Round Robin Calculator: How a Round Robin Bet Works

A round robin bet takes a list of picks and turns it into every smaller parlay those picks can make. Three teams by 2s become three two-team parlays, so one loser costs you some of the tickets instead of all of them. The round robin calculator below works out how many bets that creates, what the whole ticket costs and what it pays back once the results are in. Enter 3 to 8 legs in fractional, decimal or American odds, mark each one as won, lost or pushed, and the figures update as you type.

The rest of this page explains how round robins work at US sportsbooks, how they compare with a single parlay on the same picks, what they cost in margin and how they relate to the Trixie, Yankee and other full-cover bets sold in the UK.

What is a round robin bet

A round robin is a set of parlays built from one list of selections. You choose the picks, then the size of the parlays, and the sportsbook writes every possible combination of that size as a separate bet. The name comes from round robin tournaments, where every team meets every other team once. In a round robin by 2s, every pick is paired with every other pick once.

Take three NFL picks: Team A on the spread, Team B on the moneyline and Team C on the spread. A round robin by 2s on those three creates these parlays:

• Team A + Team B
• Team A + Team C
• Team B + Team C

Each one is a normal two-team parlay with its own stake. At $10 per parlay the ticket costs $30. Each parlay is settled on its own, so if Team B loses, the two parlays that include Team B lose and the Team A + Team C parlay can still pay. With one three-team parlay, the same loss would end the bet.

How a round robin bet works on the bet slip

At US sportsbooks that offer round robins the process is similar. Add three or more selections to the bet slip, open the round robin option and pick a size: parlays by 2s, by 3s and so on, up to one leg fewer than the total. Some books let you tick more than one size on the same ticket, such as by 2s and 3s together. The stake you type is normally the stake per parlay, not the total, and the slip shows the full cost before you confirm. How many legs are allowed and which bet types can go in vary by sportsbook, and legs from the same game are often blocked because their results are linked.

Three rules decide the payout:

• Each parlay inside the round robin wins only if all of its legs win.
• A losing leg kills every parlay that contains it and none of the others.
• A pushed or void leg is usually treated as odds of 1.00, so a parlay containing it pays at the odds of its remaining legs. A two-team parlay with one push becomes, in effect, a single bet on the other leg.

Some books grade pushes inside parlays differently, so read the house rules before you rely on that last point.

How to use the round robin calculator

The calculator opens with three legs at 1.91, 2.10 and 1.80, combinations by 2s and a stake of 10 per bet. In American odds those prices are roughly -110, +110 and -125.

• Type each price as your sportsbook shows it: 1.91, -110, 10/11 or evens all work, and formats can be mixed on one ticket.
• Set the result of each leg to Won, Lost or Push / void. Leave every leg on Won to see the full payout before the games start.
• Press Add selection for more legs, up to eight, or Remove last to drop one. The minimum is three.
• Choose the combination size, from by 2s to by 7s. The size cannot be larger than the number of legs.
• Enter the stake per bet as a plain number. There is no currency, so 10 means $10, £10 or 10 units of anything else.

The outputs are the number of bets, the total staked, the return for the results you set, the profit (return minus total staked, which can be negative) and the return if every leg wins. A push or void leg counts at odds of 1.00.

With the default inputs there are three doubles: 1.91 x 2.10 = 4.011, 1.91 x 1.80 = 3.438 and 2.10 x 1.80 = 3.78. At $10 each the ticket costs $30, and if all three legs win it returns 10 x (4.011 + 3.438 + 3.78) = $112.29, a profit of $82.29.

Set leg 2 to Lost and only the parlay without it survives: 10 x 3.438 = $34.38, a profit of $4.38. Set leg 2 to Push / void instead and the two parlays that contained it pay at the odds of their other leg: 10 x (1.91 + 1.91 x 1.80 + 1.80) = $71.48, a profit of $41.48. For a single parlay with no combinations, use the parlay calculator.

