How Round Robin Bets Work: You Are Buying Parlays, and the Vig Never Shrinks
A round robin looks like one bet. The sportsbook books the ticket as many bets. Pick four teams, choose "by 2's," and you own six separate two-leg parlays, each with its own stake and its own house edge.
The pitch is partial coverage. One loser no longer kills the ticket. The coverage is real. The part the bet slip leaves out: partial coverage changes how your results swing. The price per dollar stays the price of a parlay. A round robin built from two-leg parlays loses money at the two-leg parlay rate, every time, no matter how many teams you add.
This guide counts the tickets, prices the vig, checks the math against state revenue reports, and shows the one round robin size a 2026 economics paper says a bettor with an edge should ever use.
What the Sportsbook Builds When You Hit Round Robin
FanDuel's betting guide describes the product plainly. You add three or more selections, pick the Round Robin option, and the book builds every parlay of the size you choose, labeled "By 2's," "By 3's," and so on. The amount you type is the stake for each parlay, not the whole ticket. Your total risk is the per-parlay stake times the number of parlays. FanDuel also blocks selections from the same game from going into one round robin.
Action Network's walkthrough of the DraftKings and FanDuel slips shows the same structure: four teams by 2's produces 6 bets, and a $5 stake per parlay means $30 out of your account.
The number of parlays is a combination count. With n teams and parlays of k legs, the book builds C(n, k) tickets.
How many tickets you are buying
C(n, k) = n! / (k! × (n - k)!)
4 teams by 2's: 4! / (2! × 2!) = 6 parlays
5 teams by 3's: 5! / (3! × 2!) = 10 parlays
Every size from 2 up to n: 2^n - n - 1 parlays
| Teams | By 2's | By 3's | Every size | Cost at $10 a parlay, by 2's |
|---|---|---|---|---|
| 3 | 3 | 1 | 4 | $30 |
| 4 | 6 | 4 | 11 | $60 |
| 5 | 10 | 10 | 26 | $100 |
| 6 | 15 | 20 | 57 | $150 |
| 7 | 21 | 35 | 120 | $210 |
| 8 | 28 | 56 | 247 | $280 |
Read the last column before you read anything else. An eight-team round robin by 2's at $10 a parlay is a $280 position. If your normal straight bet is $10, the round robin is 28 of them at a worse price.
The Payout Map for a Three-Team Round Robin
Take three games at -110, by 2's, $10 per parlay. A -110 leg pays 1.9091 in decimal odds. A two-leg parlay pays 1.9091 × 1.9091 = 3.6446, so a $10 parlay returns $36.45, a $26.45 profit.
Here is every outcome next to the two obvious alternatives with the same $30: three $10 straight bets, or one $30 three-leg parlay.
| Winning legs | Round robin by 2's ($30) | Three $10 straights | One $30 three-leg parlay |
|---|---|---|---|
| 3 of 3 | +$79.34 | +$27.27 | +$178.74 |
| 2 of 3 | +$6.45 | +$8.18 | -$30.00 |
| 1 of 3 | -$30.00 | -$10.91 | -$30.00 |
| 0 of 3 | -$30.00 | -$30.00 | -$30.00 |
Two of three is the scenario the round robin sells. One parlay cashes and you clear $6.45. The three straights clear $8.18 on the same results. One winner out of three costs you the full $30 in the round robin and $10.91 in straights. The round robin sits between the parlay and the straights on every row. You pay for the middle position with a higher vig rate, shown next.
The Vig Per Dollar: (1 - m) to the Power of the Legs
Karl Whelan of University College Dublin states the core result in his 2026 paper on parlays. If a book's margin on each leg is m, the expected return on an N-leg parlay is (1 - m) raised to the N. Each leg multiplies the house edge back in.
