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Patent and Trixie Calculator: Three Selections, Every Combination
A Patent is seven bets on three selections: three singles, three doubles and a treble. A Trixie is the same slip without the singles, four bets in all. Enter three prices and three results, and the calculator shows the cost, the return and the profit of either one.
Written by: Owen Treadgold·Checked by: Maren Holt·Updated:
Three selections can be combined in seven ways: each one alone, each pair, and all three together. A Patent backs all seven; a Trixie drops the three singles and keeps the four multiples. This patent calculator doubles as a trixie calculator, so you can see what a slip costs and what it pays before the selections run.
Bet calculator
Choose the bet type, enter the odds of each selection and its result. Returns update as you type.
- Bets on the slip
- 0
- Total stake
- 0.00
- Total return
- 0.00
- Profit
- 0.00
On this page9 sectionsexpand
- Nº 01How to use the patent calculator
- Nº 02Patent and Trixie side by side
- Nº 03The formula behind the return
- Nº 04Worked example: a £1 Patent with two winners
- Nº 05The same two winners in a £1 Trixie
- Nº 06How each way doubles the cost
- Nº 07Void legs and dead heats
- Nº 08When each bet suits a bettor
- Nº 09What the patent calculator does not include
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How to use the patent calculator
- Leave the bet type on Patent (7 bets), or switch to Trixie (4 bets) in the same list. Both fix the slip at three selections.
- Enter the three prices in fractional odds, such as 2/1 or 11/4. Decimal and American are in the odds format list if you prefer them.
- Type the stake and choose whether it is per bet or the total for the slip. A £1 Patent is £1 per bet and £7 in total.
- Pick the place terms if the slip is each way. Leave “No each way” for a win-only bet.
- Set each result: won, placed, lost, void or non-runner, or a dead heat of two or three.
The number of bets, the total stake, the return and the profit change as soon as any field does.
Patent and Trixie side by side
| Patent | Trixie | |
|---|---|---|
| Selections | 3 | 3 |
| Singles | 3 | none |
| Doubles | 3 | 3 |
| Treble | 1 | 1 |
| Bets on the slip | 7 | 4 |
| Cost at £1 per bet | £7 | £4 |
| Cost at £1 each way | £14 | £8 |
| Fewest winners for any return | 1 | 2 |
The doubles and the treble are identical in both bets. The only thing a Patent buys with its extra £3 is a single on each selection, which is why a Patent bet is sometimes described as a Trixie with three singles attached.
The formula behind the return
Convert each price to decimal odds by adding one to the fraction: 2/1 is 3.00, 5/1 is 6.00 and 3/1 is 4.00. Call them a, b and c. A losing selection counts as 0, a void selection as 1.
- Singles: stake × (a + b + c)
- Doubles: stake × (ab + ac + bc)
- Treble: stake × abc
A Patent return is the sum of all three lines. That sum has a short form: stake × ((1 + a)(1 + b)(1 + c) − 1). A Trixie return is the same figure minus the singles line.
Worked example: a £1 Patent with two winners
The slip has three selections at 2/1, 5/1 and 3/1, £1 per bet, £7 staked. The 2/1 and the 5/1 win; the 3/1 loses.
| Bet | Calculation | Return |
|---|---|---|
| Single at 2/1 | £1 × 3.00 | £3.00 |
| Single at 5/1 | £1 × 6.00 | £6.00 |
| Single at 3/1 | lost | £0.00 |
| Double 2/1 and 5/1 | £1 × 3.00 × 6.00 | £18.00 |
| Double 2/1 and 3/1 | lost | £0.00 |
| Double 5/1 and 3/1 | lost | £0.00 |
| Treble | lost | £0.00 |
| Total | £27.00 |
The patent calculator shows £27.00 returned for £7.00 staked, a profit of £20.00. The short form gives the same answer: (1 + 3)(1 + 6)(1 + 0) − 1 = 27.
The same two winners in a £1 Trixie
A £1 Trixie on the same three prices costs £4.00. With the 2/1 and the 5/1 winning, only one of its four bets pays: the double, £1 × 3.00 × 6.00 = £18.00. Profit is £14.00.
