June 23, 2009 | 23 Comments
Our title comes from a famous paper by Lester Dubbins and Leonard Savage which appeared at the beginning of the Bayesian Theoretical Resurgence, a movement which, I am delighted to report, has now largely infiltrated nearly all of academia.
Import as this movement was, it was slight in gambling because analysis of games of chance were always Bayesian. Prove this by picking up any undergraduate text in statistics and find the chapter on probability (always, bizarrely, hidden in the interior whereas it should come first). You will see examples like this: “A die has probability 1/6 of showing a 6, therefore the probability of two die (or one die thrown twice) showing two 6s is 1/6 * 1/6 = 36.”
Valid answer, but an invalid, or at least incomplete, argument. Close enough, however, because of the implicit recognition that (Bayesian) logic allowed us to deduce the probability of the die showing 1/6. Once that deduction is in hand, we can prove theories of what will happen to that die under scenarios, which come in two flavors.
Simple gambles are those where the physics of the game allow us to deduce the probabilities of events of interest. Examples: “two 6s on two throws”, “a pair of jacks showing from a poker deck”, “00 showing on a roulette wheel”, “three cherries showing on a slot machine”, and so on. Casinos provide simple gambles.
Complex gambles are different from simple ones because we cannot deduce the probability of the events of interest. For example, “The person to my left in this poker game holds a hand superior to mine”, “horse A will win the race or at least come in third”, “stock B will increase in price over the next week”, or “the Detroit Tigers will win tomorrow’s game.”
Unless you are the owner of a casino or a bookie, it is impossible to consistently make money with simple gambles. You might, but probably will not, consistently make money with complex gambles. Here’s why.
Any casino game that does not involve the intelligences of other human beings can be analyzed as simple gambles. This means we can, without error, compute the probability of any outcome of any game, which we can call A, for example A = “the roulette wheel shows red”. We will always know, given the properties and setup of the game, the probability A will be true. For ease, call that probability P(A), which I emphasize we know.
It costs you D dollars to bet on A, and you will win with probability P(A) and will be paid W dollars if A happens. The casino sets the required bet D so that it is more than W * P(A) (alternatively, W is set less than 1/P(A) for every dollar bet). They do this on all simple gambles.
For example, if A = “7 shows on an American roulette wheel” then we can deduce that P(A) = 1/38 (the numbers 0-36 and the symbol “00” are on the wheel). It costs (say) 1 Dollar to play. If you win, you receive 35 Dollars. In this case, W * P(A) = 35/38 which is less than the 1 Dollar it costs to play. Roughly, the casino takes in 8 cents for every dollar bet, meaning you lose 8 cents.1
Meaning you will go hungry if you make gambling on these games a career. The only exception to simple gambles is blackjack, where strategies exist so that D < W * P(A)---you can make money. But because casinos have more money than you, and politicians desire to have that money, casinos are able to buy laws that make these strategies illegal. Just as you go to Walmart to purposely part with your cash, you are meant to go to a casino to lose money.
Money can be made with complex gambles, but it isn’t easy. In simple gambles, everybody has the same information about P(A). This isn’t true in complex gambles where to win, you need to have better information about P(A) than the person or persons betting against you. Those cigarette-wielding guys huddled around the OTB entrance aren’t just dosing themselves with nicotine. They’re trying to gain an advantage in information by subtle probes of their compatriots. Brokerages ponder quarterly reports for the same reason.
Problem is, everybody else is trying to gain an edge the same time you are, which usually means your information is not much better than the next person’s. Plus, in betting horse races and the stock market, there are transaction fees. Tracks skim a percent off the top and set the payouts by the amounts bet, making it extremely difficult to win money. Brokers and banks charge transaction fees which cause the same difficulties.
Besides bar bets and cheating, the only gamble with potential is poker (and its business equivalents, negotiating) which depends on bluffing and the ability to detect it. Being able to read tics and tells is a great skill; but it’s a rare talent and expensive to acquire.
The lesson is: stay away from simple gambles and only take bets where you are sure of your information.
1This figure is “on average” and is, therefore, metaphysical. But we can calculate the exact probabilities of winning for the casino given an assumed number of bets and amounts; the probability the casino wins is nearly 1.