At -110 on a true coin flip, one leg returns 0.5 × 1.9091 = 0.9545 per dollar. The expected loss is 4.55%. Stack the legs and the loss grows.
| Legs at -110 | Payout per $1 | Fair payout per $1 | Expected loss per $1 |
|---|---|---|---|
| 1 (straight) | 1.909 | 2.000 | 4.55% |
| 2 | 3.645 | 4.000 | 8.88% |
| 3 | 6.958 | 8.000 | 13.03% |
| 4 | 13.283 | 16.000 | 16.98% |
| 5 | 25.359 | 32.000 | 20.75% |
A round robin by 2's is a stack of two-leg parlays, so every dollar in the ticket carries the 8.88% rate. Spreading the money across more combinations does not dilute the rate. Six two-leg parlays at 8.88% each lose 8.88% in total.
Expected cost of the same $30, three ways (each leg a true 50%)
Three $10 straights: $30 × -4.55% = -$1.36
Round robin by 2's: 3 × $10 × -8.88% = -$2.67
One three-leg parlay: $30 × -13.03% = -$3.91
The round robin costs about twice what the straights cost on identical picks. The partial coverage is real. You buy the coverage with a second layer of vig.
What the State Reports Show
Regulators publish what the formula predicts. Whelan's paper reproduces New Jersey's figures. In 2025, parlays were 32% of the state's sports betting handle and 65% of sportsbook gross revenue. Books kept 19.2% of parlay handle and 4.9% of everything else.
| New Jersey | Parlay handle | Parlay hold | Non-parlay hold |
|---|---|---|---|
| 2021 | $2.48B | 17.5% | 4.0% |
| 2022 | $2.44B | 18.4% | 3.3% |
| 2023 | $2.96B | 18.3% | 5.0% |
| 2024 | $3.67B | 17.5% | 4.8% |
| 2025 | $3.94B | 19.2% | 4.9% |
The pattern holds beyond one state. InGame's 2025 year-end review totaled the six states reporting parlay results: Illinois, New Jersey, Maryland, Colorado, Oregon, and Mississippi. Books won $2.11 billion on $11.34 billion of multi-leg handle, an 18.63% hold. Maryland held 21.08% and Mississippi 23.06%.
Now check the table above against those numbers. A five-leg parlay at -110 predicts a 20.75% loss rate. Whelan cites Juice Reel data, reported by Citizens Bank, showing the average parlay grew from 4.2 legs in January 2022 to 5.0 legs in January 2024. Five legs at standard juice lands within two points of New Jersey's 19.2% hold. The math in the bet slip and the math in the state filings agree.
With an Edge, the Edge Compounds Too
The honest case for parlays starts here. If each leg wins more often than the price implies, the parlay compounds your edge the same way the vig compounds against a coin flip.
Same -110 legs, true win rate 54%
Straight: 0.54 × 1.9091 - 1 = +3.09%
Two legs: 0.54² × 3.6446 - 1 = +6.28%
Three legs: 0.54³ × 6.9579 - 1 = +9.56%
Higher expected return per dollar, so why not build long? Because expected return is the wrong yardstick when you size bets to grow a bankroll. A three-leg parlay at 54% per leg hits 15.7% of the time. The swings are huge, and the right stake shrinks to match.
Whelan models this directly. He takes a bettor with an edge, sizes every option at its utility-maximizing stake, and asks which parlay length wins. Under log utility, the Kelly criterion case, his thresholds are:
- Prefer a two-leg parlay over separate bets only when each leg wins more than 33.5% of the time.
- Prefer three legs over two only when each leg wins more than 52.6% of the time.
- Prefer four legs over three only above 63.4%.
- Prefer five legs over four only above 70.3%.
The thresholds barely move with risk tolerance or edge size. A low-risk-aversion bettor prefers two legs to one at 32.7% and a highly risk-averse one at 33.6%. Spreads, totals, and most props price near 50%. Whelan's conclusion for those legs: two legs at most, or no parlay at all. He also notes the contradiction in common betting advice. "Use parlays to compound your edge" and "size with Kelly" point in opposite directions past two legs.
