# Some spicy ways to fill out a 15 way keno ticket

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Last week we covered some of the traditional ways to split up 15 numbers to add some spicy ways to your straight 15. This week we veer off the beaten track to reach the same destination.

One interesting breakdown is to take your 15 numbers and group these 4-4-4-1-1-1. This ticket has a pleasant symmetry that promises lots of interaction between the groups. There is 1/15, 3/14, 3/13, 1/12, 3/11, 9/10, 9/9, 3/8, 3/7, 9/6, 9/5, 3/4, 1/3, 3/2 and 3/1 on the ticket for a total of 63 ways.

I would play the 1/15 and the 1/12 and then whatever down through the 5-spots. The player should also consider 3-3-2-2-2-1-1-1. This ticket will have 255 ways total and will be somewhat king-ticket-like with fewer winners in frequency but bigger ones.

To break this one down, we use the modified bridge system:

1/5 3/4 4/3 4/2 3/1

1/8

2/6

2/5

1/4

2/3

2/2

We start the modified bridge system by making a grid like a spreadsheet. On the left column down is the break out for the first half of the 3-3-2-2-2-1-1-1, namely a way ticket comprised of 3-3-2-2. You will see the 1/8, 2/6 etc for this ticket.

Across the top, the breakout for the second half 2-1-1-1 is given as if this was a stand alone ticket.

Continuing, we fill in each cell in the grid by first multiplying the numerators and then adding the denominators for each corresponding line and column:

1/5 3/4 4/3 4/2 3/1

1/10 1/15 3/14 4/13 4/12 3/11

2/8 2/ 6/ 8/ 8/ 6/

2/7 2/ 6/ 8/ 8/ 6/

1/6 1/ 3/ 4/ 4/ 3/

4/5 4/ 12/ 16/ 16/ 12/

1/4 1/ 3/ 4/ 4/ 3/

2/3 2/ 6/ 8/ 8/ 6/

2/2 2/ 6/ 8/ 8/ 6/

and:

1/5 3/4 4/3 4/2 3/1

1/10 1/15 3/14 4/13 4/12 3/11

2/8 2/13 6/12 8/11 8/10 6/9

2/7 2/12 6/11 8/10 8/9 6/8

1/6 1/11 3/10 4/9 4/8 3/7

4/5 4/10 12/9 16/8 16/7 12/6

1/4 1/9 3/8 4/7 4/6 3/5

2/3 2/8 6/7 8/6 8/5 6/4

2/2 2/7 6/6 8/5 8/4 6/3

Adding everything together: 1/15, 3/14, 6/13, 12/12, 18/11, 24/10, 31/9, 33/8, 33/7, 31/6, 24/5, 18/4, 12/3, 6/2, and 3/1 = 255 ways.

Also we should mention the 15-spot grouped 5-4-3-2-1. This curiosity is notable because it has 3/10, 3/9, 3/8, 3/7, 3/6 and 3/5 on it for those of you who like cuteness.

That’s it for now. Good luck and see you on line at [email protected]