How many bets a round robin creates

The number of parlays is the number of ways to choose k legs from n, written n choose k. Multiply n down k times, then divide by k x (k - 1) x ... x 1. Four legs by 2s is (4 x 3) / (2 x 1) = 6. Five legs by 3s is (5 x 4 x 3) / (3 x 2 x 1) = 10. These are the common setups:

• 3 legs by 2s: 3 bets
• 4 legs by 2s: 6 bets
• 4 legs by 3s: 4 bets
• 5 legs by 2s: 10 bets
• 5 legs by 3s: 10 bets
• 6 legs by 3s: 20 bets
• 8 legs by 4s: 70 bets

The cost grows quickly. Eight legs by 4s at $5 per bet is $350, even though $5 sounds like a small stake. The total staked is the figure that matters, so multiply the bet count by the stake per bet before you confirm.

A ticket described as by 2s and 3s simply adds the two sizes. Four legs by 2s and 3s is 6 + 4 = 10 bets, and five legs by 2s and 3s is 10 + 10 = 20. The calculator handles one size at a time, so run it once for each size and add the stakes and returns together. Ticking every size up to the full parlay gives the US version of a full-cover bet: four legs by 2s, 3s and 4s is 6 + 4 + 1 = 11 bets, the same structure as a Yankee in the UK.

Round robin vs one big parlay: worked numbers

Using the three default legs, compare $30 on one three-team parlay with $30 spread across a round robin by 2s at $10 per bet.

• All three win. The parlay pays at 1.91 x 2.10 x 1.80 = 7.2198, so $30 returns $216.59. The round robin returns $112.29.
• Leg 2 (2.10) loses. The parlay returns nothing. The round robin returns $34.38.
• Leg 1 (1.91) loses. The parlay returns nothing. The round robin returns 10 x 3.78 = $37.80.
• Leg 3 (1.80) loses. The parlay returns nothing. The round robin returns 10 x 4.011 = $40.11.
• Leg 2 pushes. The parlay drops to 1.91 x 1.80 = 3.438 and returns $103.14. The round robin returns $71.48.

The round robin gives up about half of the top payout in exchange for staying alive after one loss, and with these prices a single loser still returns a few dollars more than the $30 staked. Two losers sink both tickets.

A four-leg example at the standard -110 price (1.909 in decimal) shows the same pattern. A two-team parlay at -110 is 3.645, a three-team parlay is 6.958 and a four-team parlay is 13.283.

• $60 on one four-team parlay returns $797.00 if all four win and nothing otherwise.
• $60 as a round robin by 2s ($10 x 6) returns $218.68 if all four win, $109.34 if three win (three parlays survive) and $36.45 if two win (one parlay survives).
• $40 as a round robin by 3s ($10 x 4) returns $278.32 if all four win and $69.58 if three win.

With three winners from four, the by 2s ticket makes $49.34 and the by 3s ticket $29.58, while the straight parlay loses $60. With all four, the parlay pays several times more. That is the trade a round robin makes: a smaller top-end payout that can survive a miss. Spreads at -110 are the everyday price in the NFL and NBA; our guide on how to bet on the NFL explains where that number comes from.

What a round robin really costs

A round robin feels safer than a parlay, but it is still a stack of parlays, and every one of them carries the bookmaker's margin on each of its legs.

Take legs that are genuine 50% chances priced at -110. A single returns 0.50 x 1.909 = $0.955 per $1 on average, a loss of about 4.5%. A two-team parlay wins 25% of the time and pays 3.645, so the expected return is 0.25 x 3.645 = $0.911, a loss of about 8.9%. A three-team parlay wins 12.5% of the time at 6.958, an expected return of $0.870 and a loss of about 13%. A round robin by 2s is made only of two-team parlays, so its expected loss is the two-team figure, about 8.9% of everything staked, whatever happens on a given night.

