Suppose you want to play with 10 numbers instead of just 6. Naturally, you are willing to play more than one ticket. However, you want a certain guarantee. Let us say that you want a 4-win whenever 4 of the numbers drawn are in your set of 10 numbers. This means you want a set of combinations (tickets) that covers every possible quadruple out of your 10 numbers. Such a set of combinations is what we call a lottery system. In this example, the lottery system must have the property that any quadruple out of your set of 10 numbers is contained in at least one of your combinations, so that you get a guaranteed 4-win whenever 4 of your 10 numbers are drawn. You can find a lottery system with this property under # 20 in the book.
In a sense, a lottery system expands
the guarantee that you have on playing just 6 numbers (one ticket). If
you correctly guess 4 numbers, you are guaranteed a 4-win. The
lottery system in our example guarantees a 4-win on 4 numbers guessed correctly,
playing with 10 numbers. (In the book
you can find systems with 4 on 4 guarantee for playing anywhere between
7 and 19 numbers. Of course, the book contains
systems with many other types of guarantees; a total of 128 lottery systems
are presented.)