A small unit size can hide a surprisingly expensive betting slip.
A bettor selects six teams, chooses several round robin sizes, and enters $2 per wager. The stake looks modest—until the slip generates dozens of separate combinations. That $2 is not the total bet; it is charged to every wager created.
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The key number before submission is total exposure: the full amount at risk if every listed wager is accepted. Sportsbooks usually display it near the bet button, but calculating it independently helps catch an accidental selection or misunderstood stake field. If the total feels too high, reducing the unit stake or removing a round robin size brings the cost down immediately.
- Total exposure = number of wagers × stake per wager.
- For example, 35 wagers at $2 each create $70 in total exposure.
Enter the bet details
A calculator starts with selections: the individual teams, players, or outcomes being considered. The round size states how many selections belong in each wager—2s for doubles, 3s for trebles, and so on.
Six selections played by 3s therefore means every eligible three-pick grouping, not six wagers containing three picks. There are 20 unique combinations because (\binom{6}{3}=20). This distinction is central to how round robin wagers work: selections are the original picks, while combinations are the wagers created from them.
A banker, sometimes called a fixed pick, must appear in every combination. With one banker among six selections played by 3s, the calculator fixes that pick and chooses the other two from the remaining five, producing 10 wagers.
Finally, the stake field must be interpreted correctly. Most calculators use a stake per combination; some allow a total stake that is divided across all wagers. The field label should be checked before accepting the displayed outlay.
Calculate the number of combinations
The number of wagers in a round robin is calculated with the combinations formula:
[ \binom{n}{r}=\frac{n!}{r!(n-r)!} ]
Here, n is the total number of selections and r is the number included in each wager. The exclamation mark denotes a factorial: for example, (5! = 5 × 4 × 3 × 2 × 1).
For five selections played by 2s, the calculation is:
[ \binom{5}{2}=\frac{5!}{2!3!}=10 ]
Labeling the selections A through E makes those 10 doubles easy to see:
- AB, AC, AD, AE
- BC, BD, BE
- CD, CE
- DE
AB and BA are the same double, not separate wagers. A combination depends only on which selections appear together; their written order does not matter. Counting both arrangements would incorrectly double the wager total.
Quick combination lookup
| Selections | By 2s | By 3s | By 4s |
|---|---|---|---|
| 3 | 3 | 1 | — |
| 4 | 6 | 4 | 1 |
| 5 | 10 | 10 | 5 |
| 6 | 15 | 20 | 15 |
| 7 | 21 | 35 | 35 |
| 8 | 28 | 56 | 70 |
A dash means the requested wager size exceeds the number of available selections.
Add wagers across round sizes
When several round sizes are selected, each size generates its own set of combinations. Those counts are then added; they are not blended into a new combination calculation.
For five picks played by 2s and by 3s:
| Round size | Calculation | Wagers |
|---|---|---|
| Doubles | C(5,2) | 10 |
| Trebles | C(5,3) | 10 |
| Combined | 10 + 10 | 20 |
The grouped output matters because it shows exactly where the wager count comes from: 10 distinct doubles and 10 distinct trebles. The combined total is 20 wagers.
This distinction also prevents a common mistake—seeing “10” for one round size and assuming it covers the full bet. If both round sizes are active, both groups contribute to the final count.
Adjust for required bankers
Under the common operator convention, every required banker appears in every wager. If there are n total selections, b bankers, and a round size of r, the count is:
C(n − b, r − b)
For example, two bankers plus five other selections played as fourfolds produce C(5, 2) = 10 wagers. A round smaller than the number of bankers is invalid; a round equal to that number creates one wager containing only the bankers.
The mathematical result can still exceed the number accepted. Sportsbooks may remove combinations involving unavailable markets, suspended selections, incompatible bet types, or prohibited same-event relationships. Rules differ between operators, so these exclusions are not always predictable from a standalone calculator.
Before submission, compare the calculation with the bet slip’s eligible-wager count. That displayed figure is the final count for stake and exposure calculations.
If the calculated and displayed totals differ, do not multiply the stake by the theoretical total. Use the sportsbook’s eligible-wager count after all exclusions.
