# Lottery Odds (in the wild)

I’m teaching my first class this fall, and I’ve been preparing my notes for class this past week. I wanted to use keno as an example of how to compute probabilities. So I was computing some probabilities and checking them against the posted “odds” on masslottery.com. I couldn’t get my computed odds to match with what the lottery had posted, which led to a brief period of panic that I wasn’t qualified to be teaching this class. Turns out, I’m not computing anything wrong. It’s just that what the lottery is calling “odds” are actually probabilities. Take a look again at masslottery.com and look at the posted odds for a one spot game. For the one spot game they say that the odds are 1:4. This is incorrect. The probability of winning this one spot game is $\frac{1}{4}=.25$, which would make the odds of winning $\frac{.25}{.75}=1:3$. Likewise, the odds against winning are 3:1. Generally, if the probability of an event is p, the odds of this even occuring are $\frac{p}{(1-p)}$.

So what the lottery is referring to as odds are actually probabilities of winning. They actually get this correct that the bottom where they say “Probability of winning a prize in this game = 1:4.00”. The mistake is that they aren’t making any distinction between the probability of winning and the odds of winning when, in fact, these are different.

Cheers.