Two consequences follow. First, a round robin is not a hedge. Spreading money across more parlays smooths the swings but does not lower the expected loss per dollar, and it usually means more dollars are staked. The four-leg by 2s ticket above puts $60 into play on picks you could have bet as four $10 singles for $40. Second, the parlays inside a round robin share legs, so their results are linked. One bad leg costs you every parlay it appears in, which is why a two-from-four night leaves only one of six parlays standing.

None of this makes round robins pointless. If your prices are better than fair, the same compounding works in your favour, which is the case for any parlay. The guide to parlays and accumulators shows why the margin multiplies leg by leg, and the no-vig calculator shows how much margin a single price carries.

UK equivalents: Trixie, Yankee and combination bets

Outside the US the same idea is sold under fixed names. A full-cover bet includes every double, treble and accumulator (acca) from a set of selections, and some versions add singles. In round robin terms:

• Trixie: 3 selections by 2s and 3s, so 3 doubles and 1 treble (4 bets).
• Patent: a Trixie plus 3 singles (7 bets).
• Yankee: 4 selections by 2s, 3s and 4s (11 bets).
• Lucky 15: a Yankee plus 4 singles (15 bets).

UK bookmakers also take plain combination bets, such as all the doubles from four selections, which is a round robin by 2s under another name. Picture £1 doubles on four football (soccer) home wins at 6/4, 11/10, 4/5 and evens, or 2.50, 2.10, 1.80 and 2.00 in decimal. That is six £1 doubles costing £6. If all four win, the ticket returns £26.33. If the 6/4 shot loses, the three doubles without it return £3.78 + £4.20 + £3.60 = £11.58. The calculator works the same way: enter the four prices, choose by 2s and a stake of 1.

How each named bet is built, with a worked Trixie, is covered in the system bets section of parlays and accumulators explained. Some bookmakers attach extra terms to Lucky 15s and similar bets. Those terms vary and the calculator does not include them.

When a round robin makes sense, and when it does not

A round robin suits a specific situation: you have several picks you rate as good prices, you want some parlay upside, and you accept that one of them will probably lose. Plus-money underdogs are the classic case. Three underdogs at +150 (2.50) by 2s make three parlays at 6.25 each, so $10 per bet costs $30. If two of the three win, the one surviving parlay returns $62.50, a profit of $32.50 even though a pick lost. If all three win, the ticket returns $187.50.

It makes much less sense in these cases:

• Your legs are short favourites. With three legs at 1.50 by 2s, each parlay pays 2.25, and one loser leaves a single parlay returning $22.50 on $30 staked.
• You are adding picks to make the ticket bigger. Every extra leg raises the number of bets and the stake, and puts the margin to work on more money.
• You have no reason to think the prices are generous. Without an edge, the expected loss on a round robin is higher than on the same picks bet as singles.
• The total stake is more than your normal unit. Size the whole ticket, not the per-bet figure, against your bankroll.

If you want a structured way to judge whether a price is generous, the value betting guide sets out the method.

Before you place a round robin

Run through this before you confirm the ticket:

• Count the bets and multiply by the stake per bet. That is the real cost.
• Use the calculator to see what the ticket returns if one leg loses, and decide whether you are happy with that result.
• Compare each price with other books. A better price on one leg improves every parlay it appears in.
• Read how the sportsbook settles pushes, postponed games and void legs inside a round robin.
• Leave linked picks from the same game out, since many books refuse them and those that accept them price them differently.

A last worked example: five NBA spreads at -110, by 2s, $10 per bet. That is 10 bets and $100 staked. Five winners return $364.46, four return $218.68, three return $109.34 and two return $36.45. You need three of the five to show a profit, and then it is only $9.34. If each leg is a true 50% chance, three or more winners come in exactly half the time, while the expected loss stays at about 8.9% of the $100.

Check that sports betting is legal where you live and use a licensed sportsbook. Keep each ticket inside your bankroll management plan, and if bigger round robins start to feel like a way of chasing losses, the responsible gambling page lists where to get help.