Wheeling system, in full
The mathematical name is a covering design, and it long predates lotteries. The problem is combinatorial: given a set of numbers you want to play, find the smallest collection of lines covering every possible way a subset of them could be drawn. A full wheel plays every combination of the chosen group. An abbreviated wheel plays fewer lines and accepts a weaker guarantee for the saving.
Whatever a wheel guarantees is conditional and is always a smaller match than the top prize. A typical one promises a four-number match if five of your twelve numbers are drawn, promises nothing if only three come up, and cannot promise a jackpot unless the entire pool has been wheeled. What that does and does not buy, and why vendors overstate it, is worked through in our guide to lottery wheeling.
- Lottery mechanics
- Abbreviated wheel, Covering design, Lottery wheel
A worked example
Pick 10 numbers for a 6/49 game. A full wheel plays every six-number combination of those 10, which is C(10,6) = 210 lines. If all six drawn numbers sit inside your 10, one of the 210 lines is the jackpot. The chance of that is C(10,6) / C(49,6) = 210 / 13,983,816, which is exactly what 210 distinct random lines would give you.
See also
Where it comes up on this site
Wheeling system: frequently asked
That if five of the numbers you wheeled are drawn, at least one of your lines holds four of them. Nothing more.
For the jackpot, yes: 210 lines are 210 chances either way. The difference is in the small tiers, where a wheel converts a near miss into a guaranteed lower-tier hit that scattered lines might have missed.