A covering design C(v,k,t,m,=b) is a pair (V,B), where V is a set of v elements (called points) and B is a collection of b k-subsets of V (called blocks), such that every m-subset of V intersects in at least one member of B in at least t points.
When applied to lottery, in form of an abbreviated wheel:
- v: total numbers in the design; amount of numbers you choose to play the wheel
- k: size of a block or bet
- t: minimum guarantee
- m: amount of numbers that must be guessed correctly in the draw
- b: number of blocks or bets or tickets
Wheel C(10,5,3,4,=7) describes the wheel with 10 chosen numbers designed for a Pick 5 lottery. The wheel guarantees at least one prize of 3 matches if 4 officially drawn numbers are within the group of 10 chosen numbers. Finally, the number of bets generated is 7, reduced from a total of 252.00 possible combinations of 10 taken 5 at a time. The coefficient of reduction is 36.00.