Let us consider our basic example, System # 20 (you play with 10 numbers in 20 tickets and you get a 4-win whenever 4 of the numbers drawn are in your set of 10 numbers). Recall that 20 is the minimum number of tickets that will guarantee you this prize. Now, suppose you want to play for two 4-wins guaranteed whenever 4 of your numbers are drawn. The simplest way is to play twice the System # 20 (so you have to fill 40 tickets). This way you will have repeated tickets and repeated wins correspondingly. However, it is possible to have the same guarantee (two 4-wins if 4 of your numbers are drawn) in just 30 tickets and no repetition! You can find the system with this property under # 88 in the book. We should mention that 30 is again the minimum possible number of tickets, but now, it is the minimum for the double guarantee, so that you have an example of another mathematically minimal system. Indeed, all of the systems in the second part of the book have the same nice property: THEY GIVE YOU THE DOUBLE GUARANTEE IN A NUMBER OF TICKETS WHICH IS LESS THAN TWICE THE NUMBER OF TICKETS NEEDED FOR THE SINGLE GUARANTEE.

Part III of the book contains systems with multiple guarantees. The systems in this part have the same nice properties as described for the double guarantees. We have chosen to present the most economical systems, that is, systems which give you the multiple guarantee in much less than the corresponding multiple number of tickets. In addition, we have selected only highly balanced systems for this section: Not only every number appears the same number of times in the combinations of the system, but, in many cases, every pair of numbers appears the same number of times, and, in some cases, every triple or even every quadruple appears the same number of times! Information on the balance is supplied in the author's comments on the qualities of each particular system.