The ups and downs
of top/bottom card

Mar 6, 2006 2:21 AM

The Top and Bottom ticket has been around for 50 years or so in various forms and has always enjoyed some popularity. These days (since computerization) you will find Right and Left tickets and even occasionally Odd and Even tickets but these are all similar, math-wise.

Almost all these tickets nowadays work the same, you make your wager (typically five dollars, though sometimes as low as two bucks or as high as 10) and you win if the pattern of the draw comes up in an unbalanced fashion.

You win for example if the draw comes up either four on top and 16 on the bottom or 16 on top and four on the bottom, and the more unbalanced the draw the more you win. Most of these tickets do not pay on the most common catch, 10-10, and the next most common 9-11 or 11-9. These are the catches where the casino makes its money.

Historically there have been other ways to play this ticket. Once upon a time, you could play a top OR bottom. You would simply give the writer $11 and designate either a top draw or a bottom draw. If the draw came up the way you had designated you would get back your wager plus ten dollars (lay 11 to make 10 like a sports bet) and a 10-10 draw was a push.

A few casinos also used to offer a top and bottom exacta, where you would pick the exact balance of the draw. These tickets paid much better, but of course would win far less often.

Below are the odds for the Top and Bottom:

Hits

Frequency

Odds for one

0 / 40

0.000000038991288

25,646,754.927203

1 / 40

0.000001485382389

673,227.316839

2 / 40

0.000025015189773

39,975.711121

3 / 40

0.000247976663834

4,032.637525

4 / 40

0.001624763766162

615.474090

5 / 40

0.007486911434474

133.566426

6 / 40

0.025196336558326

39.688309

7 / 40

0.063457440220968

15.758593

8 / 40

0.12153232970891

8.228263

9 / 40

0.17880618623839

5.592648

10 / 40

0.20324303169097

4.920218

11 / 40

0.17880618623839

5.592648

12 / 40

0.12153232970891

8.228263

13 / 40

0.063457440220968

15.758593

14 / 40

0.025196336558326

39.688309

15 / 40

0.007486911434474

133.566426

16 / 40

0.001624763766162

615.474090

17 / 40

0.000247976663834

4,032.637525

18 / 40

0.000025015189773

39,975.711121

19 / 40

0.000001485382389

673,227.316839

20 / 40

0.000000038991288

25,646,754.927203

It must be noted that the above 40-spot odds apply to a one-way 40-spot ticket, in other words a top OR bottom, right OR left, etc.

To calculate the odds on a two-way 40-spot ticket, (a top and bottom, right and left, odd and even, etc.) you need to add the frequency (or halve the odds) on every catch except the 10/40, which can only be caught one way.

Thus the odds against a 9-11, or 11-9 catch on a top and bottom ticket are roughly one in 2.8. Keno managers would be wise to consult an expert before getting fancy with this ticket. There have been several mathematical disasters in the last 20 years involving Top and Bottom tickets.

Well that’s it for this week! Good luck, I’ll see you on the net! e-mail: [email protected]