Full-Cover Bets Compared: What the Extra Singles Actually Buy
A Trixie and a Patent cover the same three selections. A Yankee and a Lucky 15 cover the same four. A Canadian and a Lucky 31 cover the same five. The only difference inside each pair is the singles, and the singles are the whole of the choice you are being asked to make. This guide sets out the one formula that prices every bet in the family, the exact price at which each number of winners gets your money back, what the singles cost as a percentage, and the point in the bet at which paying for them stops being worth it.
The family in one table
A full-cover bet buys every combination of your selections. With the singles included the number of lines is two to the power of the number of selections, minus one; without them it is the same figure minus the number of selections. That is the entire difference between the two halves of the family, and it explains every number further down this page.
| Bet | Selections | Lines | Singles | Outlay at £1 a line |
|---|---|---|---|---|
| Trixie | 3 | 4 | No | £4.00 |
| Patent | 3 | 7 | Yes | £7.00 |
| Yankee | 4 | 11 | No | £11.00 |
| Lucky 15 | 4 | 15 | Yes | £15.00 |
| Canadian (Super Yankee) | 5 | 26 | No | £26.00 |
| Lucky 31 | 5 | 31 | Yes | £31.00 |
| Heinz | 6 | 57 | No | £57.00 |
| Lucky 63 | 6 | 63 | Yes | £63.00 |
Two practical notes before the arithmetic. Each-way doubles every outlay in that last column, because each line is placed twice. And the stake you type into a betting slip is almost always the stake per line, not the total, which is why a £2 Lucky 15 takes £30 out of the account. Our bet calculator settles any of these for a real mix of prices, and there is a dedicated page for the Patent, Lucky 15 and Lucky 31.
One formula covers every bet with singles
Put all your selections at the same decimal price and the fifteen bets of a Lucky 15, or the seven of a Patent, stop being a list and become a binomial expansion. If k of your selections win at decimal price p, the total return per unit staked is one plus p, raised to the power k, minus one. Every line that contains only winners pays; every line that contains a loser does not; and the sum of all the winning subsets is that expression.
Set that return equal to the outlay and the break-even price falls out in one line. The outlay is two to the power n minus one, so the price at which k winners out of n selections return exactly the stake is two to the power of n divided by k, minus one. Nothing else survives the algebra: not the size of the bet, not the number of lines, not the stake.
The consequence is the most useful thing on this page. The break-even price depends only on the ratio of selections to winners. Half your selections coming in breaks even at 2/1 whether that is two of four on a Lucky 15 or three of six on a Lucky 63. A third of them coming in breaks even at 6/1 whether that is one of three on a Patent or two of six on a Lucky 63. The bet gets bigger, the arithmetic does not move.
| Share that wins | Selections per winner | Break-even price | In fractions | Where you meet it |
|---|---|---|---|---|
| All of them | 1 | 1.00 | any price at all turns a profit | Lucky 15 with 4 winners |
| Two thirds | 1.5 | 1.83 | just under 5/6 | Patent with 2, Lucky 63 with 4 |
| Half | 2 | 3.00 | 2/1 exactly | Lucky 15 with 2, Lucky 63 with 3 |
| A third | 3 | 7.00 | 6/1 exactly | Patent with 1, Lucky 63 with 2 |
| A quarter | 4 | 15.00 | 14/1 exactly | Lucky 15 with 1 |
| A fifth | 5 | 31.00 | 30/1 exactly | Lucky 31 with 1 |
| A sixth | 6 | 63.00 | 62/1 exactly | Lucky 63 with 1 |
Read the same identity bet by bet and it becomes a table you can carry to a betting shop. Each cell is the price every selection needs to be for that number of winners to return the outlay and not a penny more.
| Bet | 1 winner | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Patent (7 lines) | 7.00 | 1.83 | 1.00 | — | — | — |
| Lucky 15 (15 lines) | 15.00 | 3.00 | 1.52 | 1.00 | — | — |
| Lucky 31 (31 lines) | 31.00 | 4.66 | 2.17 | 1.38 | 1.00 | — |
| Lucky 63 (63 lines) | 63.00 | 7.00 | 3.00 | 1.83 | 1.30 | 1.00 |
One number in that table deserves to be memorised: 3.00. Two winners out of four at 2/1 return the fifteen units of a Lucky 15 exactly, and three winners out of six at 2/1 return the sixty-three units of a Lucky 63 exactly. Below 2/1 those winners leave you short; above it, the next winner is paying for the losing lines.
