How to calculate Yankee, Patent, Trixie and Lucky 15 returns: the complete worked-example guide

Every formula, every bet count, and full step-by-step worked examples showing exactly how to calculate your own returns by hand - for Trixie, Patent, Yankee, Lucky 15, Canadian, Lucky 31, and Lucky 63

This site's guide to accumulator betting covers what system bets like the Yankee and Patent actually are. This guide picks up from there and focuses specifically on the calculation itself - the exact formulas, the precise number of bets inside each system, and full worked examples showing exactly how a real return is calculated by hand, step by step, using real numbers rather than abstract descriptions.

The core structures, precisely

Every system bet covered in this guide follows the same underlying logic: instead of one all-or-nothing accumulator, your selections are broken down into every possible smaller combination - doubles, trebles, and so on - so that a partial win still produces a partial return.

The pattern worth understanding once, since it explains every row in this table: each "Lucky" variant is simply its equivalent Yankee-family bet (Yankee, Canadian, or the six-selection equivalent) with singles added on top. Adding singles is what allows a return from just one winning selection - without them, you need at least two winners before anything comes back. This is exactly why Lucky 15 exists as the more forgiving, more popular sibling to the Yankee: same four selections, same 11 combination bets, plus 4 more single bets layered on top for a total of 15.

The key rule. Short odds (2/1 or shorter) favour the Yankee. Longer odds favour the Lucky 15, where a single winner can produce a meaningful standalone return. A Lucky 15 costs exactly 36% more than the equivalent Yankee.

The total stake formula

Your total stake is simply your chosen unit stake multiplied by the number of bets in the system. A £1 Lucky 15 costs £15 total (15 bets × £1). A £2 Yankee costs £22 total (11 bets × £2). This is worth calculating and confirming before you place any system bet - it's the single most common point of confusion for anyone new to these bet types, since a "£1 Lucky 15" doesn't mean a £1 total stake, it means £1 on each of the 15 individual bets within it.

Full worked example: Yankee (4 selections, 11 bets)

Let's use four horses - A, B, C, and D - with odds of 2/1, 3/1, 5/2, and 4/1 respectively, and a £1 stake per bet (£11 total).

The 11 bets that make up the Yankee:

• 6 doubles: AB, AC, AD, BC, BD, CD
• 4 trebles: ABC, ABD, ACD, BCD
• 1 fourfold: ABCD

Scenario: A and B win, C and D lose.

Only combinations containing exclusively A and/or B (with no C or D) can possibly settle as winners. That's a single bet: the AB double.

Calculating the AB double's return: A's odds of 2/1 mean a £1 bet returns £3 (£2 profit plus your £1 stake back). Rolling that £3 onto B at 3/1 returns £3 × 4 = £12 (since 3/1 means the bet quadruples: 3x profit plus the stake itself).

Total return: £12, from an £11 total stake - a £1 profit. Every other bet in the Yankee (the remaining 5 doubles, all 4 trebles, and the fourfold) contains either C or D and therefore loses, since both those selections lost. This illustrates precisely why our accumulator betting guide describes Yankees as needing genuine care in selection - a modest two-winner result here barely breaks even, even though a "partial win" technically occurred.

If three selections had won instead (say A, B, and C, with only D losing): three doubles (AB, AC, BC) and one treble (ABC) would all settle as winners, producing a meaningfully larger combined return, since compounding odds across a winning treble adds considerably more than a single winning double alone.

Full worked example: Lucky 15 (4 selections, 15 bets)

Using the same four selections and odds as above (A: 2/1, B: 3/1, C: 5/2, D: 4/1), a £1 Lucky 15 costs £15 total.

The 15 bets:

• 4 singles: A, B, C, D
• 6 doubles: AB, AC, AD, BC, BD, CD
• 4 trebles: ABC, ABD, ACD, BCD
• 1 fourfold: ABCD

Scenario: only A wins, B, C, and D all lose.

Because Lucky 15 includes singles, this single winning selection still produces a return - something a Yankee, with no singles at all, cannot do under the identical scenario.

Calculating the return: the single bet on A at 2/1 returns £3 (as calculated above). Every double, treble, and the fourfold all require at least one additional winner, so none of them settle. Your total return is £3 from a £15 stake - a loss overall, but genuinely better than the Yankee's equivalent single-winner scenario, which would return nothing at all.

