How do you count a trifecta formation?

Pick one horse each from the 1st, 2nd and 3rd candidates and count every combination in which no horse appears twice. With 1st: 1, 2; 2nd: 1, 2, 3, 4; 3rd: 1–6, there are 3 × 4 = 12 combinations when 1 wins and another 12 when 2 wins, 24 in total (2,400 yen). It is not simply 2 × 4 × 6 = 48.

How many combinations is a trifecta wheel with one key horse multi or two key horses multi?

With m other horses, one key horse multi is 3 × m × (m − 1) combinations, so 60 with 5 other horses. Two key horses multi is 6 × m, so 30 with 5 other horses. A one key horse wheel with the key horse fixed in 1st is m × (m − 1) (20 with 5 other horses).

How do you calculate combined odds?

Add up the reciprocals of the odds and take the reciprocal of the sum. For three bets at 3.5, 6.0 and 12.0, it is 1 ÷ (1/3.5 + 1/6 + 1/12) ≈ 1.87. Splitting 3,000 yen so every bet pays about the same gives stakes of 1,600, 900 and 500 yen and payouts of 5,600, 5,400 and 6,000 yen.

What is a losing win (torigami)?

It is when your bet wins but the payout is less than the total you spent. If you buy 10 combinations at 100 yen each, you spend 1,000 yen, so any bet with odds under 10.0 loses money even when it wins (8.0 pays 800 yen). It gets more likely the more you spread your bets, so check the combined odds and stake allocation first.

When can you buy a same-bracket bracket quinella?

Only when there are 2 or more horses in that bracket. In JRA races, a second horse goes into the outer bracket (bracket 8) from 9 runners; with 16 runners every bracket has 2 horses, and with 18 runners brackets 7 and 8 have 3. In a 10-runner race, the only same-bracket pairs are 7-7 and 8-8.

Horse Racing Bet Calculator | Number of Combinations and Cost for Trifecta, Trio, Exacta, Quinella, Quinella Place and Bracket Quinella by Box, Key Horse Wheel (1 or 2 Key Horses, Multi) and Formation, Full List of Bets, Combined Odds, Losing-Win (Torigami) Check and Stake Allocation, WIN5 Combinations, Combination Charts and Post Position Bracket Chart

The Horse Racing Bet Calculator answers “how many combinations is this bet, and how much will it cost?” and “how far can I spread my bets before a win still loses money?” before you buy tickets. Choose the bet type (win, place, bracket quinella, quinella, quinella place, exacta, trio or trifecta) and the way you bet (box, key horse wheel or formation), then tap the horse numbers, shown in their post-position bracket colours. It counts the real number of combinations with duplicates removed, multiplies by the stake per combination (in units of 100 yen) and lists every bet in the form 1→2→3. Wheels support one or two key horses, a fixed finishing position for the key horse in exactas and trifectas (1st, 2nd or 3rd) or multi, and wheeling to all runners. For the bracket quinella it also checks, from the field size, whether a same-bracket pair can be bought. In the combined odds tab, paste the bets with their odds to get combined odds = 1 ÷ (sum of 1/odds), the bets that would lose money even if they win when you bet 100 yen on each, and a stake allocation that spreads your budget in 100 yen units so every winning bet pays about the same (dutching). It also counts WIN5 combinations (the product of the picks in five races), and includes box and wheel combination charts, the payout rate of each bet type and the number of combinations in an 18-runner race, a chart of horse numbers in each bracket by field size, and a glossary of box, wheel, multi, formation and losing wins.

Count combinations and cost

Choose a bet type and how to bet, then tap horse numbers to see the number of combinations, the total cost and the list of bets.

Bet type

Pick the top 3 horses in exact order

Runners

horses

How to bet

1st

2nd

3rd

Stake per combination

yen

Bets are bought in units of 100 yen.

