64→ Racing
What your ticket costs
Pick the bet and your horses. The calculator counts the combinations, multiplies them by the programme base and shows the chance of hitting, blind and by the win board.
Your horses, any order
Chance model
This ticket costs $12,000 and has 6 combinations: it pays if one of them is exactly the result.
Your combinations
- 3–4–7
- 3–7–4
- 4–3–7
- 4–7–3
- 7–3–4
- 7–4–3
Show the formula
Box of n horses: exacta and trifecta count every order, n × (n − 1) × ...; imperfecta counts pairs, n × (n − 1) ÷ 2.
Key by place: every way to take one horse from each place, never the same horse twice.
Cost = combinations × base
Harville: P(i first, j second) = p(i) × p(j) ÷ (1 − p(i)); p from 1 divided by each dividend.
The maths of a box
cost = combinations × base
Example: Trifecta box with 4 horses: 24 combinations × $2,000 = $48,000.
Combinations by number of horses
| Horses | Exacta | Quinella | Trifecta | Superfecta |
|---|---|---|---|---|
| 2 | 2 | 1 | – | – |
| 3 | 6 | 3 | 6 | – |
| 4 | 12 | 6 | 24 | 24 |
| 5 | 20 | 10 | 60 | 120 |
| 6 | 30 | 15 | 120 | 360 |
Box: every order of your horses. The quinella (imperfecta) has no order, so it counts half as many as the exacta.
Box or key
- BoxYour horses may finish in any order. With 5 horses a trifecta box already costs $120,000.
- KeyYou choose who goes in each place. One fixed first, two second and four third make 6 combinations: $12,000.
- Several racesIn the double, pick 3 and pick 4 the horses of each race multiply. Two, three, one and two: 12 combinations, $24,000.
Blind or by the board
Blind
- With 8 horses there are 336 possible trifectas
- A single one hits 0.30% of the time
- Three horses boxed: 1.8%
By the win board
- Uses what each horse would pay
- Harville model (1973)
- Those three, with the board of race 10 at San Isidro on 28 October: 16.1%
More racing
Questions
What is a trifecta box?
Playing several horses for the first three places in any order. With three horses it is 6 tickets, one for each possible order.
What is the ticket base?
What each combination costs. The racecourse sets it and prints it in the programme; at San Isidro on 1 November 2026 it was $2,000 for the exacta and the trifecta.
Does the Harville model pick the winner?
No. It takes the probabilities the public gives each horse and works out, with a formula, the chance of each finishing order. It is an approximation.
How much does a ticket return on average?
Less than it costs. The levy comes off the pool before it is shared: at San Isidro, at most 28%. Playing more combinations raises the chance of hitting, but also the cost: the average does not improve.