Set the stake and total risk
A round robin’s stake may mean either the amount on each wager or the total amount risked. Confusing the two can make a modest-looking entry cost far more than expected.
Use these equations to move in either direction:
- Total stake = number of wagers × stake per wager
- Stake per wager = total stake limit ÷ number of wagers
For example, a round robin containing 20 wagers at $2 each has a total stake of:
20 × $2 = $40
The bet slip therefore risks $40—not $2. Any projected return should be judged against that full outlay.
A preset unit limit makes the reverse calculation useful. First calculate the betting-unit value, then convert the session limit into dollars. If the round robin is capped at 20 units and one unit equals $2, the maximum total stake is $40; divided across 20 wagers, that permits $2 per wager.
If the same bet has only a $20 limit, the appropriate stake becomes $20 ÷ 20 = $1 per wager. Rounding down may be necessary when a sportsbook accepts only fixed stake increments.
Price each combination separately
A round robin does not carry one universal payout. Each ticket contains a different subset of selections, so its price comes from the odds on those legs. A standard parlay payout calculation can verify the arithmetic for any one ticket.
Convert and multiply
Decimal odds make calculation direct. Positive American odds convert as 1 + odds/100; negative odds as 1 + 100/|odds|. Thus, +150 becomes 2.50 and -200 becomes 1.50. For a double at 2.50 and 1.80, the combined decimal price is 2.50 × 1.80 = 4.50.
Ticket gross return equals stake × combined price. At a $5 stake, that double returns $22.50 if both legs win. Every other double or treble must be priced from its own included selections.
Add settled tickets
After settlement, add returns only from winning tickets. If three $5 wagers return $22.50, $18, and $0, the gross return is $40.50. Profit is gross return minus the full round-robin stake, including losing tickets—not merely stakes attached to winners.
Pushes and voids usually remove that leg and recalculate the ticket at lower odds; a voided double may become a single. House rules may instead void certain markets or entire tickets. Final settled prices should therefore replace the odds originally entered.
Audit a four-pick round robin
Label the four selections A, B, C, and D. Playing them by 2s and 3s creates every possible double and treble, with no importance attached to order.
List every wager
| Round size | Generated tickets | Count |
|---|---|---|
| Doubles | AB, AC, AD, BC, BD, CD | 6 |
| Trebles | ABC, ABD, ACD, BCD | 4 |
| Total | 10 |
The count can be checked with combinations: (\binom{4}{2}=6) doubles and (\binom{4}{3}=4) trebles. This written list is also a practical audit—it makes duplicated or omitted tickets easy to spot.
At a $5 stake per wager, the exposure is:
- Doubles: 6 × $5 = $30
- Trebles: 4 × $5 = $20
- Total: 10 × $5 = $50
The stake is not $5 for the whole round robin. It applies separately to each of the ten tickets.
Trace one losing pick
Suppose C loses, while A, B, and D win. Every ticket containing C loses immediately.
- Surviving doubles: AB, AD, BD
- Losing doubles: AC, BC, CD
- Surviving treble: ABD
- Losing trebles: ABC, ACD, BCD
Four tickets survive: three doubles and one treble. Six tickets lose, showing how one failed selection affects more wagers in larger combinations. Actual profit still depends on the individual odds: the four winning returns must be added together, then compared with the full $50 exposure—not merely the $20 staked on surviving tickets.
Run the pre-bet check
- Verify every input
Match the calculator’s selections, odds, bankers, and chosen round sizes against the bet slip.
- Check selection eligibility
Confirm that the sportsbook permits every market combination. Related outcomes or operator restrictions may exclude some wagers.
- Recheck the wager count
Compare the calculated combinations with the number of wagers shown on the slip, including every selected round size.
- Confirm the staking mode
Establish whether the displayed stake applies to each wager or to the whole round robin; confusing the two can multiply exposure.
- Apply the risk limit
Compare total exposure with the preset bankroll limit. If it is too high, lower the unit stake, remove a round size, or reconsider using a multi-leg format.
- Match the sportsbook total
Do not submit until the calculator’s expected outlay agrees with the sportsbook’s final total, allowing for any excluded combinations.