Thanks, Connie

September 25, 2007 1:42 AM
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Dear Keno Lil,

What is the formula you used to determine the odds of catching a one spot in 10 games? Thank you.

Connie Majors

Pahrump, NV

First of all, thank you very much for your letter. It’s always a pleasure for a writer to hear from her readers! I believe that you are referring to a question in an earlier column this year, so I will quote it here with the answer.

If you’re playing a one spot, what are the chances of going 10 games in a row without hitting it? You have one chance in 17.7 of going 10 games without hitting!

Most people realize that you have one chance in four of hitting a one spot each time you play it. Conversely, you have three chances in four of NOT hitting it. Since each of a 10 game stretch is a statistically independent event, (the results of a game do not influence the results of later ones) we need only multiply the odds against hitting for one game (3/4) by itself 10x to determine the odds for the 10 that won’t hit the one spot. Since 3/4 = .75 the calculation looks like this: .75 x .75 x .75 x .75 x .75 x .75 x .75 x .75 x .75 x .75 = .0563

So the frequency of NO hits in 10 games is .0563, or one in 17.7! The odds for one against are just the inverse of the frequency. (1/17.7 = .0563)

Note that the way I originally phrased the question, I was referring to the chances of NOT hitting in ten games, while your question concerns HITTING the one spot in a 10 game period. This is just a special case of what is known in statistics as a binomial

distribution, which we would have to use to determine the frequency of

one, two and three hits within a 10-game period.

Since the chance of not hitting at all in 10 games is .0563, the chance of one or more hits in 10 games must be 1-.0563, or .9437. Thus, you have almost a 95 percent chance of hitting at least one spot in 10 games!

If you have a Keno question that you would like answered, please write to me care of this paper, or contact me on the web via email at kenolil@gmail.com. Well, that’s it for now. Good luck! I’ll see you in line!

EXACTA ODDS

Exactas are Keno tickets that pay off if you hit the same catch two games in a row. Although this seems somewhat easy, especially on small tickets, the odds are surprising. Below you will find the exact odds for your favorite exacta ticket.

(Odds of getting same catch
two games in a row.)
Catch Frequency Odds for 1 against
(1/frequency)
0/1 5.63E-01 1.777778
1/1 6.25E-02 16
0/2 3.14E-01 3.187334
1/2 1.44E-01 6.934445
2/2 3.62E-03 276.6094
0/3 1.73E-01 5.764489
1/3 1.86E-01 5.386595
2/3 1.93E-02 51.9411
3/3 1.93E-04 5194.11
0/4 9.51E-02 10.51944
1/4 1.87E-01 5.340259
2/4 4.52E-02 22.11712
3/4 1.87E-03 534.6507
4/4 9.38E-06 106560.1
0/5 5.16E-02 19.37509
1/5 1.65E-01 6.076029
2/5 7.31E-02 13.67106
3/5 7.05E-03 141.9428
4/5 1.46E-04 6838.793
5/5 4.16E-07 2404263
0/6 2.78E-02 36.02806
1/6 1.32E-01 7.568395
2/6 9.51E-02 10.51944