaves out is the one that lost.

In the round robin calculator the boxes stop one size below the number of picks, so the full parlay is not part of a round robin. To price a Trixie, Yankee or Heinz exactly, choose it in the bet calculator, which builds every full-cover bet from a Trixie to a Goliath.

Where round robins are used

Round robins are most common on American sports, where a weekend slate gives you many games at similar prices. On the NFL betting page the usual building blocks are point spreads and totals near −110. On the basketball betting page the nightly schedule makes it easy to collect five or six picks for one ticket. Both pages explain how those lines are priced.

What the round robin calculator does not include

• Each site's parlay rules. Most sites settle a pushed leg by dropping it, as the round robin calculator does, but some grade ties or postponed games differently. Their terms decide.
• Rounding. Some sites round each parlay's price before paying it; the figures here are worked from the exact odds, so a final cent may differ.
• Payout limits. A large round robin by 4s or 5s can run past a site's maximum payout per ticket.
• Odds boosts and parlay insurance. Promotions that change the price or refund a leg are not in the figures.

Before you deposit, check how the betting sites with no ID verification we cover handle large withdrawals.

Related pages: Each way calculator, Odds calculator and all betting calculators.

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