KEY TAKEAWAYS
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A round robin payout is the total return from every smaller parlay inside the round robin that wins, compared against the combined stake placed on all of those parlays. To calculate it, you count how many combinations the round robin creates, multiply the stake per combination by that count to get the total risk, price each combination by multiplying its legs’ decimal odds, and add up the combinations whose legs all won. That sounds mechanical, and it is, but the result often surprises bettors: a round robin can return money when one pick loses, yet it can also finish at a net loss even when half the picks win. If you need the basic definition first, start with what a round robin bet is and how it splits picks into parlays. This article stays on the numbers: the combination formula, stake per combination versus total stake, how each sub-parlay is priced, and full payout scenarios for by-2s, by-3s and every-combination round robins built from the same four hypothetical legs.
What Determines a Round Robin Payout
Every round robin payout comes from three inputs: the number of combinations, the stake placed on each combination, and the odds of the legs inside each combination. The combination count is fixed by math, not by preference. Once you choose how many selections go into the round robin (n) and how many legs each smaller parlay contains (k), the sportsbook builds every possible group of k legs from the n selections. That count is the binomial coefficient, usually written “n choose k” and calculated as n! / (k! × (n − k)!).
The stake works differently from a single parlay. Most bet slips ask for a stake per parlay, sometimes labeled “per bet” or “per combination.” Total stake equals stake per combination multiplied by the number of combinations, so a round robin of 6 parlays at $10 each costs $60, not $10. This is the single most important number to read before confirming a ticket, because it is the amount genuinely at risk.
Finally, each combination is a normal parlay. It is priced by converting every leg to decimal odds and multiplying them together, exactly as described in how to calculate parlay odds and payouts. A combination pays only if every leg inside it wins; one losing leg makes that combination lose its full stake, while the other combinations that do not contain the losing leg are unaffected. The total round robin payout is simply the sum of the winning combinations’ returns.
How to Calculate a Round Robin Payout Step by Step
The calculation follows the same four steps every time, whether the slip has three selections or eight. Working through them by hand is exactly what a round robin payout calculator does in the background, and doing it once makes any calculator’s output easy to check.
Step 1: Count the combinations
Apply n choose k to the number of selections and the parlay size. Combination counts grow quickly as selections are added, as the table below shows. The “every combination” column counts all parlays of two legs or more (2n − n − 1), which is what some sportsbooks offer as a full-cover option.
| Selections (n) | By 2s | By 3s | Every combination (2+ legs) |
|---|---|---|---|
| 3 | 3 | 1 | 4 |
| 4 | 6 | 4 | 11 |
| 5 | 10 | 10 | 26 |
| 6 | 15 | 20 | 57 |
| 7 | 21 | 35 | 120 |
| 8 | 28 | 56 | 247 |
Read the table as a cost multiplier: eight selections by 3s means 56 separate stakes, so even a small stake per combination becomes a large total quickly.
Step 2: Work out the total stake
Multiply the stake per combination by the count from Step 1. Four selections by 2s at $10 each is $60 of total risk; the same four by 3s is $40, and every combination is $110.
Step 3: Convert every leg to decimal odds
Decimal odds make parlay math a straight multiplication. For positive American odds, decimal = 1 + (odds ÷ 100); for negative American odds, decimal = 1 + (100 ÷ |odds|). Decimal odds already include the returned stake, which is why multiplying them gives a payout rather than a profit. If this conversion is unfamiliar, decimal odds explained covers it in detail.
Step 4: Price each combination and add the winners
For each combination, payout = stake per combination × the product of its legs’ decimal odds. Add the payouts of only the combinations where every leg won, then subtract the total stake from Step 2 to get the net result. A positive number is profit; a negative number is a net loss even if some combinations paid.
Worked Example: A 4-Leg Round Robin by 2s
Suppose a bettor builds a round robin by 2s from four hypothetical selections, at $10 per combination: Leg A at -125 (decimal 1.80, implied probability 55.56%), Leg B at +100 (decimal 2.00, 50%), Leg C at +150 (decimal 2.50, 40%), and Leg D at -200 (decimal 1.50, 66.67%). Four selections by 2s create 6 two-leg parlays, for $60 of total risk. These prices are illustrative examples, not current lines.
| Combination | Calculation | Combined decimal odds | Payout on $10 |
|---|---|---|---|
| A + B | 1.80 × 2.00 | 3.60 | $36.00 |
| A + C | 1.80 × 2.50 | 4.50 | $45.00 |
| A + D | 1.80 × 1.50 | 2.70 | $27.00 |
| B + C | 2.00 × 2.50 | 5.00 | $50.00 |
| B + D | 2.00 × 1.50 | 3.00 | $30.00 |
| C + D | 2.50 × 1.50 | 3.75 | $37.50 |
If all four legs win, every combination pays: $225.50 returned on $60, a profit of $165.50. Now suppose Leg D loses while A, B and C win. Only the three combinations without D survive (A + B, A + C, B + C), returning $36.00 + $45.00 + $50.00 = $131.00, a profit of $71.00. If instead only B and C win, a single combination pays $50.00 and the round robin finishes $10.00 down despite two correct picks.