Combinations

Trifecta Formation

Total cost

2,400 yen

100 yen each

All combinations in this field

3,360 combinations

0.7% of all

List of bets

1→2→31→2→41→2→51→2→61→3→21→3→41→3→51→3→61→4→21→4→31→4→51→4→62→1→32→1→42→1→52→1→62→3→12→3→42→3→52→3→62→4→12→4→32→4→52→4→6

WIN5 combinations

Enter how many horses you pick in each of the five races to get the number of combinations (their product) and the cost. WIN5 costs 100 yen per combination.

Race 1Race 2Race 3Race 4Race 5

Combinations

2 × 3 × 1 × 4 × 2

Total cost

4,800 yen

ABOUT

About Horse Racing Bet Calculator | Number of Combinations and Cost for Trifecta, Trio, Exacta, Quinella, Quinella Place and Bracket Quinella by Box, Key Horse Wheel (1 or 2 Key Horses, Multi) and Formation, Full List of Bets, Combined Odds, Losing-Win (Torigami) Check and Stake Allocation, WIN5 Combinations, Combination Charts and Post Position Bracket Chart

The Horse Racing Bet Calculator counts the combinations and total cost of trifecta, trio, exacta, quinella, quinella place, bracket quinella and other bets placed as a box, a key horse wheel (one or two key horses, multi) or a formation. It also lists every bet, works out combined odds and losing wins, allocates your stake so every winning bet pays about the same, and counts WIN5 combinations.

How to use Horse Racing Bet Calculator | Number of Combinations and Cost for Trifecta, Trio, Exacta, Quinella, Quinella Place and Bracket Quinella by Box, Key Horse Wheel (1 or 2 Key Horses, Multi) and Formation, Full List of Bets, Combined Odds, Losing-Win (Torigami) Check and Stake Allocation, WIN5 Combinations, Combination Charts and Post Position Bracket Chart

1In “Count bets”, choose the bet type (trifecta, quinella, etc.), the number of runners and the way you bet (box, key horse wheel or formation)
2Tap horse numbers to select them. For a wheel, choose the key horses and the other horses; for a formation, choose the candidates for 1st, 2nd and 3rd (for a trio: 1st, 2nd and 3rd pick)
3Choose the stake per combination and check the number of combinations, the total cost and the list of bets
4Press “Calculate combined odds for these bets” and add the odds after each bet
5In “Combined odds & stakes”, check the combined odds, the bets that would lose money and how to split your budget

Great for

Checking how many combinations a trifecta formation is before you buy it
Working out the combinations and cost of a trifecta wheel with one or two key horses and multi
Finding how many horses you can box and stay within your budget
Checking the odds to make sure spreading your bets will not turn a win into a loss
Splitting your budget across bets so that any winning bet pays about the same
Looking up which brackets allow a same-bracket bracket quinella and which horse numbers are in each bracket

Good to know

The count is not taken from a formula: the tool actually lists the combinations and removes those with the same horse twice and duplicates. The same horse in several formation columns is never counted twice.
A trio formation groups the three horses chosen from the 1st, 2nd and 3rd pick candidates into one bet regardless of finishing order.
Combined odds = 1 ÷ (1/odds 1 + 1/odds 2 + …). The stake allocation adds 100 yen at a time to the bet with the lowest payout (stake × odds), so the payouts are as even as possible.
The payout is odds × stake, with amounts under 10 yen rounded down. Odds change until betting closes, so recheck them with the odds just before you buy.
The bracket quinella is not sold for races with 8 or fewer runners. With 9 or more runners, the outer brackets (from bracket 8) get 2 or 3 horses, and a same-bracket pair can be bought only for a bracket with 2 or more horses.
In Japan you must be 20 or over to buy betting tickets. This tool gives estimates of combinations and cost; follow JRA's guidance when you actually buy.

