8. Multiples, systems, combinations

Single, multiple, system: which is which?

On a single bet you stake on one tip: if it comes in, it pays; if not, you lose the stake. A multiple (accumulator, parlay) ties several tips into a single bet: for the payout every leg must hit, and in return the odds multiply. Two 1.90 tips in a multiple pay 3.61, five such already pay 24.76 — the numbers quickly become tempting.

A system bet is the "insured" version of the multiple: from the selected tips you don’t place a single big multiple, but all possible smaller combinations at once. This way you get some payout even if not every leg hits, in return for paying for more part-bets. The best-known, named systems:

• 1Trixie: 3 tips, 4 bets (3 doubles + 1 treble). Any payout requires at least 2 winners.
• 2Patent: 3 tips, 7 bets (3 singles + 3 doubles + 1 treble). Even 1 winner pays something.
• 3Yankee: 4 tips, 11 bets (6 doubles + 4 trebles + 1 fourfold).
• 4Lucky 15: 4 tips, 15 bets (the yankee + 4 singles).
• 5Canadian (super yankee): 5 tips, 26 bets; Heinz: 6 tips, 57; Super Heinz: 7 tips, 120; Goliath: 8 tips, 247 bets.
• 6"2/4", "3/5" type systems: only the combinations of the given size (for example all trebles from five tips), a favourite format of the local bookmakers.

The stake is per bet. A "€10" trixie actually costs 4 × €10 = €40, and a goliath at the same base stake costs €2,470. The first risk appears already here: the name of the system sounds small, the total exposure is large.

Margin compounding: every leg pays again

In chapter 4 you calculated that every odds contains the bookmaker’s margin. In a multiple the odds multiply, and the margin multiplies with them: with every added leg you pay the bookmaker’s "price" again. This is the most important, numerically demonstrable property of multiples.

Take a tip whose true chance is 50%, so the fair odds are 2.00, but the bookmaker gives 1.90: as a single, in the long run you get back 95% of your money, an expected loss of 5%. Tie three together: the multiple pays 1.90 × 1.90 × 1.90 = 6.86, while the fair odds would be 8.00 and the true winning chance is 12.5%. The expected return is 0.95 × 0.95 × 0.95, i.e. 85.7%, the loss already 14.3%. With five legs 22.6%, with eight legs 33.7%: in a goliath-sized multiple the margin takes a third of your money before a single match has been decided.

The system bet does not help with this, because every part-combination is built from the same margin-loaded odds. The trixie from the three tips above has an expected return of 89.1%, the patent 91.6%: better than the plain treble, but only because it also contains shorter multiples and singles, not because the system "gives back" anything from the margin.

Rule of thumb: if a leg’s expected loss is v, then the expected return of a multiple of n independent legs is (1 − v) to the power n. The margin does not add up, it compounds.

Variance explosion and correlated legs

A multiple is not only more expensive but also far more capricious. A multiple of three 50% legs comes in 12.5% of the time, and a full hit on a four-leg yankee 6.25% of the time: the typical experience is a long, unbroken losing streak, rarely interrupted by a big payout. In Module IV (especially in chapter 21) you will calculate how long a losing streak counts as "normal": for multiples these numbers grow several times over, and psychologically this is the most dangerous terrain, because the memory of the big win covers up the continuous, tiny bleeding.

A separate trap is the multiple within a single match (same game parlay): here the legs are not independent. If your team wins, it is more likely that their striker also scored, but the multiplied odds would assume independence. Bookmakers know this exactly, and either ban or reprice correlated combinations — to their own benefit, of course: the actual margin measured on such products is, according to industry reports, several times that of singles.

The more legs there are, and the more interrelated they are, the less you are betting on your knowledge and the more on the bookmaker’s pricing.

Why does the bookmaker advertise it, and when is it rational anyway?

It is no accident that ads almost always feature a multiple: acca boost, bet insurance, "boosted odds". From the bookmaker’s perspective the multiple is the perfect product: high margin, huge variance (so even a good player loses for a long time), and a lottery-ticket experience — a big dream from a small stake. The promotions give back a little of this increased margin so that you play more of it.

Is there a situation where the multiple is mathematically defensible? One: if every leg is individually positive expected value (chapter 10) and the legs are independent, then the edges multiply too and the multiple’s EV is higher than that of the singles. Only the variance grows even faster, so the rules of stake sizing (chapter 25) would allow only a very small stake on it, and finding +EV legs is itself the hardest task of the course (chapter 14). In practice this also includes targeted promotion exploitation (chapter 18), when the boost or the insurance actually covers the margin — always work this through.

If you place multiples for fun, that is fine, but know the price: according to the calculation above, a larger multiple or system gives 20–30% of your money to the bookmaker, regardless of how well you know the sport. As an earning plan, the multiple is the market’s most expensive product.

If you play it: few legs, a small and pre-set stake, avoiding correlated legs, and the rules of chapter 39 (responsible gambling). The multiple is entertainment, not strategy.