Betting mathematics
Horse Racing Bet Calculator: Trifecta, Exacta & Payouts
Calculate horse-racing ticket combinations and costs, then scale a published payout to your winning stake. Exacta and trifecta payouts require the official dividend; win odds alone cannot determine them.
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Trifecta box calculator: combinations and cost
A trifecta requires the first three finishers in exact order. A box covers every possible finishing order of three of your chosen runners. With n runners, there are n × (n − 1) × (n − 2) combinations. Multiply by the stake per combination for the full ticket cost.
A three-runner trifecta box has 6 combinations; four runners have 24; five runners have 60. At $0.50 each, those tickets cost $3, $12 and $30. Selecting “Trifecta box” above calculates both the cost and return for your chosen size. A straight trifecta is one ordered combination, not a box.
Exacta, superfecta and quinella boxes
An exacta requires the first two finishers in order, so an n-runner box has n × (n − 1) combinations. Three runners make 6 exactas. A superfecta requires four in order: n × (n − 1) × (n − 2) × (n − 3). Four runners make 24 combinations; at $0.10 each, the ticket costs $2.40.
A quinella selects the first two in either order, so the box count is n × (n − 1) ÷ 2. Four runners make 6 pairs. Select the appropriate type above; a quinella dividend is not interchangeable with an exacta dividend. Wheels, keys, coupled entries and scratch substitutions require the operator’s ticket-specific rules and are not modeled.
How to calculate exacta or trifecta payout
Use the official return for the winning combination and its stated base stake. Return = winning stake ÷ dividend base × published dividend. Then subtract the cost of the entire ticket, including losing combinations, to find the net result. Do not multiply the dividend by every combination on a winning box.
For a $0.50 winning trifecta within a $12 box, a $120 dividend based on $1 gives $60 back and $48 net. An exacta or superfecta uses the same scaling rule with its own official dividend. These are pari-mutuel payouts: pool betting determines the dividend. Multiplying individual horses’ win odds cannot predict an exotic payout.
Pick 5 ticket calculator
Multiply the number of selections in each of five races, then multiply by the stake per combination. Two × three × one × two × four selections make 48 combinations; at $0.50, that is $24. All five selections on a combination normally need to win. Enter the applicable official dividend to model a return; consolation payouts, carryovers, jackpot restrictions and scratches are not inferred.
Win, place and show payouts
Select the straight-ticket option to scale one published win, place or show dividend. For example, a $5 winning place stake with a $6.40 return per $2 pays $16. Use each pool’s own dividend. The displayed win price does not tell you the place or show payout. For an across-the-board ticket, calculate each paying portion separately and subtract all three stakes.
For a fixed-odds win bet, use the horse-racing odds payout calculation. A fixed-odds win/place split at a fraction of the win odds belongs in the each-way bet calculator.
Daily Double and Pick 3, 4, 5 or 6 costs
Choose the ticket type and enter one selection count for each race. Multiply the counts to find the number of combinations, then multiply by your stake per combination. A Daily Double with 3 selections in each race has 9 combinations; at $2 each it costs $18. A Pick 4 with 2, 3, 1 and 4 selections has 24 combinations and costs $12 at $0.50 each.
The same horse number in different races represents separate selections, so no subtraction is needed across races. Within a single race, a horse cannot fill two finishing positions. Box calculations above handle that restriction. Keys, wheels, coupled entries and scratches require the exact selection sets and settlement rules; this count-based tool does not approximate them.
Methodology and references
For the underlying terminology, see TwinSpires wager types and ticket costs. This independent calculator uses the assumptions explained above; check your operator’s current settlement terms. The reference is not an endorsement or an account integration.