Let me count the ways of keno ‘way’ tickets, part 3

January 29, 2001 6:26 AM
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We’ve spent the last couple of weeks counting the ways or "breaking out" the ways, as a keno writer would say. As we discussed the "bridge system" last week, I mentioned that the system uses two partial groupings of the ticket in question.

This week, I’ll show you it doesn’t matter which partial groupings are used. Any may do.

Let’s take the 12-spot ticket, grouped 3-3-2-2-1-1. If we take half the groups for each partial grouping to initiate the bridge system, we’ll get a 3-3-2 and a 2-1-1. Although this partial grouping is usable, it may not be the easiest one to use, especially on more complex tickets.

So, let’s use the partial groupings 3-3 and 2-2-1-1. It’s much easier to eyeball the breakouts of these partial groupings, to wit: 3–3 = a 1-way 6 and a 2-way 3, while 2-2-1-1 = a 1-way 6, 2-way 5, 3-way 4, 4-way 3, 3-way 2 and a 2-way 1. Charting these ways like last week, we get:

0

6

5

5

4

4

4

3

3

3

3

2

2

2

1

1

6

12

11

11

10

10

10

9

9

9

9

8

8

8

7

7

3

9

8

8

7

7

7

6

6

6

6

5

5

5

4

4

3

9

8

8

7

7

7

6

6

6

6

5

5

5

4

4

And this chart displays all 63 ways on the ticket.

We can alternatively use the partial groupings 3-3-2-2 and 1-1 where 1-1 = 1-way 2 and 2-way 1 and 3-3-2-2 = a 1-way 10, a 2-way 8, a 2-way 7, a 1-one way 6, a 4-way 5, a 1-way 4, a 2-way 3 and a 2-way 2. Charting this, we get the alternative breakout:

10

8

8

7

7

6

5

5

5

5

4

3

3

2

2

2

12

10

10

9

9

8

8

8

8

8

6

5

5

4

4

1

11

9

9

8

8

7

6

6

6

6

5

4

4

3

3

1

11

9

9

8

8

7

6

6

6

6

5

4

4

3

3

which contains the same ways as the first breakout in a different configuration.

The moral is that, when using the bridge system to break out a way ticket, you can choose the most convenient format.

Well, that’s it for now. Good luck! I’ll see you in line.