Lucky 31 Calculator: Five Horses, 31 Bets Settled, Win or Each Way

A Lucky 31 has more moving parts than most people ever check, so the Lucky 31 calculator above shows all 31 of them. It is loaded with 20p on five horses at 7/4, 11/4, 4/1, 6/1 and 10/1. Three of them won, the 7/4, 4/1 and 10/1 shots, and two didn’t. The bet cost £6.20 and returns £53.80.

That return comes from seven of the 31 lines. The other 24 each contained at least one of the two losers. Knowing which seven survived, and why, is the quickest way to understand what a Lucky 31 is really doing.

What survived on the example day

Number the horses 1 to 5 in the order above, so the losers are 2 and 5 is the 10/1 winner. The winners are 1, 3 and 5.

The singles on those three pay: 20p at 7/4 is 55p, 20p at 4/1 is £1, 20p at 10/1 is £2.20. That is £3.75.

The doubles among them pay: 1+3 at 7/4 and 4/1 returns £2.75, 1+5 at 7/4 and 10/1 returns £6.05, 3+5 at 4/1 and 10/1 returns £11. That is £19.80.

The one treble without a loser, 1+3+5, returns 20p × 2.75 × 5 × 11, which is £30.25.

No four-fold or five-fold can avoid both losers, so they all lose. Add the rest and you get £53.80. The calculator’s summary says the same: singles three of five paying, doubles three of ten, trebles one of ten, the rest none. Over half the return came from one treble. That is typical of a three-winner Lucky 31: the singles are small change, and the doubles and the one clean treble do the real work.

Using the Lucky 31 calculator

Choose Lucky 31 and the Lucky 31 calculator shows five rows. Enter each price as the bookmaker showed it, set the results, and type the stake per bet. “20p Lucky 31” means 20p in the stake box and £6.20 in the total; “£1 Lucky 31” costs £31.

To spend a fixed sum instead, press Total. £10 in total works out at about 32p a line, and on the example day it returns £86.77. Tick each way to double the bet to 62 lines. Each of the five rows then has its own place terms, which matters, because five races on one day almost never share the same field sizes.

How the return grows with winners

Using the same five prices at 20p, the gap between a poor day and a good one is enormous.

One winner pays only its single: 55p if it is the 7/4 shot, £2.20 if it is the 10/1 shot. Either way it is a small refund on a £6.20 bet. At any stake, a lone winner only covers a Lucky 31 at 30/1 or bigger: try it on the slip with one horse at 30/1 and the rest beaten, and the 20p bet returns exactly £6.20.

Two winners pay two singles and one double. The two shortest prices return £3.36, still a loss. The two longest, 6/1 and 10/1, return £19.00.

Three winners pay three singles, three doubles and a treble. The three shortest return £21.18 and the three longest £115.00. The example day, a mix, returned £53.80.

Four winners return £170.80 at the four shortest prices, and all five winning returns £2,051.80. On that last day the singles are £5.90 of the total. The five four-folds bring in £844.94 and the single five-fold £794.06, which says everything about where the money in a Lucky 31 lives.

Each way Lucky 31s

Each way turns 31 bets into 62, so 20p each way costs £12.40. With 1/5 terms on every race, the example day returns £58.86: the £53.80 from the win side and £5.06 from the place lines on the three winners.

The place side can do much more than that. If the two losers had placed instead, every place line would pay, and the bet would return £96.55. If all five had placed and none had won, the place lines alone would return £42.75 from the £12.40 stake.

Terms matter more here than on a smaller bet, simply because there are more place lines for them to act on. A single race paying 1/4 instead of 1/5 lifts the place price of one horse, and that horse sits in sixteen place lines. Set each row’s terms from the race it ran in, not from a general rule, and the place side of the settlement will match.

That is the case for each way on a big full-cover bet. With five horses, the chance of a day where several run well without winning is real, and the place lines turn that day from a loss into a return. It is weakest with short prices, because a quarter or a fifth of a short price is very little.

Non-runners, Rule 4 and dead heats

Each of these is set on one row and applied across every line that horse is in, which in a Lucky 31 is sixteen of the 31.

A non-runner. If the 11/4 horse had been withdrawn instead of losing, its single would refund 20p and all its other lines would be settled on the remaining horses. With three of those four winning, far more lines would survive, and the bet would return £107.80 instead of £53.80. The same horse running and losing cost the bet half its return.

Rule 4. A 25p deduction on the 7/4 winner cuts a quarter off its winnings in every line it appears in, and the return drops to £47.50.

A dead heat. If the 7/4 horse dead heated for first with one other, every line containing it would be settled on half the stake at that leg, and the bet would return £34.00.

Settling a Lucky 31 on paper

Thirty-one lines sound like a lot to settle by hand, but a Lucky bet has a tidy property: the whole return can be found in one sum. Write each winner’s decimal price plus one, multiply those figures together, subtract one, and multiply by the line stake.

For the example day, the three winners are at 2.75, 5 and 11 in decimals. Add one to each and you have 3.75, 6 and 12. Their product is 270. Take one away, 269, and multiply by the 20p line stake: £53.80, the same as the slip. The losers simply don’t appear in the sum, because no line containing them pays.

A non-runner fits the same pattern. It counts as a price of 1.0, so its “plus one” figure is 2. With the 11/4 horse withdrawn instead of beaten, the sum becomes 3.75 × 2 × 6 × 12, which is 540, minus one, times 20p: £107.80, again matching the slip. The Heinz guide explains why the trick works and how to adapt it for the bets without singles.

The sum stops working as soon as anything is split: each way terms, a dead heat or a Rule 4 deduction give a horse more than one value, and then the calculator is the practical route.

Planning one before the races

Because the Lucky 31 calculator settles any set of results, it is just as useful before the races as after. Enter your five horses and prices, then try the days that are likely to happen rather than the one you hope for.

Mark two horses as winners and three as beaten, and look at the return. Then try a different two. At the example prices, four of the ten possible pairs of winners lose money and six show a profit, so on a two-winner day it is which two that decides whether the bet is up or down. If most two-winner days lose money at your prices, the bet is really a three-winner bet, and it helps to know that before you place it. Then try each way on the same results and compare the extra cost with the extra return.

None of this predicts anything. It simply shows the range of what the bet can do, which is the part of the decision you can know in advance.

Lucky 31 or Canadian?

The Canadian, or Super Yankee, is the Lucky 31 without the five singles: 26 bets instead of 31, £5.20 at 20p instead of £6.20. On the example day it would return £50.05, against £53.80 for the Lucky 31. The singles added £3.75 and cost £1.

With one winner, the difference is starker. The Canadian returns nothing; the Lucky 31 returns the single. That is the one-winner insurance the “Lucky” bets are named for. With four or five winners, the singles are a rounding error in a large total.

On four horses the same choice is the Lucky 15 or the Yankee, and on six it is the Lucky 63 or the Heinz. The bet itself, with the Canadian and the rest of the big full-cover bets, is covered in the Heinz and big full-cover bets guide.

Stakes and checking a settlement

Every line scales with the stake. On the example day, a 10p Lucky 31, £3.10 in total, returns £26.90. A 50p Lucky 31 returns £134.50 and a £1 Lucky 31 £269.00. The structure, and which lines pay, never changes.

To check a settlement, enter the prices you were paid at and the declared results. If you backed at SP, use the returned starting prices from each race. With 31 lines the full list is long, so start with the summary by size: if the number of paying singles, doubles and trebles matches what you expect, the results are right, and any difference is in a price. If a count is wrong, one of the results is. A Rule 4 deduction in one of the five races is the most common reason a Lucky 31 settles below the figure you worked out.