The bets without singles have their own line
A Trixie, a Yankee, a Canadian and a Heinz are the same bets with the singles removed, so their return is the same expression minus the k singles, and their outlay is smaller by the number of selections. The break-even prices no longer collapse into a neat power of two, but they are still fixed numbers, and one of them is the tidiest in the family.
| Bet | 2 winners | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|
| Trixie (4 lines) | 2.00 | 1.00 | — | — | — |
| Yankee (11 lines) | 3.32 | 1.55 | 1.00 | — | — |
| Canadian (26 lines) | 5.10 | 2.23 | 1.39 | 1.00 | — |
| Heinz (57 lines) | 7.55 | 3.07 | 1.84 | 1.30 | 1.00 |
Two winners on a Trixie break even at exactly evens: the single double between them returns four units on the four staked. There is no equivalent round number anywhere else in the column, and it is the reason a Trixie is the least punishing of the no-singles bets at short prices. A Yankee needs 3.32 for the same two winners, and a Canadian needs 5.10. With no singles, a bet with one winner returns nothing at any price, which is the plainest statement of what the singles are for.
What the singles cost
The upgrade from the no-singles bet to its lucky twin always adds exactly one line per selection. As a proportion of what you were already staking, that gets steadily cheaper as the bet grows.
| From | To | Lines | Added | Extra outlay |
|---|---|---|---|---|
| Trixie | Patent | 4 to 7 | +3 lines | +75.0% |
| Yankee | Lucky 15 | 11 to 15 | +4 lines | +36.4% |
| Canadian | Lucky 31 | 26 to 31 | +5 lines | +19.2% |
| Heinz | Lucky 63 | 57 to 63 | +6 lines | +10.5% |
Turning a Trixie into a Patent costs three quarters as much again. Turning a Heinz into a Lucky 63 costs a tenth. The upgrade you are most likely to be sold is the middle one, and the Yankee to Lucky 15 step adds 36.4% to the ticket.
What the singles buy, and where they stop paying
Comparing the two bets fairly means holding the money fixed rather than the stake per line. Give a Yankee the same £15 as a Lucky 15 and each of its eleven lines carries £1.36 instead of £1. Now the two bets cost the same and the only question left is which one pays more, at four selections all priced 2/1.
| Winners | Yankee at £1.36 a line | Lucky 15 at £1 a line | Lucky 15 advantage |
|---|---|---|---|
| 0 | £0.00 | £0.00 | £0.00 |
| 1 | £0.00 | £3.00 | +£3.00 |
| 2 | £12.27 | £15.00 | +£2.73 |
| 3 | £73.64 | £63.00 | −£10.64 |
| 4 | £331.36 | £255.00 | −£76.36 |
The shape of that last column is the answer to the question this guide asks. The singles are worth having when the bet goes badly and cost you when it goes well, and the crossover sits between two winners and three. They are not cover bolted on top of the multiples: they are money moved from the good outcomes to the bad ones, and the transfer is not free, because the four singles that rescue a one-winner afternoon are the same four units that are no longer riding on the four-fold.
The same crossover exists in the other pairs and moves with the price. At 2/1 a Trixie given the Patent's £7 has already overtaken it with two winners, £15.75 against £15.00, because each of its four lines is 75% bigger. A Canadian holds its Lucky 31 off until four winners. The rule that survives all three comparisons: the more of your selections come in, the more the singles version costs you, and the fewer come in, the more it saves you.
The consolation is not one rule, and "double the odds" has two readings
Only the lucky bets carry bonuses, and they are the reason the family is split in two. The usual pair is a consolation when exactly one selection wins and all the others run, plus a percentage uplift when every selection wins. Both are the bookmaker's terms, not a property of the bet, and they vary in two ways at once.
The first is the multiple. Some bookmakers pay double the odds on the sole winner; at least one pays five times the odds on a Lucky 15, four times on a Lucky 31 and three times on a Lucky 63, so the concession shrinks as the bet grows. The second is what the multiple multiplies. A fractional reading doubles the odds themselves, so a 7/1 winner is paid at 14/1. A decimal reading doubles the return, which is a different and slightly more generous number. The wording on a promotions page rarely settles which is meant, so both are set out here.
| Bet | Consolation | Stake back at (odds doubled) | Stake back at (return doubled) |
|---|---|---|---|
| Lucky 15 | Double the odds | 8.00 (7/1) | 7.50 (13/2) |
| Lucky 15 | Five times the odds | 3.80 (14/5) | 3.00 (2/1) |
| Lucky 31 | Double the odds | 16.00 (15/1) | 15.50 |
| Lucky 31 | Four times the odds | 8.50 (15/2) | 7.75 |
| Lucky 63 | Double the odds | 32.00 (31/1) | 31.50 |
| Lucky 63 | Three times the odds | 21.67 | 21.00 |
The gap between the rows is not decoration. Under a double-the-odds concession a lone Lucky 15 winner has to be a 7/1 shot before the bet gets its money back. Under a five-times concession the same bet is square at 2.80. Those are two different products wearing the same name, and the difference is larger than any edge available in the prices themselves. Whatever the multiple, the consolation is not insurance: it softens the single worst outcome that still pays anything, and it does nothing at all when none of your selections wins.