Questions this tool answers

Use Horse Racing Bet Calculator | Number of Combinations and Cost for Trifecta, Trio, Exacta, Quinella, Quinella Place and Bracket Quinella by Box, Key Horse Wheel (1 or 2 Key Horses, Multi) and Formation, Full List of Bets, Combined Odds, Losing-Win (Torigami) Check and Stake Allocation, WIN5 Combinations, Combination Charts and Post Position Bracket Chart for searches like these:

Count the combinations of a trifecta formation
Calculate the combinations of a box bet
Find the combinations of a trifecta multi wheel
Calculate combined odds
Check whether a winning bet would still lose money
Work out a stake allocation for horse racing bets

FAQ

How many combinations is a 5-horse trifecta box?: 5 × 4 × 3 = 60 combinations, which costs 6,000 yen at 100 yen each. A 5-horse trio box is 10 combinations, an exacta box 20, and a quinella or quinella place box 10. A 6-horse box is 120 for the trifecta and 20 for the trio.
How do you count a trifecta formation?: Pick one horse each from the 1st, 2nd and 3rd candidates and count every combination in which no horse appears twice. With 1st: 1, 2; 2nd: 1, 2, 3, 4; 3rd: 1–6, there are 3 × 4 = 12 combinations when 1 wins and another 12 when 2 wins, 24 in total (2,400 yen). It is not simply 2 × 4 × 6 = 48.
How many combinations is a trifecta wheel with one key horse multi or two key horses multi?: With m other horses, one key horse multi is 3 × m × (m − 1) combinations, so 60 with 5 other horses. Two key horses multi is 6 × m, so 30 with 5 other horses. A one key horse wheel with the key horse fixed in 1st is m × (m − 1) (20 with 5 other horses).
How do you calculate combined odds?: Add up the reciprocals of the odds and take the reciprocal of the sum. For three bets at 3.5, 6.0 and 12.0, it is 1 ÷ (1/3.5 + 1/6 + 1/12) ≈ 1.87. Splitting 3,000 yen so every bet pays about the same gives stakes of 1,600, 900 and 500 yen and payouts of 5,600, 5,400 and 6,000 yen.
What is a losing win (torigami)?: It is when your bet wins but the payout is less than the total you spent. If you buy 10 combinations at 100 yen each, you spend 1,000 yen, so any bet with odds under 10.0 loses money even when it wins (8.0 pays 800 yen). It gets more likely the more you spread your bets, so check the combined odds and stake allocation first.
When can you buy a same-bracket bracket quinella?: Only when there are 2 or more horses in that bracket. In JRA races, a second horse goes into the outer bracket (bracket 8) from 9 runners; with 16 runners every bracket has 2 horses, and with 18 runners brackets 7 and 8 have 3. In a 10-runner race, the only same-bracket pairs are 7-7 and 8-8.

ARTICLES

Guides for Horse Racing Bet Calculator | Number of Combinations and Cost for Trifecta, Trio, Exacta, Quinella, Quinella Place and Bracket Quinella by Box, Key Horse Wheel (1 or 2 Key Horses, Multi) and Formation, Full List of Bets, Combined Odds, Losing-Win (Torigami) Check and Stake Allocation, WIN5 Combinations, Combination Charts and Post Position Bracket Chart

How It WorksHow to Count Horse Racing Bet Combinations | Trifecta and Trio Box, Key Horse Wheel and Formation Formulas and Charts, Multi, Bracket Quinella Pairs, Combined Odds and Losing Wins“How many combinations is a 5-horse trifecta box?” “How many more does a multi add?” “Can I just multiply the candidates in a formation?” If you don't work out the number of combinations and the cost before you bet, you can end up with far more bets than you planned and go over budget, or win and still get back less than you spent (a “losing win”, called torigami in Japan). This guide covers the eight JRA bet types (win, place, bracket quinella, quinella, quinella place (wide), exacta, trio and trifecta): formulas and charts for boxes, key horse wheels (one or two key horses, multi, and wheeling to all runners) and formations, how to count overlapping bets in a formation, the total number of combinations and the bracket assignments for each field size, when same-bracket pairs can be bought in the bracket quinella, how to calculate combined odds and spot losing wins, how to split a budget so every winning bet pays about the same, the payout rate of each bet type, and WIN5 combinations, all with worked examples.

Special Thanks

SOLO GUILD | サービス作るAIエンジニア

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