A dozen ‘ways’ to cash a ticket

Mar 22, 2005 5:13 AM

Another favorite ticket of mine is the 12-spot ticket grouped 3-3-2-2-1-1. Since there are six groups on the ticket, we know from Pascal’s Triangle that there are 63 total ways on the ticket. Let’s use the bridge system to calculate all the ways on the ticket. Let’s split the ticket into two pieces, 3-3-2, and 2-1-1. We know that the 3-3-2 is a seven-way ticket, and it has a one-way 8, a one-way 6, a two way 5, a two way 3, and a one way 2, and we’ll use it for the top row of our table. The 2-1-1 is also a seven way ticket, and it has a one way 4, a two way 3, a two way two, and a two way 1 (king), and we’ll use it for the first column of the table. Adding the columns and rows gives us these results:

 

8

6

5

5

3

3

2

4

12

10

9

9

7

7

6

3

11

9

8

8

6

6

5

3

11

9

8

8

6

6

5

2

10

8

7

7

5

5

4

2

10

8

7

7

5

5

4

1

9

7

6

6

4

4

3

1

9

7

6

6

4

4

3

This has traditionally been a popular way to play a ten way six. As you can see by perusing the table, there is one six on the top row (3-3), one six on the second row, (2-2-1-1), four sixes on the third and fourth rows, (3-2-1), and four more on the last two rows (also 3-2-1). But if we’re interested in playing the sixes, we might want to split the ticket in a different way. (Remember that when you use the bridge system you can split the ticket into two pieces in any arbitrary fashion.) There are two natural sixes on the ticket, the 3-3 and the 2-2-1-1. So let’s use the 3-3 (a one way 6 and a two way 3) for the top row and the 2-2-1-1 (a one way 6, a two way 5, a three way 4, a four way 3, a three way 2, and a two way 1) for the first column, and add the columns and rows:

 

6

3

3

6

12

9

9

5

11

8

8

5

11

8

8

4

10

7

7

4

10

7

7

4

10

7

7

3

9

6

6

3

9

6

6

3

9

6

6

3

9

6

6

2

8

5

5

2

8

5

5

2

8

5

5

1

7

4

4

1

7

4

4

Now all our six spots are broken out in a more convenient manner; the two natural sixes appear by themselves, and the eight 3-2-1 sixes are all grouped together in the table.

The question is, is this a good way to play a ten way six? Well, there is a good chance of multiple winners on the ticket, for example one hit on a five out six might probably produce another, but the trade