Which one to take
The arithmetic does not name a winner, but it does sort the reasons. If you would have backed these selections as singles anyway, the singles version is the honest bet: you are keeping the bet you wanted and buying the multiples on top. If you are really betting the multiples and telling yourself the singles are insurance, you are paying between 10% and 75% more for cover that stops paying at exactly the point the bet starts working.
Three practical readings follow. The Trixie to Patent step is the expensive one and also the one that most often decides whether you collect anything at all, because with three selections a single winner is a common afternoon. The Heinz to Lucky 63 step is the cheap one and changes the least, because six selections rarely produce exactly one winner. Our Heinz calculator and our Lucky 63 calculator price that step outcome by outcome from either side: at equal outlay the six singles stop paying for themselves above 19.00 with two winners and above 4.05 with three. And since the break-even prices depend only on the ratio of winners to selections, choosing between four selections and six is a question about how many opinions you actually hold, not about the shape of the bet.
One thing every bet on this page shares with a straight accumulator is that the bookmaker's margin is applied to every leg and compounds across the lines; the accumulator guide sets out how much that costs at each number of legs, and the margin calculator measures it in the market in front of you. If you are adding place terms, every line is placed twice and the each-way calculator shows when that second half earns its stake.
Frequently asked questions
What is the difference between a Trixie and a Patent?
The three singles, and nothing else. Both cover three selections; a Trixie is four lines, three doubles and a treble, while a Patent is those four plus the three singles, so seven lines in total. At the same stake per line the Patent costs 75% more. The practical consequence is that a Trixie with one winner returns nothing at any price, while a Patent with one winner returns that single, and gets the whole outlay back if the winner was 6/1 or bigger.
How many winners do you need for a Lucky 15 to break even?
It depends entirely on the price, and the thresholds are exact. At a uniform price, one winner returns the fifteen units staked only at 14/1, two winners at 2/1, three winners at 1.52, and four winners at any price at all. Two winners at 2/1 is the number worth remembering: two singles at 3.00 and the double between them return 3.00 plus 3.00 plus 9.00, which is the fifteen units to the penny.
Is a Lucky 15 better than a Yankee?
Neither is better in general; they pay in opposite conditions. Held to the same total outlay of £15 on four selections at 2/1, the Lucky 15 is £3.00 ahead with one winner and £2.73 ahead with two, and then £10.64 behind with three and £76.36 behind with four. The singles move money from the outcomes where the bet does well to the outcomes where it does badly, and the crossover sits between two winners and three.
Is there a break-even formula for full-cover bets?
For the bets that include the singles, yes, and it is short. With n selections all at the same decimal price and k of them winning, the break-even price is two to the power of n divided by k, minus one. Because only the ratio of n to k appears, half your selections winning always breaks even at 2/1 and a third of them always at 6/1, whether the bet is a Patent, a Lucky 15, a Lucky 31 or a Lucky 63. The bets without singles need their own numbers: two winners break even at evens on a Trixie, 3.32 on a Yankee, 5.10 on a Canadian and 7.55 on a Heinz.
Does the one-winner consolation make a Lucky 15 safe?
No, and how much it helps varies more than most bettors expect. The consolation only applies when exactly one selection wins and the others all run, so it pays nothing on the most common losing afternoon of all. Its size is set by the bookmaker: a double-the-odds concession returns the fifteen units only when the lone winner was a 7/1 shot, while a five-times concession does it at 2.80. Check the wording as well as the multiple, because doubling the odds and doubling the return are different sums.
Sources and method
Every figure on this page was recalculated before publication rather than taken from a source. Returns use the identity that k winners at a uniform decimal price p return one plus p to the power k, minus one, per unit staked, with the k singles subtracted for the bets that do not include them. Break-even prices solve that expression against an outlay of two to the power n minus one, giving two to the power of n over k, minus one, for the bets with singles and a numerical solution for those without. The consolation thresholds solve a single winner's return against the outlay under both readings of the multiple.
Three limits are worth stating plainly. Every threshold assumes the selections share one price; mixed prices move all of them, which is what a calculator is for. The percentages ignore bookmaker margin and assume the results are independent of each other, and selections from the same meeting rarely are. And the consolation and all-winners bonus terms belong to whoever is taking the bet, change without notice, and are the one part of this page you should read in the operator's own words rather than ours.
18+ only. A full-cover bet multiplies the number of lines, not your chances, and the arithmetic here is meant to help you see what a ticket really costs rather than to encourage placing one. Gambling should be entertainment you can afford to lose. Set a deposit limit before you start and use it. If gambling is causing you harm, help is available — see our responsible gambling resources.