Set the two slips against each other and the trade-off is plain. The Patent cost £3.00 more and returned £9.00 more, the £9.00 being the two winning singles. With two winners at these prices, the singles paid for themselves three times over.
If all three had won, the Patent would return £139.00 (singles £13.00, doubles £54.00, treble £72.00) and the Trixie £126.00. If only the 5/1 had won, the Patent would return £6.00 against £7.00 staked, and the Trixie nothing at all.
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How each way doubles the cost
An each-way Patent is two Patents on one slip: one on the win and one on the place, where each selection pays at a fraction of its odds if it finishes in the places. Fourteen bets, so £1 each way costs £14.00. A £1 each-way Trixie is eight bets and £8.00.
Take the same three prices at 1/5 the odds for a place. The 2/1 and 5/1 win, and this time the 3/1 finishes third and places. Place odds in decimal are 1.40, 2.00 and 1.60.
- Win part: as in the example above, £27.00.
- Place part: singles £5.00, doubles £8.24, treble £4.48, so £17.72.
- Total: £44.72 for £14.00 staked, a profit of £30.72.
The each-way Trixie on the same results returns £18.00 on the win part and £12.72 on the place part, £30.72 in all, for a profit of £22.72 on £8.00. Place terms depend on the race and the number of runners, which the horse racing betting guide sets out.
Void legs and dead heats
A non-runner does not sink the slip. Its decimal value becomes 1.00, so with the 3/1 void and the other two winning, the £1 Patent returns £55.00: £10.00 from singles, £27.00 from doubles and £18.00 from the treble, which is now in effect a double. Choose “Void / non-runner” for that selection and the patent calculator does this for you.
A dead heat halves the stake on that selection's win part for a tie of two and cuts it to a third for a tie of three, at full odds. Pick “Won, dead heat of 2” or “of 3” in the result list.
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Our view: the Patent suits a bettor who is confident about one selection and less certain of the rest. The singles keep the slip alive on one winner, and at bigger prices a lone winner can cover the whole stake. It suits longer prices better than short ones: three favourites at evens or shorter make singles that barely return their own stake.
A Trixie bet suits a bettor who expects at least two of the three to come in and would rather spend £4.00 than £7.00 on the same doubles and treble. One winner is a total loss, so it is a slip for three selections you rate roughly equally.
If you have a fourth selection, the Yankee calculator covers the four-selection version of the Trixie. For accumulators, round robins and the larger full-cover bets, use the general bet calculator.
What the patent calculator does not include
- Rule 4 deductions. A withdrawal after a market forms cuts fixed-odds winnings in racing. The figures shown come before any deduction.
- Bookmaker bonuses. Some sites add extra on full-cover bets, such as a bonus when all selections win or double odds on a lone winner. Terms differ by site, and none are added here.
- Starting price. If you took SP, enter the returned price once the race is over; the calculator cannot look it up.
- Payout limits. Every site caps what it pays on one bet, and a winning treble at long prices can reach that cap.
When you are ready to bet, the shortlist of no KYC betting sites shows each site's ID trigger before you sign up.
More in the same section: Round robin calculator, Each way calculator and all betting calculators.
What is the difference between a Patent and a Trixie?
Both cover three selections with every double and the treble. A Patent adds a single on each selection, so it is seven bets instead of four and costs three stakes more.
How much does a £1 Patent cost?
£7, because it is seven bets at £1 each. A £1 each-way Patent is fourteen bets and costs £14.
Does a Patent pay with one winner?
Yes, the single on that selection pays. Whether it covers the £7 stake depends on the price: a single at 6/1 or longer returns £7 or more. A Trixie with one winner returns nothing.
What happens to a Patent when one selection is a non-runner?
The void leg counts as decimal odds of 1.00, so its single returns the stake, the doubles that include it become singles and the treble becomes a double.
Can I work out a Trixie with this calculator?
Yes. Choose Trixie (4 bets) in the bet type list. The prices and results you have entered stay in place, so you can compare the two slips on the same three selections.