Lucky 31 Calculator

A Lucky 31 is a full-cover combination bet placed on five selections, encompassing all 31 possible non-empty subsets of those five selections. Specifically, it consists of 5 singles (one on each selection individually), 10 doubles (every possible pair from five selections), 10 trebles (every three-selection combination), 5 fourfolds (every four-selection combination), and 1 fivefold accumulator covering all five selections simultaneously. The total of 31 bets is a direct application of the mathematical formula 2^5 − 1 = 31 — the number of non-empty subsets of five elements. Like all full-cover bets in the Lucky series, the inclusion of singles means a return is guaranteed if even one selection wins.

The Lucky 31 is the natural extension of the Lucky 15 (four selections, fifteen bets) to five selections. It inherits the same core principle: every possible combination of winning selections generates at least one paying bet, and the singles ensure the bet never results in a complete loss as long as at least one selection wins. The five-selection structure means that when four or five selections win, the cumulative effect of multiple winning doubles, trebles, fourfolds, and potentially the fivefold creates returns that can be many multiples of the total stake. Even three winners from five creates a scenario where multiple doubles and one treble are all paying out simultaneously.

The name 'Lucky' refers primarily to the inclusion of singles and the promotional bonuses that bookmakers traditionally offer on Lucky bets — terms like double-odds consolation bonuses when only one selection wins, or percentage bonuses on total return when all selections win. These promotions, detailed in the bonuses section below, are an important part of why the Lucky 31 and its siblings (Lucky 15, Lucky 63) are so widely used by UK bettors. Without the promotional terms, the Lucky 31 is simply a mathematically complete five-selection full-cover bet; with them, it becomes a bet type with specifically enhanced value compared to its constituent parts.

The return from a Lucky 31 is calculated by summing the returns from all winning bets within the 31-bet structure. A bet within the Lucky 31 is a winner only if every selection within that particular combination won its event. The calculation begins by identifying all winning selections, then determining which of the 31 combinations consist exclusively of winning selections. For each such winning combination, the return is the unit stake multiplied by the decimal odds of all selections in that combination multiplied together. Singles return odds × stake; doubles return product of two odds × stake; trebles return product of three odds × stake; and so on up to the fivefold.

As an example, suppose five selections are priced at 2.0, 3.0, 4.0, 5.0, and 6.0, and three of them — priced at 3.0, 4.0, and 5.0 — all win. The winning bets within the Lucky 31 are: 3 singles (returning £3, £4, and £5); 3 doubles (returning £12, £15, and £20); and 1 treble (returning £60). Total gross return: £119. Total stake: £31 at £1 per line. Net profit: £88 from three of five selections winning. The two losing selections do not activate any bets involving them, so all combinations containing the 2.0 or 6.0 selections lose. This example demonstrates the substantial returns achievable from a Lucky 31 even in a partial-win scenario.

With all five selections winning, all 31 bets pay simultaneously. The fivefold alone — which multiplies all five selections' odds together — can produce a spectacular single-bet return. At odds of 2.0, 3.0, 4.0, 5.0, and 6.0, the fivefold returns £1 × 2 × 3 × 4 × 5 × 6 = £720. Combined with the ten doubles, ten trebles, five fourfolds, and five singles, the total gross return from a clean sweep at these prices would be in the thousands. This ceiling-potential from the fivefold is one of the Lucky 31's most exciting features for five-race festival bettors who have identified five strong selections and want to maximise their upside if all five win.

Most major UK and Irish bookmakers offer promotional bonuses specifically for Lucky 31 bets, similar to the bonuses available for Lucky 15s and Lucky 63s. The most common bonus type is a consolation bonus for single-winner scenarios: if only one of your five selections wins, some bookmakers will double the winnings from the single on that selection, effectively paying out at double odds on the winner. This consolation bonus makes single-winner scenarios significantly more palatable by partially or fully recovering the 31-unit total stake when your winner is a reasonably priced selection.

