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How a Lucky 15 is built

Four football selections become fifteen separate bets. Here is how the lines are formed and how a £1 Lucky 15 settles with four, three, two or one winner.

Four football selections: four home wins, each at its own price.

A Lucky 15 starts with exactly four selections. In this example they are four football matches, each backed for a home win: Match A at evens, Match B at 11/10, Match C at 6/4 and Match D at 2/1. In decimal odds those prices are 2.00, 2.10, 2.50 and 3.00, which is the form the settlement arithmetic uses.

Four singles: each selection is also a bet on its own.

The first part of a Lucky 15 is four singles, one on each selection. A single depends on nothing else on the slip, so it is settled at its own price whatever happens in the other three matches. This is the part that separates a Lucky 15 from a Yankee, which uses the same four selections without the singles.

Six doubles: every possible pair from the four selections.

Next come the doubles. Each double joins two selections, and both have to win for it to return anything. Four selections can be paired in six different ways: A with B, A with C, A with D, B with C, B with D and C with D. Each pair is a separate bet with its own stake.

Four trebles: every group of three selections.

The trebles join three selections at a time, and all three must win. Choosing three of four is the same as leaving one out, so there are four trebles: one without Match D, one without Match C, one without Match B and one without Match A. Each treble is its own bet at the same stake.

One four-fold joins all four: 15 bets, £1 each, £15 staked.

The last line is a single four-fold accumulator that needs all four selections to win. That completes the slip: four singles, six doubles, four trebles and one four-fold make fifteen separate bets. A £1 Lucky 15 therefore costs £15, because the stake is placed on every line rather than on the slip as a whole.

Count it by hand: 4 + 6 + 4 + 1 = 15 lines.

The number of lines is not a convention; it follows from counting. The number of ways to choose k selections from four is 4! divided by k! times (4 − k)!. That gives 4 ways to choose one, 6 to choose two, 4 to choose three and 1 to choose all four. Added together they make 15, the number in the bet's name.

All four won: all 15 bets return, £129.20 back for £15.

When all four selections win, every one of the fifteen bets returns. Each line pays £1 multiplied by the decimal odds of its legs: the four-fold alone returns 2.00 × 2.10 × 2.50 × 3.00 = £31.50. The four singles return £9.60, the six doubles £34.25 and the four trebles £53.85, a total return of £129.20 against £15 staked.

Match D at 2/1 lost: 7 bets still return, £31.55 in total.

If Match D loses, every line that contains it returns nothing: one single, three doubles, three trebles and the four-fold. Seven lines remain live, all built from A, B and C. Three singles return £6.60, three doubles £14.45 and the one treble without Match D returns £10.50. The total return is £31.55 for the £15 staked.

Only the evens and 11/10 selections won: 3 bets return, £8.30.

With two winners, Match A and Match B, only three lines return: their two singles, at £2.00 and £2.10, and the one double that joins them, at 2.00 × 2.10 = £4.20. Every treble needs a third winner and the four-fold needs four, so they return nothing. The total return is £8.30, which is £6.70 less than the £15 staked.

Only the evens selection won: its single returns £2.00.

With a single winner, every double, treble and the four-fold contains at least one losing leg, so the only line that returns is the single on Match A. At evens, £1 comes back as £2.00. Fourteen lines return nothing, and the slip as a whole returns £2.00 of the £15 staked.

Remove the four singles and it is an 11-bet Yankee: 0 bets return.

Take the four singles away and the remaining six doubles, four trebles and four-fold form a Yankee: eleven bets, £11 at £1 each. With the same single winner on Match A, none of those eleven lines returns anything, because each one needs at least two winners. The singles are the only part of a Lucky 15 that can return money from one winning selection.

Sources: Bet calculator (Lucky 15 and Yankee settlement, same arithmetic as every figure here) · Line count: the number of ways to choose k of n selections, C(n,k) = n! ÷ (k! × (n − k)!)