What Are The Odds?

I just made a pun and you don't even realize it yet.

I might've learned something "useful" in a class this week. Well, it was in a book, actually: Against the Gods, The Incredible Story of Risk. It's slightly more interesting than it sounds. Slightly.

This week's lesson is about odds. Specifically, odds on horse (or dog, rabbit, turtle, or other raceable animals) racing. Let's say my horse, Brice Lord's Testicle, has odds of 1-to-1 (1:1), and your two horses, Crippleplex and Wendy's Testicle, have odds of 3:1 and 6:1, respectively. Since there's only 3 horses allowed on the track at Brice Lord Memorial Downs at anytime, then my horse has a 50% chance of winning, and yours have 33.3% and 16.7% chances. For example, with 3:1 odds there's a 1/4 chance Crippleplex will win, and with 6:1 odds there's a 1/7 chance that Wendy's Testicle will win. See the pattern? You've learned something already. Anyway, notice how the three horses' odds add up to 100%; this is because some horse must win the race, unless of course they all break their legs.

Wait, it gets a little bit more interesting. At a track that isn't named after me things work a little differently, because they're interested in making money, whereas I am already so goddamned rich I make money from giving it away. The odds at Charlestown Races & Slots for tomorrow are as follows:

Horse, Odds, Relative Probability
1, 5:1, 16.7%
2, 42:1, 2.3%
3, 3/5:1, 62.5%
4, 3:1, 25%
5, 12:1, 7.7%
6, 7:1, 12.5%
7, 53:1, 1.9%
8, 48:1, 2.0%

Right now you're probably thinking, "Brice comma this is boring as shit semicolon go back to writing about the cola wars period" Exactly! The relative probabilities of all the horses in the race does not add up to 100%, it adds up to 130.6%.

So, what the shit is going on here? How can we be 130.6% certain that a horse is going to win this race? Ever notice how attending races is free? No? Never been to a horse race because it's really boring, simultaneously low- and high-brow, far away, and quite possibly cruel to the animals? Well, it's because that extra 30.6% is the house's take. They skim off the top. It's the bookie fee, the Jew's usury, the Cossack's bargain, the what-have-you.

So next time you rush off to the races to see Cunnilingus 2 run around a dirt path twice in a matter of minutes and then forget where you parked remember that your hard-earned recession-proof cash is lining someone else's lined pockets.

By the way, I don't really know anything about horse racing, so if you do and I'm wrong about any of this, please don't hesitate to immediately explain how you know so much about horse racing.