The other standard Lucky 31 promotion is an all-winners bonus: if all five of your selections win, bookmakers may add a percentage bonus to your total return — commonly 10% to 25% above the calculated return. On a large Lucky 31 return where the fivefold and fourfolds have multiplied substantially, this percentage bonus can be worth a considerable sum in absolute terms. Some bookmakers also offer a compound bonus structure where both the consolation and all-winners bonuses are available on the same ticket. Always read your bookmaker's specific Lucky 31 terms before placing, since the bonus terms can vary significantly between providers and are sometimes limited to specific events or sports.

The availability and generosity of Lucky 31 bonuses is one of the key practical reasons to prefer the Lucky 31 over the Canadian (26 bets, no singles) as a five-selection full-cover bet. The Canadian offers lower total stake (26 vs 31) but qualifies for no Lucky bonus terms, since it is not structured as a Lucky bet. The Lucky 31's five additional unit stakes buy not only singles coverage but also access to bookmaker promotional terms that can meaningfully enhance returns. Comparing the effective value of the Lucky 31 with bonuses against the Canadian without bonuses should be part of any five-selection betting decision.

The choice between a Lucky 15 (four selections, fifteen bets) and a Lucky 31 (five selections, thirty-one bets) is fundamentally a choice about how many selections to include. If you have four confident selections, the Lucky 15 is the appropriate vehicle. If you have a fifth selection you are confident about, upgrading to a Lucky 31 is generally worthwhile — the fifth selection doubles the number of bets from 15 to 31 but multiplies the potential return substantially more when all five win. The incremental cost of adding a fifth selection to the Lucky 15 structure is sixteen additional unit stakes.

From a risk management perspective, the Lucky 31 distributes your stake across more combinations, meaning more partial-win scenarios still produce a return compared to the Lucky 15. Five selections instead of four means you could have three of five winning (creating multiple doubles and a treble) versus only three of four winning — mathematically, having more selections in a full-cover bet provides more distinct winning scenarios that produce a payout. However, the total stake is also higher, so the Lucky 31 requires more capital commitment than the Lucky 15 for the same unit stake per line.

A practical rule of thumb: use the Lucky 15 on days when you have exactly four strong selections and do not want to add a speculative fifth pick just to fill a larger bet. Use the Lucky 31 when you have five genuine selections across five different races or matches, each researched with similar confidence. Forcing a fifth selection into a Lucky 31 when you are not confident about it wastes the extra stake on a selection that will likely drag down your results. The Lucky 31 works best when all five selections are assessed on their own merits as value bets, not when one is added simply to participate in the larger bet structure.

The total stake of a Lucky 31 is thirty-one times your unit stake per line. At £1 per line, the total is £31. At £0.50 per line, it is £15.50. At £0.10 per line — the minimum at most UK bookmakers — the total is just £3.10, making the Lucky 31 accessible even for bettors with very limited bankrolls. This flexibility in unit stake is one of the bet type's key practical advantages: a 10p Lucky 31 provides the same structural coverage across all 31 combinations as a £1 Lucky 31, just with proportionally smaller absolute returns. Bettors on festival days often choose a modest unit stake to participate across multiple Lucky 31s on different race cards.

When setting your unit stake for a Lucky 31, consider the total stake in the context of your overall betting bankroll. A common guideline is that no single bet ticket should represent more than 2-5% of your total betting bankroll, to ensure that a losing day does not cause disproportionate damage. At that guideline, a bettor with a £500 bankroll might comfortably place Lucky 31s at £0.10 to £0.25 per line (£3.10 to £7.75 total per ticket). The goal is to size the bet so that the potential returns from multiple winners are meaningful relative to your bankroll, while the total loss from a complete losing day remains within acceptable parameters.

An important consideration when staking Lucky 31s is that the expected return-to-stake ratio is lower than betting singles on the same selections, because the bookmaker's margin compounds across multiple legs of the doubles, trebles, and accumulators. The value proposition of the Lucky 31 is not superior expected value but rather superior return distribution — you get back something in more scenarios, and you get back more when multiple selections win simultaneously. For bettors who bet recreationally and value the experience of having multiple bets active simultaneously rather than purely maximising expected value, the Lucky 31 provides excellent entertainment value relative to its cost.