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Reducing the cost of complex tickets

Jan 8, 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:

3-1-1-1-1-1

2-2-1-1-1-1

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,

8,7-1,6-2,6-1-1,5-3,5-2-1,5-1-1-1,4-4,4-3-1,4-2-2,4-2-1-1,4-1-1-1-1,3-3-2,3-3-1-1,3-2-2-1,3-2-1-1-1,3-1-1-1-1-1,2-2-2-2,2-2-2-1-1,2-2-1-1-1-1,2-1-1-1-1-1-1,1-1-1-1-1-1-1-1.

Thus there are 22 "partitions" of eight numbers!

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