Way tickets to seventh heaven

Aug 24, 2004 3:22 AM

This week we’ll look at a couple of way tickets constructed out of seven numbers. Note that both of these tickets have the same number of groups, the same number of total ways, and the same number of total spots (seven).

They differ only in the manner of grouping, and hence the distribution of ways. The ticket on the bottom, one of my favorites, has a five-way five and a five-way two-spot. The ticket on the right has a six-way five and a six-way two-spot. These two tickets offer a good example of why it pays to be careful when constructing a way ticket to play. At left are the odds for one of hitting each possible catch.

2 2 1 1 1

3 1 1 1 1

1-way 7, 3-way 6, 1-way 7, 4-way 6, 5-way 5,7-way 4, 6-way 5, 5-way 4, 7-way 3, 5-way 2, 5-way 3, 6-way 2, 3-way 1, 4-way 1

7/7

40979.31

40979.31

6/7

1365.977

1365.977

5/7

115.760

115.760

4/7

19.160

19.160

3/7

5.714

5.714

2/7

3.061

3.061

1/7

3.172

3.172

0/7

8.225

8.225

6/6

2957.27

2258.703

5/6

144.876

122.902

4/6

18.226

16.852

3/6

4.531

4.401

2/6

2.076

2.013

1/6

1.823

1.680

0/6

3.896

3.314

5/5

355.458

343.539

4/5

23.340

24.424

3/5

4.267

4.665

2/5

1.822

1.842

1/5

1.377

1.418

0/5

1.943

2.531

4/4

54.982

83.931

3/4

5.908

6.952

2/4

1.777

1.886

1/4

1.229

1.264

0/4

1.358

1.661

3/3

12.953

16.738

2/3

2.019

2.755

1/3

1.185

1.250

0/3

1.131

1.168

2/2

3.931

3.861

1/2

1.190

1.452

0/2

1.025

1.048

1/1

1.713

1.445

0/1

1.014

1.003

Note that although the right hand ticket has one more way five and one more way deuce than the ticket on the left, the odds of hitting a solid five or deuce are not that much better. In fact, if you play the five-way five for a dollar per way, you would expect to hit a five-spot solid on the average of once every 355 games, or after a gross expenditure of $1,775.

If you play the six-way five for a dollar a game, you will expect a solid five on the average of once every 344 games, or after a total gross expenditure of $2,064. The same comparison holds true of the deuces. You expect to hit a two-spot after a gross expenditure of about $20 on the five-way two spot, while it will take nearly $24 to do the same on the six-way deuce. (When I say gross expenditure, I mean the amount of money played, irrespective of small winners).

Both tickets will return the same amount of money in the long run, if you play millions of games. This may seem paradoxical at first, because I have just told you that the ticket on the left pays solid hits more often. The explanation is that the right hand ticket offers more chance of multiple winners, more than one solid hit on one catch. It’s just that you have to wait longer for them. This is an important point, because all of us operate on finite (limited) bankrolls, and if we play a ticket that pays more often, there is less chance of us going broke!

So here is a little rule of thumb: When you’re playing a mixed group way ticket, a way ticket that consists of different sized groups, you’re better off if you stick to groups that are almost equal in size, rather than one that has widely varying sizes. For example, if you play a four-way nine, you’re better off playing 5-5-4-4 than 7-7-2-2.

Incidentally, here is one more damning fact about the tickets above: If you hit a six out of seven, you are guaranteed at least one or more solid fives on the left hand ticket. This is not so on the right hand ticket, as a cursory examination will reveal!

Well, that’s it for this week, good luck, I’ll see you in line!