This is precisely why Lucky 15's classic bonus structure matters, and why it's worth checking for directly before placing the bet. Many UK bookmakers offer two specific consolation bonuses on Lucky 15 bets: a "one winner" bonus, commonly tripling the odds on your single winning selection specifically, and an "all four winners" bonus, commonly doubling your total combined return if every selection in the bet comes in. Applying the one-winner bonus to the scenario above: A's odds are tripled from 2/1 to an effective 6/1 for this specific calculation, turning your £3 return into £7 - a meaningfully better outcome than the unenhanced figure, and specifically why Lucky 15 is often chosen over a plain Yankee when you're less than fully confident in all four selections. These bonus terms vary by bookmaker and aren't universal - always check the specific operator's current Lucky 15 terms before assuming either bonus applies.

Check for these bonuses. Many bookmakers offer a one-winner bonus (commonly 3x odds) and an all-four-winners bonus (commonly 2x total return) on Lucky 15 specifically - not universal, always verify your bookmaker's current terms.

Full worked example: Patent (3 selections, 7 bets)

Using three selections - A, B, C - at 2/1, 3/1, and 5/2, a £1 Patent costs £7 total.

The 7 bets: 3 singles (A, B, C), 3 doubles (AB, AC, BC), 1 treble (ABC).

Scenario: A and B win, C loses.

Three bets settle as winners: the single on A (£3 return), the single on B (£4 return, since 3/1 quadruples a £1 stake), and the AB double (calculated the same way as the Yankee example above - A's £3 return rolled onto B at 3/1 produces £12).

Total return: £3 + £4 + £12 = £19, from a £7 total stake - a £12 profit. This worked example directly illustrates the core advantage a Patent holds over the equivalent Trixie (covered next) built from the same three selections: because the Patent includes singles, both individual winners contribute their own direct returns on top of the winning double, not just the double itself.

Trixie (3 selections, 4 bets): the same scenario, without singles

Using the identical A, B, C selections and the identical A-and-B-win, C-loses scenario: only the AB double settles, for the same £12 return calculated above, from a £4 total stake - an £8 profit. The Patent's total profit is actually higher than the Trixie's in this specific scenario (£12 profit versus £8), despite costing more to place - because the Patent's two winning singles (A and B) each contribute their own direct return on top of the identical winning double both bets share. This is worth understanding directly: adding singles doesn't just add a lower floor for near-miss scenarios - when your selections do win, the extra singles can genuinely add to your net profit too, not just protect against a worse outcome. A Trixie's real advantage over a Patent shows up specifically in scenarios where none of your selections would have won as standalone singles anyway, since you're not paying for coverage that wouldn't have paid out regardless.

Canadian, Lucky 31, and Lucky 63: the same logic, scaled up

These larger systems follow the identical underlying principle covered throughout this guide, simply extended to more selections. A Canadian (5 selections, 26 bets) is the Yankee-family structure extended by one more selection, adding fourfolds and a fivefold on top of the doubles and trebles. Lucky 31 is the Canadian with singles added, exactly mirroring the Lucky 15/Yankee relationship. Lucky 63 extends the same pattern to six selections and 63 total bets.

The practical calculation approach for these larger systems is identical to the worked examples above - identify which specific combinations contain only your winning selections, calculate each one's individual return by rolling the odds through sequentially exactly as shown in the Yankee and Patent examples, then sum every winning bet's return together. The math doesn't change with scale; there are simply more individual combinations to check.

Choosing between a three-selection and a four-selection system

This is worth stating plainly as a practical decision-making point: a Patent is the right choice when you have three genuinely confident selections and want a real safety net from just one winner. A Trixie suits the same three selections if you're specifically confident in at least two of them landing and want a lower total outlay in exchange for needing that stronger result. A Yankee suits four selections where you're reasonably confident in at least two. Lucky 15 suits four selections where you want the same coverage as a Yankee, plus a genuine safety net from just one winner - at the cost of a larger total stake, partially offset by the bonus structure covered above when it's available.

Choosing between Yankee and Lucky 15: a rule worth knowing

Beyond the general "how confident are you" framing already covered, there's a more specific, genuinely useful rule that independent betting analysis converges on consistently: the right choice depends heavily on how short or long your selections' odds actually are.

Short-odds selections (roughly 2/1 or shorter) tend to favour the Yankee. At low odds, the extra singles a Lucky 15 adds don't contribute much - a single bet at 6/4 or evens simply doesn't return enough on its own to justify the 36% higher total stake (15 bets versus 11) the Lucky 15 requires for that extra coverage.

Longer-odds, less-certain selections tend to favour the Lucky 15. At bigger prices, a single winning selection can produce a genuinely meaningful return on its own - precisely the scenario the worked example earlier in this guide illustrates, where a single 2/1 winner returned £3, and considerably more once the one-winner bonus was applied. The extra cost of the singles is more clearly justified when the singles themselves carry real standalone value.