Apply the thresholds to the round robin menu. By 2's on legs near even money is the only size consistent with the paper. By 3's needs every leg above 52.6% true probability, an edge most bettors never hold on a full card. Every-size round robins, the 11, 26, and 57-ticket bundles, fail the test outright.
The Shared-Leg Problem
The tickets inside a round robin are not independent. In a by 2's round robin, each team appears in n - 1 of the parlays. One loss wipes out every ticket holding the losing leg.
Four teams by 2's, $10 a parlay, $60 total, all at -110:
| Winning legs | Parlays cashed | Net result |
|---|---|---|
| 4 of 4 | 6 | +$158.68 |
| 3 of 4 | 3 | +$49.34 |
| 2 of 4 | 1 | -$23.55 |
| 1 of 4 | 0 | -$60.00 |
| 0 of 4 | 0 | -$60.00 |
You need three of four to profit. Going 2 and 2 is a coin-flip night for straight bettors and a $23.55 loss for the round robin. The same structure sets your sizing. If your Kelly stake on one leg is 1% of bankroll, a by 2's round robin on four legs puts the same leg in three tickets. Size the whole bundle from the leg count, not from the per-parlay box on the slip. The quarter-Kelly guide and the Kelly calculator cover the single-bet math.
Correlation inside a game is a separate issue. FanDuel already blocks same-game legs in round robins. For same-game pricing, see the SGP correlation math.
Calculator: What Your Round Robin Costs
Enter each leg's American odds, separated by commas, pick the parlay size, and set your stake per parlay. Set a true win probability per leg to see expected value. At 50%, you see the pure vig cost. Leave the probability blank to use each leg's no-vig break-even, which shows zero edge.
Round robin cost and expected value
When a Round Robin Is the Right Ticket
- Every leg is a bet you would place as a straight bet at the posted price. Check each one against the market's fair line with the no-vig calculator first.
- The size is by 2's. By 3's needs every leg above 52.6% true probability.
- The legs come from different games. Shared outcomes turn six tickets into one bet with extra vig.
- You sized the total stake, not the box on the slip. Multiply the per-parlay amount by the ticket count before you confirm.
- You track each leg's closing line, not each ticket's result. The CLV guide explains the tracking.
One more use case shows up in limited accounts. Some books cap straight bets on sharp accounts and leave parlay limits looser. A by 2's round robin on positive-CLV legs keeps volume on the same picks. You pay the 8.88% coin-flip rate on any leg without an edge, so the trade only works on legs with a record of beating the close. The limits guide covers how books flag accounts.
Want legs to test these rules on? Read the free picks in the free Discord room. No card needed.
The verdict: a round robin is a bundle of parlays, and each dollar in the bundle pays the parlay rate. By 2's at -110 costs 8.88% per dollar on coin flips, about twice the 4.55% on straights. New Jersey kept 19.2% of parlay handle in 2025, close to what five -110 legs predict. With a real edge, Whelan's 2026 utility math caps the useful size at two legs for anything near even money. Build by 2's from bets you would make anyway, or bet the legs straight.
Sources and Method
FanDuel's betting guide supplies the product rules: per-parlay stakes, By 2's and By 3's groupings, and the same-game restriction. Action Network's slip walkthrough supplies the six-bet, $30 example. Whelan's 2026 paper supplies the (1 - m) to the N result, the optimal leg-length thresholds, the New Jersey parlay table, and the Juice Reel leg-count figures. InGame's year-end review supplies the six-state 2025 parlay hold. Kelly's 1956 paper is the source of the log-utility sizing rule behind Whelan's middle column. Every payout, count, and expected value in the tables comes from the formulas shown, and you recompute each one in a spreadsheet with COMBIN and PRODUCT.
Limits: the coin-flip tables assume each leg is a true 50% at -110. Real legs carry different prices and different margins, which is why the calculator takes your own odds. State hold figures include same-game parlays and longshot-heavy tickets, so the 19.2% is a market average, not the cost of any one ticket.