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 game of a 10 game stretch is a statistically independent event, (the results of one game do not influence the results of later games), we need only multiply the odds against hitting for one game (3/4) by itself 10 times to determine the odds for the 10 games for NOT hitting 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 10 games, while most would think the more pertinent 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 hit, two hits, three hits, etc. within a ten 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% chance of hitting at least one 1-spot card in 10 games!
Well, that’s it for this week. Good luck, ladies and gentlemen, pick your one spots!