Settling a Lucky 15 with a Rule 4, a non-runner and a loser
A curious thing happens when you try to settle a Lucky 15 in your head and one of the legs has been withdrawn. The bet looks cursed — a Rule 4, a non-runner, a loser — and the natural assumption is that the return will be disappointing at best. In fact, as we shall see, the arithmetic often runs the other way, and a Lucky 15 with one clean winner and one winner-under-deduction can pay considerably more than a casual glance would suggest. Understanding why requires working through the settlement line by line. That is what this piece is for.
The bet
Four selections across the Saturday card, backed in a £1 unit Lucky 15. Total stake: £15, made up of four singles, six doubles, four trebles and one four-fold, each at £1.
- Horse A, 3/1 in the 2.00 at Newbury
- Horse B, 5/1 in the 2.30 at Ripon
- Horse C, 10/1 in the 3.00 at Newbury
- Horse D, 2/1 in the 3.30 at Ripon
Now, the afternoon unfolds as follows. Horse A runs out the winner at 3/1, all perfectly normal. In the 2.30 at Ripon, the 7/4 favourite is withdrawn at the start before the flag goes up, triggering a Rule 4 deduction of 40p in the pound; Horse B then goes on to win at its quoted 5/1. Before the 3.00 at Newbury, Horse C is withdrawn under orders and becomes a non-runner, voiding every line it appears in. Horse D, favourite for the 3.30, trails in fifth of twelve and loses.
So we have: one clean winner (A), one winner with a Rule 4 applied (B), one non-runner (C), and one loser (D). Three of the four selections having done something awkward. The question is, what does the slip actually pay?
Two rules you have to hold in your head at once
Before we can settle the fifteen lines, we need to be clear about how each complication propagates.
The Rule 4 deduction on Horse B. A 40p-in-the-pound deduction means 40% comes off the winnings — not the stake, not the total return. Horse B at 5/1 ordinarily pays £5 profit on a £1 winning single. After the deduction, that £5 becomes £3, and the return is £4 (stake plus reduced profit). In effective-price terms, Horse B has been reduced from 5/1 to 3/1. That effective price is what we use in every line where B wins. The Rule 4 calculator handles this for a single bet; for a multiple, we apply the reduction to B's leg and then compound as normal.
The non-runner on Horse C. A non-runner does not void the whole Lucky 15. It reduces every line that includes Horse C by one level. The single on C becomes void and the stake is refunded. Any double involving C becomes a single on the other horse. Any treble involving C becomes a double on the other two. The four-fold (which includes C) becomes a treble on A, B and D. The stake on each reduced line remains £1 — the stake is not refunded on the doubles, trebles and four-fold; they simply settle at one level smaller.
With those two rules in hand, we can walk through all fifteen lines.
The four singles
Simple enough. Each of the four singles is a £1 bet on one horse.
- Single on A (wins at 3/1): returns £4. Profit £3.
- Single on B (wins at 5/1, Rule 4 40p): returns £4. Profit £3. The £5 winnings are reduced by 40% to £3, plus stake returned.
- Single on C (non-runner): stake refunded. Returns £1. Profit £0.
- Single on D (loses): returns £0. Loss £1.
Singles subtotal: £9 returned on £4 staked, profit £5.
The six doubles
A Lucky 15 contains every possible pair of selections. With four horses, that is six doubles: AB, AC, AD, BC, BD, CD. We take each in turn. Remember: Horse B's effective price is 3/1 (decimal 4.00) after the Rule 4; Horse C being a non-runner reduces its double to a single on the other horse.
- AB (both win, R4 on B): combined decimal odds 4 × 4 = 16. Returns £16. Profit £15.
- AC (A wins, C non-runner): reduces to a single on A at 3/1. Returns £4. Profit £3.
- AD (A wins, D loses): the double fails. Returns £0. Loss £1.
- BC (B wins with R4, C non-runner): reduces to a single on B at effective 3/1. Returns £4. Profit £3.
- BD (B wins, D loses): the double fails. Returns £0. Loss £1.
- CD (C non-runner, D loses): reduces to a single on D, which lost. Returns £0. Loss £1.
Doubles subtotal: £24 returned on £6 staked, profit £18.
The four trebles
Four combinations of three from the four selections: ABC, ABD, ACD, BCD.
- ABC (A wins, B wins with R4, C non-runner): reduces to a double on AB, decimal odds 4 × 4 = 16. Returns £16. Profit £15.
- ABD (A wins, B wins with R4, D loses): the treble fails on D. Returns £0. Loss £1.
- ACD (A wins, C non-runner, D loses): reduces to a double on AD, which fails on D. Returns £0. Loss £1.
- BCD (B wins with R4, C non-runner, D loses): reduces to a double on BD, which fails on D. Returns £0. Loss £1.
Trebles subtotal: £16 returned on £4 staked, profit £12.
The four-fold
One line: ABCD. With C a non-runner, this reduces to a treble on A, B and D. D lost, so the treble fails. Returns £0. Loss £1.
The full total
Putting it all together:
- Singles: £9 returned
- Doubles: £24 returned
- Trebles: £16 returned
- Four-fold: £0 returned
- Total return: £49 on a £15 stake. Profit: £34.
A little arresting, isn't it. The bet has been mauled by a Rule 4 deduction, a non-runner, and a loser in the four-fold leg, and yet the Lucky 15 still returns better than three to one on stake. The reason, on reflection, is obvious: with only two horses actually delivering winning results (A cleanly, B with a deduction), we still have one winning double (AB), one winning treble that collapses into the same AB double after the non-runner, and three winning singles (including the non-runner's voided stake). The structure of the Lucky 15 means that any two winners give you at least one winning double and several supporting singles; when one of the other selections is a non-runner rather than a loser, more lines survive than you might expect.
Some observations worth taking away
The first and most important point is that non-runners behave very differently from losers in a multiple. A losing leg kills every line it appears in. A non-runner merely shrinks those lines by one level. If you have four selections in a Lucky 15 and one is a non-runner, what you actually have is approximately a Patent on the other three plus a refunded single — which, if the remaining three all win, pays out extremely well. Punters who routinely replace tight favourites in multiples with more speculative prices rarely appreciate this particular structural asymmetry: a non-runner is a much softer outcome for a Lucky 15 than a loser, even at apparently equivalent prices.
The second point is about Rule 4. The 40p deduction on B turned what would have been a £5 profit on a single into a £3 profit, and reduced the winning double from £24 to £16. On a small Lucky 15 those are not life-changing sums, but on a larger unit stake — or in a Yankee or Heinz — the compounding gets meaningful quickly. A 40p Rule 4 on one leg of a Heinz with three winners can take a five-figure return down by several hundred pounds. Worth knowing in advance, rather than discovering at settlement.
The third point is that the Lucky 15 structure is unusually robust to the kind of mixed-signals afternoon described here, precisely because of the four singles and the six doubles. The four-fold is almost decorative on a typical afternoon — you need all four to come up to collect, and the expected-value contribution of the single four-fold line at realistic prices is small. It is the singles and the doubles that do the work, and the Lucky 15 gives you plenty of both. The comparison with the Yankee is worth reading if you haven't come across the structural case for each.
If you want to replicate the arithmetic in this piece with your own selections and results, the multiples calculator handles the full Lucky 15 settlement including Rule 4 deductions per leg and the reduction of lines containing non-runners. It produces the same answer as the line-by-line walkthrough above, which is the point of the calculator existing at all — but running through an example on paper once in a while is a useful exercise in understanding what the calculator is doing under the bonnet.