Lucky 15 Calculator

Each of the 15 bets is settled on its own. A single pays stake × odds; a double multiplies two winning selections together; a treble multiplies three; the four-fold multiplies all four. Any bet that includes a losing selection returns nothing, but every other bet still stands — which is why a Lucky 15 can pay out even with two losers.

Take a £1 Lucky 15 (total outlay £15.00) on four selections at decimal odds of 2.00, 3.00, 4.00 and 5.00, with all four winning:

That is £359.00 back from £15.00 staked — a profit of £344.00. The picture changes quickly with losers, though. With only the 2.00 and 4.00 selections winning, you collect two singles (£2.00 + £4.00) and one double (£8.00) for £14.00 — a net loss of £1.00 on the £15.00 outlay. With a single winner at 5.00, only that single pays: £5.00 back, £10.00 down.

When a Lucky 15 Makes Sense

Compared with a straight four-fold on the same selections — which you can price up with the Accumulator Calculator — a Lucky 15 costs 15 times as much but keeps paying when one or two legs fail. It suits selections at moderate odds where singles carry real value; at very short prices, the 15-bet outlay is hard to recover unless everything wins.

The worked example above prices one particular set of selections. The more useful question is the general one: how many of your four have to win before the bet stops losing money. Put all four at the same decimal price and the answer falls out of one line of algebra, because the fifteen bets are the binomial expansion of four selections. The total return per unit staked is (1 + odds) raised to the fourth power, minus one.

That identity is worth keeping. Four selections at 3.00 returning everything pay 4 to the fourth minus one, or 255 units on the 15 staked; at 6.00 they pay 7 to the fourth minus one, or 2,400. It also settles the break-even question immediately, because setting the return equal to the 15-unit outlay gives an answer of exactly 1.00 — with all four winning, any price at all turns a profit.

Two winners at 2/1 is the number to remember. Two singles at 3.00 and the double between them return 3.00 + 3.00 + 9.00, which is the 15 units staked to the penny. Below 2/1 a pair of winners still leaves you short; above it the second winner starts paying for the twelve losing lines. The consolation is not insurance, and it is not one rule either. Where a bookmaker doubles the odds, a sole winner returns the fifteen units only at 7/1, and every price below that leaves a one-winner Lucky 15 in loss. Two qualifications belong with that number. Doubling the odds and doubling the decimal return are different sums, and the second reading puts the line at 13/2 instead. And double is not the only concession offered: five times the odds on a Lucky 15 squares the bet with a single winner at 2.80, which is a different product wearing the same name. Read the multiple and the wording before you count on either. Our comparison of the full-cover bets sets the same thresholds out for the Patent, Lucky 31 and Lucky 63.

Where the Return Actually Sits

A Lucky 15 is sold as the bet that spreads your risk across fifteen lines. The arithmetic says the opposite at the prices it is usually played on: the longer the selections, the more of the full-house return collapses into the single line that needs all four to win.

At 2/1 the four-fold carries under a third of the full-house return, and the singles, doubles and trebles do most of the work — which is the bet behaving as advertised. At 10/1 the four-fold carries 70.6% of it, on an outcome that comes in once in roughly fourteen thousand attempts if the prices are fair. The last column assumes the odds carry no bookmaker margin and that the four results are independent of each other; real margin makes those percentages smaller, and selections from the same meeting or the same accumulator theme are rarely independent at all. To see how much margin is priced into the market you are betting into, use the Bookmaker Margin Calculator.

Read together, the two tables give the bet a shape. A Lucky 15 is at its best on four selections around 2/1 to 4/1 that you would have backed as singles anyway, where two winners return the outlay and three make it pay without needing the four-fold at all. It is at its worst as a long-priced flutter, where it is a four-fold wearing the costume of a spread bet. Dropping the four singles turns the same selections into a Yankee for eleven units instead of fifteen, and adding place terms turns it into a 30-bet each-way Lucky 15 — the Each-Way Calculator sets out when that second half earns its stake.

One caveat on all of the above: these thresholds assume the four selections share the same price. Mixed prices move every number, and the calculator at the top of this page settles those exactly.

A Lucky 15 is a Yankee with the four singles added: fifteen lines instead of eleven, so 36.4% more outlay on the same four selections. Comparing them at the same unit stake flatters the Lucky 15, because it is simply the bigger bet. The only fair comparison puts the same money at risk — £15.00 into each, so £1.00 across the fifteen Lucky 15 lines against £1.36 across the eleven Yankee lines — and then asks at which price each outcome changes hands.

The two crossovers are the whole answer, and they fall on opposite sides of ordinary betting. A four-selection slip priced above 5.50 is unusual, so with two winners the Lucky 15 is ahead in practice; a price shorter than 1.74 is rarer still, so with three winners the Yankee is ahead in practice. What the four singles buy, then, is not a better bet at three or four winners but a floor under the bad afternoons: they turn one winner from nothing into a return, and they own the two-winner row at every realistic price. They are paid for out of every multiple, and the bill arrives exactly when the card goes well.

What the All-Win Bonus Is Actually Worth

Most bookmakers pay a bonus when all four selections win, commonly 10% of the return, and some pay a consolation at double the odds when only one wins. Both are terms of the operator rather than rules of the bet, so they should be read off your own slip before they are counted. Neither changes the shape above, and only the bonus touches the row where the Lucky 15 is behind.

Take the four-winner row at 3.00 (2/1). The Lucky 15 returns £255.00 on its £15.00, and a 10% bonus adds £25.50 for £280.50. The Yankee, holding the same £15.00 in eleven lines, returns £331.36. The bonus closes a third of the gap and leaves £50.86 of it standing. For the two bets to finish level at that price the bonus would have to be 29.95%. Shorten the prices and the bonus does more of the work — at 2.00 (evens) it needs to be 22.73% — but the figure an operator actually pays only overtakes the Yankee below 1.30, and four selections at 1.30 are not what a Lucky 15 is for. The single case in the family where the standard 10% is enough is the Lucky 63, where the six singles are only 9.5% of the slip against 26.7% here; the full comparison across the four pairs is set out on the Yankee calculator, and every bet in the family is worked through in our comparison of full-cover bets.