This originally ran 4 December 2015, but since we need it for tomorrow’s crucial article on whether fantasy sports are “games of chance”, it is best to refresh our memories. This is also complementary to yesterday’s post.
What is a game of chance? There is no such thing as chance. Chance does not exist, though many think it does. Given that the term crops up repeatedly, and people do take meaning from it, we have to figure what it is that people think the term means with respect to gambling. Best guess, as I’ll show, is that chance appears to be as a synonym of mostly not predictable. “Games of chance”, therefore, could be translated as “games which are mostly not predictable”.
Take craps. On the come-out, the shooter wins with a 7 or 11. The two-dice total will come to something, possibly this 7 or 11. Is this total “chance”? Well, craps is taken by the law (and by everybody else) as a game of “chance.” But what is really meant is that that outcome of the roll is not predictable beyond the constraints that the two-dice total must fall in the range 2 to 12. This knowledge of the bounds is a form of predictability, albeit a weak one.
If the only—pay attention here: I mean this word in its literal sense—information that we have is that “There will be a game played which will display a number between 2 and 12 inclusive”, then we can quantify our uncertainty in this number, which is that each number has probability 1/11 of showing (there are 11 numbers in 2 to 12).
Craps players have more information than this. They know the total can be from 2 to 12, but they also know the various ways how the total can be constructed, e.g. 1 + 1, 1 + 2, 2+ 1, …, 6 + 6. There are 36 different ways to get a total using this new information, and since some of the totals are identical, the probability is different for different totals. For example, snake eyes, 1 + 1, has 1/36 probability; there are 6 ways to get a total of 7, for a probability of 1/6.
It should be clear that these different probabilities are not a property of the dice (or the dice and table and shooter, etc.). If probability were a physical property, then it must be that the total of 2 has 1/11 physical probability and 1/36 physical probability! How does it choose between them? Quantum mechanics? (There is a big hint here about interpreting QM, which I’ll skip today.) No, probability is a state of mind; rather, it states our uncertainty given specific information. Change the information, change the probability.
There are any number of physical mechanisms that cause each dice total, causes of which we are mostly or completely ignorant. We know the causes must be there, we just don’t know what they are. We do know there are many causes: imagine the bouncing rolling dice flopping around, buffeted by this and that. If we knew some of these causes for individual rolls—perhaps we could measure them in some way as the dice fly; say, by noting the walls of the table are cushier and more absorbent than usual—then we could incorporate that causal information and, again, update the probabilities of the totals. A 7 might be more or less probable depending on hos the information “plays”.
Casinos base their craps payouts on their “vig” (or cut, or “percentage”) and on the probabilities calculated only using the information of how the totals are reached. If you had extra information about causes, you could use that to “beat” the system—assuming their vigorish is not too vigorous; it’s the transaction fees that always kill you. Unless your knowledge of cause is complete, you might not necessarily beat the casino for any single game, but if you have good causal knowledge, you will beat them over multiple games. It is for this reason that casinos ban contrivances that could measure causes or proxies of causes.
Nobody could, in the scenario of a casino (but in a physics lab, the situation would be different) measure all causes of a dice roll; but to win consistently, all causes don’t need to be measured, just some of them, or their proxies (things related to a cause which is measurable). It is the measurement and knowledge of cause, and not just bounds, that requires skill and turns “games of chance” into “games of skill.”
Think of it this way: take two craps players, one a novice but who knows the rules, and the other an expert who claims, falsely, that he is able to measure some of the relevant causes. Pitted against one another, each is as likely to win (more money) as the other. But if the second player truly can measure some of the relevant causes—perhaps he is a physicist with secret measurements devices which allow him to know some but not all causes—he will beat the first fellow consistently. How consistently depends on the extent of his causal knowledge.
We have arrived at a better definition of “game of chance”. It is “game where the causes are unknown but where the outcomes are defined”. Once any of the causes become known, the game becomes, at least partially, a game of skill.