Is lottery all luck? Can random numbers be all luck? How about a “luck” lottery? Does luck depend on the skill of the players? Does luck depend on the luck of the drawing? And, is there something like a “luck” lottery but with only one random number?
Let’s put these questions to the test and try to find out. There is one problem, though: we don’t have a good measure to put to random numbers. We just have a measure of probability. When you want to see whether the numbers are unpredictable, you might just have to ask the person with the winning deck of cards, who’ll often be very good at guessing the probabilities of every possible hand. But how are you going to determine whether the random numbers are unpredictable because of the player’s own skill, or because of some “luck?”
The first step, in theory, is for you to look around the table and see if any one of the players are using the same numbers in every hand. If you say, “Well, there aren’t that many of those numbers, so they must be random, then you’ve just shown up with an argument that the randomness of the game depends on the skill level of the players,” guess what: it doesn’t. It doesn’t depend on anything — not the way the game is played, not the way the other players are playing, not the way the player chooses to play the game (although it seems to depend on the player’s skill to be random). It has nothing to do with either player’s skill level or on the outcome of any particular hand they’re rolling. So in most situations, you’ll get the same numbers in every hand. That’s how we describe real-world outcomes. The same should be true of the game.
The second step is to measure the players’ skill level. If there’s a large group of people, there should be a strong randomness component to the players. But that’s because for most people, the number of different ways to do an action is low. Consider this example: a woman rolls a die. Every time the die comes up a number 1, she puts the die in her hand. When the die comes up a number 1, she rolls the die again, and gets a new number. The first time she does that, she has the same number and chance of rolling the same number. So the woman is rolling randomly.
Here, the numbers she rolls are random, not unpredictable. So the
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