Round Robin Calculator — Parlay Combinations and Payouts

A round robin turns a list of picks into every smaller parlay that can be made from them, each one a separate bet. To price one:

1. Choose the number of selections (3 to 8 — the range US sportsbooks allow).
2. Tick the parlay sizes you want. "By 2's" means every two-team parlay, "By 3's" every three-team parlay, and so on. Each chip shows how many parlays that size creates. You can tick several sizes at once, just as on a betting slip.
3. Enter the stake per parlay. The total stake (number of parlays × stake) updates as you go.
4. Enter the odds of each leg in American, decimal or fractional format. The format switch at the top is saved for all CalcVault betting calculators.
5. Leave every leg on Win to see the maximum payout. Once games finish, mark legs as Loss or Push to settle the round robin.

The results show:

• the number of parlays by size, the total stake and the maximum payout and profit;
• an "if some legs lose" table: for every number of winning legs, how many parlays cash and the range of returns, from the cheapest legs winning to the longest-priced ones;
• the full list of parlays with combined odds, payout and, once you mark results, whether each one won, lost or was void.

Share results copies a link with every leg, size, stake and result, so the round robin opens exactly as you built it.

Number of parlays

The number of k-team parlays from n picks is the binomial coefficient C(n, k) = n! ÷ (k! × (n − k)!). A round robin over several sizes adds them up.

• 3 picks by 2's: C(3, 2) = 3 parlays
• 4 picks by 2's and 3's: C(4, 2) + C(4, 3) = 6 + 4 = 10 parlays
• 8 picks, every size from 2 to 8: 2⁸ − 1 − 8 = 247 parlays

Total stake

Total stake = number of parlays × stake per parlay. Sportsbooks take your entered amount per parlay, so a $10 round robin of 4 picks by 2's costs $60, not $10.

Payout of each parlay

A parlay pays stake × D₁ × D₂ × … × Dₖ, where D is each leg's decimal odds. One losing leg makes the whole parlay lose. The maximum payout of the round robin is the sum over all parlays when every leg wins.

Pushes and voids

A pushed (tied) or void leg is taken out of every parlay it is in. Its odds count as 1.00, so a three-team parlay with one push is paid as a two-team parlay. A parlay whose legs all push is void and the stake comes back. This is how US sportsbooks settle them.

"If w of n win"

With w winning legs and the rest losing, the parlays that cash are the ones made only of winners: C(w, k) for each size k. How much they return depends on which legs won, so the calculator works out every possible set of winners and shows the lowest and highest total return.

Example 1 — 3 picks by 2's at -110

Three NFL sides at -110 each, $10 per parlay:

• Parlays: C(3, 2) = 3 · Total stake: $30
• Each two-team parlay: 1.909 × 1.909 = 3.645 → $36.45
• All three win: $109.34 returned, $79.34 profit
• Two of three win: one parlay cashes → $36.45 returned, a $6.45 profit

A single three-team parlay on the same picks would have lost everything with one miss. That is the trade a round robin makes: a smaller top prize for a cushion against one loss.

Example 2 — 4 picks by 2's and 3's, one loss

Legs at -110, +120, +150 and -150; $5 per parlay:

• Parlays: 6 two-team + 4 three-team = 10 · Total stake: $50
• All four win: $300.55 returned, $250.55 profit
• The +150 leg loses: 4 parlays win and 6 lose → $90.24 returned, a $40.24 profit
• Any three of the four win: $90.24 to $124.86 returned, depending on which leg misses

Example 3 — a push

Three legs at -110 by 2's for $10, and leg 1 pushes. The two parlays with leg 1 are paid as straight bets on the other leg ($19.09 each); the parlay of legs 2 and 3 pays $36.45. Total return: $74.63 on $30, a $44.63 profit.

Round robin or parlay?

For one all-or-nothing ticket, the Parlay Calculator is the simpler tool. UK bettors who bet fixed full-cover combinations on four picks can use the Lucky 15 Calculator, and the Accumulator Calculator handles a single acca in decimal odds.