This column was inspired by an interview I did with sports reporter Mark McGuire at the Albany Times Union. His story, in anticipation of the Saratoga races, can be found here.
The late, and, yes, great philosopher David Stove opened an essay on Epistemology—that’s not the name of a horse, but a branch of philosophy—with the following words, which should be ready closely by anybody who bets on horses or “invests” in stocks:
In newspapers advertisements, systems of betting on horse-races, guaranteed to make money for anyone who adheres, to them, are always being offered for sale at a moderate price. It is therefore to be presumed that there are people silly enough to give some credence to such offers. Sensible people, however, decline to enter into the details of any offers of this kind, but reject all of them, out of hand, as fraudulent, They reason that if the advertisers did know of an infallible system for winning money on horse-races, they would not tell other people about it; but they do tell, ergo, etc.
Betting on horse races and the stock markets requires knowing about probability—which always is conditional on information. Think of the simplest bet: a coin flip. I’ll pay $5 if a flip shows a tail and charge the same for a head. What is the probability that you win? The information you have, or think you have, is that “This coin has one head and one tail, will be flipped, and only one side will show.” Conditional on that information, the probability, as we all know, is 1/2. The odds (see the note below) are 1 to 1.
But I know how to cheat—I can make the coin show a head whenever I want. That changes the information, doesn’t it? The probability of a tail given this information is 0. A tail just won’t happen. In probability—and betting—information is everything!
Now horse racing. Eight horses are at the gate. If that is all you know, what is the probability that horse number one will win? Simple: 1 in 8, or about 13%. But you generally know more than just that there are eight horses. You might have some idea of form, the state of the track, the historical performance of the different horses and jockeys, and so on. But how to calculate a probability given this information?
The other punters are in the same position. The information is out there, but not everybody knows exactly what to do with it, but each person who bets knows what to do with a little of it. Now, the amount bet on a horse changes its posted odds: more bet on a horse means people think that that horse has a better chance of winning.
Collectively, then, the posted odds (and subsequent probability) are direct result of the information available. It’s information that makes favorites. Further, the payouts are adjusted according to the bets: favorites have very low payouts, so betting on horse with a high probability of winning will not often win you much.
To win real money, you need information that is both different and better than the information available to everybody else—just like in the coin flip example. The probability you calculate will then be different than everybody else’s. If you find a horse which everybody else has underestimated, then you might come ahead.
Finding that information is a tough job, but one that shady track touts, and the publishers of the “sure thing” systems Stove talked about, claim to have done. They’ll sell their system for only fifty bucks! Which makes them fools, because, of course, they could have used their system themselves and made a million, right?
Stock markets are no different than horse races. Information on stocks is (supposed to be) publicly available. And some people know what to do with some of it, so they bet on the stock based on what they know. As with horses, the amount “bet” on a stock changes the price of that stock. And to “win”, or make money on a stock, just like at the track, you need to find better information than anybody else. Without breaking insider trading laws, of course.
Brokers claim this ability. They’ll sell a red hot tip on a stock for fifty bucks (or more!). Which makes them fools, because, again, they could have used that tip and made themselves a million. Right?
It’s more complicated than this, of course. But consider: every couple of years somebody throws darts at a list of stocks and bets on those that are hit. This system does as well as, or even better than, professional brokers’ picks. Same thing is true in horse races. Further, everybody knows this. So why do people still bet? It’s as Dr Johnson said about second marriages: the triumph of hope over experience.
Technical note: Probability is a number between (and including) the numbers 0 and 1. Odds give the same information as probability, and they are calculated simply using this formula: odds = p/(1-p), where p is the probability. If you want to calculate probability with known odds, then use this formula: p = odds/(1+odds), but first make the odds into a decimal number. Thus, odds = 7 to 2 becomes odds = 3.5 (or 3.5 to 1, from 7/2).