The precise cost difference, worth having as a reference figure: a Lucky 15 costs exactly 36% more than the equivalent Yankee (15 bets versus 11, on the same four selections), or equivalently, a Yankee costs about 27% less than the Lucky 15 covering the same picks. Neither figure changes regardless of your specific stake size - it's a fixed ratio built into the bet structures themselves.

A rough rule of thumb for Yankee profitability, worth treating as directional rather than absolute: independent analysis suggests that hitting three of your four selections in a Yankee typically produces at least a break-even result, with genuine profit becoming more likely from that point - though this depends heavily on the specific odds involved, and shouldn't be treated as a guaranteed threshold.

System bets don't create value - they only redistribute how existing value pays out. The most important factor remains whether your individual selections are genuinely good value bets in the first place.

An honest caveat worth including: system bets don't create value

This is worth stating plainly, consistent with the honest approach this site takes throughout its betting guides. Restructuring your selections into a Trixie, Yankee, or Lucky 15 doesn't create genuine betting value that wasn't already present in your original picks - it simply redistributes how that value (or lack of it) pays out across different winning scenarios. If your four selections don't individually represent good value bets in their own right, wrapping them into a system bet doesn't improve their underlying odds or your genuine expected return; it only changes the shape of your risk, spreading a chance of partial return across more scenarios in exchange for a higher total stake. The single most important factor in whether any system bet is worth placing remains identical to what matters for a straight bet or a standard accumulator: whether your individual selections are genuinely good value in the first place, a principle covered in full in our guide to reading betting odds. A cleverly structured bet built from weak selections is still a bet built from weak selections.

A sensible bankroll guideline worth applying here specifically: consistent with the general principles covered in our guide to bankroll management, keeping your total stake on any single system bet to a small percentage of your overall bankroll - commonly cited around 1-2% - helps ensure that even a disappointing result from a larger system like a Lucky 63 doesn't meaningfully damage your bankroll in one placement.

Frequently asked questions

Should I choose a Yankee or a Lucky 15?

It depends heavily on your selections' odds. Short-odds picks (roughly 2/1 or shorter) tend to favour the Yankee, since Lucky 15's extra singles don't add much value at low prices. Longer-odds, less-certain selections tend to favour the Lucky 15, where a single winner can produce a genuinely meaningful return on its own. The Lucky 15 costs exactly 36% more than the equivalent Yankee for the same four selections.

Does building a system bet like a Yankee or Lucky 15 improve my actual betting value?

No - restructuring selections into a system bet doesn't create value that wasn't already there. It only changes how existing value (or lack of it) pays out across different scenarios. The most important factor remains whether your individual selections are genuinely good value bets in their own right.

How much does a £1 Lucky 15 actually cost in total?

£15 - a "£1 Lucky 15" means £1 staked on each of the 15 individual bets that make up the system (4 singles, 6 doubles, 4 trebles, 1 fourfold), not a £1 total stake.

What's the minimum number of winners needed for a Lucky 15 to pay out?

Just one - because Lucky 15 includes four singles, a single winning selection still produces a return, unlike a Yankee (built from the same four selections but without singles), which needs at least two winners before any return occurs.

What are the Lucky 15 bonuses?

Many UK bookmakers offer two specific consolation bonuses, though terms vary by operator: a "one winner" bonus commonly tripling the odds on your single winning selection, and an "all four winners" bonus commonly doubling your total combined return. Always check a specific bookmaker's current terms before assuming either applies.

Is a Patent or a Trixie better for three selections?

It depends on your confidence level. A Patent costs more (7 bets versus 4) but can still return something from just one winner, and the worked example in this guide shows it can also produce a genuinely higher net profit than the equivalent Trixie when your selections do win, since each winning single adds its own return on top of the shared winning double. A Trixie's real advantage is a lower total stake specifically in scenarios where your individual selections wouldn't have won as standalone singles anyway.

How do I calculate my own system bet returns by hand?

Identify which individual bets within the system contain only your winning selections (any bet including a losing selection settles as a loss), calculate each surviving bet's return by rolling the odds through sequentially - your stake times the first selection's odds, then that result rolled onto the next selection's odds, and so on - then sum every winning bet's individual return together for your total payout.

This guide is for educational purposes and does not guarantee any betting outcome. All system bet calculations shown use example odds for illustration - always confirm exact terms, bonus structures, and current odds with your specific bookmaker before placing a bet. Gambling problem? BeGambleAware.org | 0808 8020 133. Information correct as of September 2026.