Ticket cost calculator
Trifecta box cost calculator
Enter the number of horses in your box and the base amount charged for each combination. The result updates automatically.
Formula: P(n, 3) = n! / (n - 3)!
4 x 3 x 2 = 24 combinations
Enter a whole number from 3 to 20 and a base amount from $0.01 to $100.
This tool calculates ticket cost only. Minimums, wagering menus, and pool availability vary by host track and race; confirm the displayed total before submitting a wager.
The cost tables
A trifecta asks you to pick the first three finishers in exact order. Boxing horses covers every possible order among them, and you pay for every combination separately. These are the standard costs at the two most common base amounts.
| Horses in the box | Combinations | $0.50 base | $1 base |
|---|---|---|---|
| 3 horses | 6 | $3 | $6 |
| 4 horses | 24 | $12 | $24 |
| 5 horses | 60 | $30 | $60 |
| 6 horses | 120 | $60 | $120 |
| 7 horses | 210 | $105 | $210 |
| 8 horses | 336 | $168 | $336 |
How the math works
The formula is the number of horses multiplied by one fewer, multiplied by two fewer: N x (N-1) x (N-2). With four horses that is 4 x 3 x 2 = 24 combinations. Multiply the combinations by your base amount and you have the ticket cost.
The count grows this fast because order matters in a trifecta. Four horses can fill the top three spots in 24 different sequences, and the box buys every one of them. Only one sequence can actually happen, so 23 of those 24 combinations are guaranteed losers before the gate opens.
Box, straight, or key
A straight trifecta costs one combination: a $1 straight 5-3-7 costs $1. A box covers every order for the same horses. A key sits in between: you single one horse in a position, usually first, and cover the others behind it.
Keying is one way to cut the combination count. A $1 trifecta keying one horse to win over four others (1 x 4 x 3) costs $12 instead of the $60 it would take to box all five. The trade is narrower coverage: if the key horse runs second, the whole ticket loses.
A box is really a statement that you have no opinion about order among those horses. That is sometimes true. But if you like one horse clearly best, the box is paying full price for combinations you don't believe in.
Minimums vary by track and pool
Most major wagering menus offer a $0.50 trifecta (Del Mar's official menu lists one, and TwinSpires' wagering FAQ notes its menu mirrors each host track's), but minimums are set per track and per pool. Check the specific race's wagering menu before building a ticket around a price.
Common questions
Is a $0.50 trifecta box worth half of a $1 box?
Yes. The base amount scales the payout proportionally. If a $1 trifecta pays $240, the same combination at $0.50 pays $120. The smaller base simply lets you cover the same horses for half the ticket cost.
Can I box more than eight horses?
Usually yes, up to the field size, but the cost keeps multiplying: a $1 ten-horse box is 720 combinations, or $720, while the payout still comes from the single combination that wins. Wider coverage raises the ticket price much faster than it raises what a winning ticket returns.
Does a trifecta box pay more than a straight trifecta?
No. The winning combination pays the same whether it came from a box or a straight ticket at the same base amount. The box just bought more losing combinations along with the winning one.
Further reading