Reducing the cost of complex tickets

January 08, 2001 9:28 PM


The opposite process of our subject last week is a method of reducing the number of ways, and thus the cost of playing, a complex way ticket. Suppose we have eight favorite numbers selected and they’re all individually grouped. As we discovered last week, this will produce a way ticket with 255 total ways on it. Playing all these ways may drain even a large bankroll very quickly.

If we take the ticket with the eight kings and combine two of the kings into a group of two, we’ll have a way ticket with eight total numbers, grouped 2-1-1-1-1-1-1. This process, which I call "melding," produces what has traditionally been called a "poor man’s king ticket." That’s because it preserves many of the ways and features of a full king ticket, but it has only 127 ways on it — roughly half the ways on the original ticket.

To wit:
1-way 8,
6-way 7,
16-way 6,
26-way 5,
30-way 4,
26-way 3,
16-way 2,
6-way 1

You could cut the price of the ticket in half again. There are two ways to do this. You may combine an additional two kings into another two-spot, resulting in a ticket grouped 2-2-1-1-1-1; or combine one additional king into the existing two-spot, resulting in a ticket grouped 3-1-1-1-1-1. Either ticket has 63 ways on it!

To wit:



1-way 8

1-way 8

5-way 7

4-way 7

10-way 6

8-way 6

11-way 5

12-way 5

10-way 4

14-way 4

11-way 3

12-way 3

10-way 2

8-way 2

5-way 1

4-way 1

So you can pay your money and take your choice. You may continue in this fashion with either ticket until you ultimately end up with the solid eight-spot that we started with last week.

These are all known as "partitions" of eight numbers,


Thus there are 22 "partitions" of eight numbers!

That’s it for this week. Good luck! I’ll see you in line!