Round Robin Payout Chart: By 2s vs. By 3s vs. Every Combination
The same four legs produce very different results depending on the parlay size chosen. The chart below shows the net result (total payout minus total stake) for each structure at $10 per combination. Which leg loses matters, not just how many legs lose, because longer-priced legs carry more of the payout.
| Outcome | By 2s (6 bets, $60) | By 3s (4 bets, $40) | Every combination (11 bets, $110) |
|---|---|---|---|
| All four win | +$165.50 | +$246.50 | +$537.00 |
| A, B, C win (D loses) | +$71.00 | +$50.00 | +$111.00 |
| B, C, D win (A loses) | +$57.50 | +$35.00 | +$82.50 |
| A, B, D win (C loses) | +$33.00 | +$14.00 | +$37.00 |
| Only B and C win | −$10.00 | −$40.00 | −$60.00 |
| Only A and D win | −$33.00 | −$40.00 | −$83.00 |
Three patterns stand out. By 3s pays more on a clean sweep but returns nothing with only two winners, because every three-leg combination needs three correct picks. By 2s pays less at the top but softens the damage when one leg misses. The every-combination version has the largest upside and the largest cost, so it loses the most when only two legs come in. For comparison, a single four-leg parlay at $10 has combined decimal odds of 13.50 (1.80 × 2.00 × 2.50 × 1.50) and returns $135.00 for a $125.00 profit if all four win, but loses its $10 on any other outcome.
It also helps to put rough probabilities next to the payouts. Using the legs’ implied probabilities as stand-ins and treating the legs as independent, all four win about 7.4% of the time and at least three win about 35.6% of the time. In this example, the by-2s round robin finishes in profit only when three or more legs win, so under those assumptions roughly 64% of outcomes are net losses. Because implied probabilities include the sportsbook margin, real chances for an average bettor are typically a little lower, not higher.
Common Round Robin Payout Mistakes
The most frequent error is reading the stake field as the whole bet. A “$10 round robin” by 2s on four picks is a $60 wager, and comparing its payout to a $10 single parlay without adjusting for that is comparing two different amounts of risk.
A second mistake is treating any winning combination as a winning ticket. Seeing “1 of 6 parlays won” on a settled slip can feel like success, but the round robin is profitable only when total payout exceeds total stake. In the chart above, two correct picks always produce a net loss.
Third, many bettors confuse payout and profit when using a calculator. Decimal-odds math returns the payout including the stake; profit is payout minus the stake for that combination, and the net round robin result is total payout minus total stake.
Finally, a round robin does not reduce the sportsbook’s edge. Every combination carries the margin of each leg inside it, compounding across legs just as it does in a regular parlay. Spreading picks across more tickets changes how often you see a return, not the price you pay for each leg.
Reading the Numbers on a Round Robin Bet Slip
On a typical bet slip, a round robin shows a line such as “By 2s × 6,” followed by a stake-per-bet field and a total-wager figure. “By 2s × 6” means six two-leg parlays, and the total wager shown should equal six times the stake per bet. Checking that one multiplication confirms the slip was built the way you intended.
The “potential payout” figure on most slips assumes every leg wins, which is the best case rather than the expected case. Settlement of pushes and voids also changes the math. Under common house rules, a pushed or voided leg is treated as decimal odds of 1.00, so a two-leg combination containing it effectively becomes a single bet on the other leg; see what a push is in sports betting for how a push is graded. In the worked example, if Leg C pushed and the other three won, the by-2s round robin would return $146.00 for an $86.00 profit. Rules differ between sportsbooks, so check the house rules before relying on any settlement assumption.
Related Odds Concepts to Learn Next
Round robin math sits on top of single-parlay math, so the next logical step is understanding how likely each sub-parlay is to hit. Parlay probability and the chance of hitting every leg shows how quickly that chance falls as legs are added, which explains why by-3s combinations pay more but miss more often. Full-cover bets apply the same combination logic with a fixed menu of bet sizes; Yankee, Trixie and Lucky 15 bets are the closest relatives. Because a round robin multiplies a single stake across many tickets, sizing the stake per combination relative to your total budget matters more than the payout figure. Treat that total as money you can afford to lose, since most outcomes in the examples above end in a net loss.
