Systems, wheels and syndicates
A system entry plays every combination of the numbers you pick. Here is exactly how many games that is, what it costs, and what it does to your odds — with the arithmetic shown.
Walk into a newsagent in Australia, Canada or the UK and you can buy an entry that lets you pick more numbers than the game asks for. Pick eight numbers in a game that draws six, and the terminal prints a "System 8". The marketing calls it a way to increase your chances. That is true, and it is also the least interesting thing about it, because the increase is exactly proportional to what you pay.
Here is what you are actually buying.
If a game asks you to pick 6 numbers and you nominate 8, the entry plays every possible 6-number combination that can be made from your 8. The count is a binomial coefficient:
C(8, 6) = 8! / (6! × 2!) = (8 × 7) / (2 × 1) = 28 games
That is the whole idea. There is no cleverness in the machine, no special draw, no weighting. A System 8 is a bundle of 28 ordinary tickets that happen to be built from the same pool of eight numbers. If you would rather fill out 28 slips by hand with those same combinations, you would hold an identical position.
The counting generalises. For a game where a standard entry picks k numbers, a System N plays C(N, k) games:
| System | Games in a 6-pick game | Games in a 7-pick game |
|---|---|---|
| System 7 | C(7,6) = 7 | — |
| System 8 | C(8,6) = 28 | C(8,7) = 8 |
| System 9 | C(9,6) = 84 | C(9,7) = 36 |
| System 10 | C(10,6) = 210 | C(10,7) = 120 |
| System 11 | C(11,6) = 462 | C(11,7) = 330 |
| System 12 | C(12,6) = 924 | C(12,7) = 792 |
| System 15 | C(15,6) = 5,005 | C(15,7) = 6,435 |
| System 20 | C(20,6) = 38,760 | C(20,7) = 77,520 |
Notice how fast the numbers climb. Going from System 8 to System 12 does not double the entry — it multiplies it by 33.
Australia's Saturday Lotto draws 6 numbers from 45. The total number of possible combinations is:
C(45, 6) = 8,145,060
A single standard game covers one of those, so division 1 odds are 1 in 8,145,060. A System 8 covers 28 of them, so:
8,145,060 ÷ 28 = 1 in 290,895
That is a genuine 28-fold improvement. It is also exactly 28 times the price. At roughly $0.90 a game, a System 8 costs about $25.20 — 28 times the cost of one game, for 28 times the chance. Every system size behaves the same way:
| System | Games | Approx. cost at $0.90/game | Division 1 odds | Improvement |
|---|---|---|---|---|
| Standard | 1 | $0.90 | 1 in 8,145,060 | 1× |
| System 7 | 7 | $6.30 | 1 in 1,163,580 | 7× |
| System 8 | 28 | $25.20 | 1 in 290,895 | 28× |
| System 9 | 84 | $75.60 | 1 in 96,965 | 84× |
| System 10 | 210 | $189.00 | 1 in 38,786 | 210× |
| System 12 | 924 | $831.60 | 1 in 8,815 | 924× |
| System 15 | 5,005 | $4,504.50 | 1 in 1,627 | 5,005× |
Run any game's numbers yourself with the system and wheel cost calculator, or see the live table on each game's systems page — for example Oz Lotto systems.
Cost and odds improve by exactly the same factor. There is no size at which a system becomes better value per dollar than buying the equivalent number of standard games. The expected return on a System 12 is precisely 924 times the expected return on one game, and the price is precisely 924 times the price. If the game has a negative expected value — and every draw game does at normal jackpots — then a system multiplies the loss along with the chance.
This is not an argument against systems. It is an argument against believing they are a strategy rather than a quantity. A System 10 is not a smarter bet than ten standard games; it is a bigger bet than one, arranged in a particular pattern.
Because of what happens when several of your numbers come up. A system entry's combinations overlap heavily — each of the 28 lines in a System 8 shares five numbers with several others. That correlation means your outcomes cluster: most draws you win nothing at all, but when a handful of your numbers are drawn, you collect several prizes at once across multiple divisions rather than a single small one.
That trade — more nothing, bigger somethings — is the real difference between a system and the same money spread over unrelated lines. It is worked out ball by ball in System 8 vs 12 standard games, and the general principle is in do wheeling systems improve your odds?.
If you are splitting the cost with other people, the maths changes again — see syndicate maths.
Last verified: 2026-08-29