Dear Keno Lil,
What is the formula you used to determine the odds of catching a one spot in 10 games? Thank you.
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 firstname.lastname@example.org. Well, that’s it for now. Good luck! I’ll see you in line!
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|