An interesting question. Let's start with the word "chance," which you seem to see as an essential part of luck. If I follow you correctly, we have chance, hence luck, only if determinism isn't true. I think we'll see that what people mean by "luck" doesn't presuppose indeterminism, but let's start with your golfing example, Joe tees off and his shot goes wild. That's not what he wanted to happen and not what he was trying to do. However, there happens to be a rock in the right place, his ball hits it and ends up in the hole. That he did want to happen. Was he lucky? Since this seems to be a paradigm case of luck, we'd need a good reason for saying otherwise. Although it's doubtful that a real-life Joe intended to sink a hole in one (golfers seldom do), let's suppose he did. Given how things turned out, Joe himself would surely consider himself lucky: he got what he wanted but the way it happened was nothing like what he had in mind. He didn't intend to swing wild, he didn't mean to hit the rock,...

As it stands, your question contains some crucial ambiguities. You ask about a case where more As are observed in group X than in group Y, but it's really not clear what "observed" means here. Do you mean that quite literally, more things that are A have been, so to speak, counted in group X? And if so, were the observations random? That is: did each thing in X have an equal chance of being observed? And then there's the question of how large the subsets we take are. I assume you mean them to be equal, but you don't say and it matters a lot. If you do, mean equal size samples, are they random? That matters too. And consider this: suppose group X contains far more objects than Y. Of the 10,000 objects in X, 100 are A. Of the 20 objects in Y, 18 are A. Suppose we take a random sample of 10 from each set. Though I'm not going to work through the details, even though there are far more As in X than in Y, the random sample from Y is likely to contain more As than the same-size random sample from X. ...

Good question. In fact, most people who work on these matters wouldn't agree that a roll of a die is a perfect example of randomness. And you are quite right: we believe that if we knew enough about the prevailing conditions when the die was rolled (and if we could do the calculations!) we could figure out how the die would land. That convinces many people that dice rolls aren't really chance events at all, though not everyone agrees. The issues about "deterministic chance" tend to get technical, but they have partly to do with the amount of complexity involved in disentangling the causes and effects. But your question still stands whatever our view on whether determinism and chance can somehow fit together. That question is: are all apparent examples of chance cases where a complete account of the details would determine the outcome of the supposedly "chance" process? The answer is a solid "Maybe not." The reason is quantum mechanics. Quantum mechanics, as you may know, is a theory in which...

Yes. From "Very probably not-X" it simply doesn't follow that X is false. Of course, that doesn't mean it's reasonable to ignore probabilities...

It depends on what you think probability is, but even then the answer is probably (heh!) no. Nothing in the mathematical theory of probability requires that all events have probabilities. Probability theory simply imposes coherence conditions on any probability assignments there may be. And the mathematical theory of probability doesn't tell us what probability is but only what its formal properties are. Some believe that there are objective probabilities—that if we specify our probability question appropriately, then there may be an answer to the question independent of what anyone thinks. For example: someone might think that if a quantum system has been prepared in a certain way, then the probability that a measurement interaction will have a certain result is, say, 1/3 regardless of what anyone thinks. This may or may not be right, though it still leaves us in the dark about what exactly this probability is. Is it a propensity or tendency of some sort? Is it a disguised way of talking about...

Let's suppose that the machine is my computer and I'm using the function =TRUNC(100*RAND(),0). Then as I put the function in more and more cells, I'll get a list of integers between 0 and 100 that pass various tests for randomness. Let's suppose that the fifth integer on the list is 12. Is there a reason for that? There is, at least superficially. The function =TRUNC(100*RAND(),0) works by performing various well-defined mathematical operations on an input. The input is the time when you hit "ENTER," according to the computer's clock. Given that input and the cell, the output is determined. Put another way, if two computers ran the program starting at the same time according to their clocks, they would give the same output. So there's an explanation for why the fifth cell ends up containing 12 rather than some other integer. It's a matter of the input and the program. You might protest that this isn't truly random. If it were, two computers with the same input wouldn't produce the same supposedly ...

I guess I'd have to disagree with the idea that "all of philosophy and logic point to a reason or cause for everything." There's certainly no argument from logic as such; it's perfectly consistent to say that some events are genuinely random. Some philosophers have held that there's a reason (not necessarily a cause in the physical sense, BTW) for everything, but the arguments are not very good. On the other hand... quantum mechanics is a remarkably well-confirmed physical theory that, at least as standardly interpreted, gives us excellent reason to think that some things happen one way rather than another with no reason or cause for which way they turned out. An example: suppose we send a photon (a quantum of light) through a polarizing filter pointed in the vertical direction. We let the photon travel to a second polarizing filter, oriented at 45 degrees to the vertical. Quantum theory as usually understood says that there's a 50% chance that the photon will pass this filter and a 50% chance that it...

What you say about the individual problems is right: if I get a point for each right answer, then each time someone comes to the site, the best strategy is to guess that it's a man. (At least this is right if knowing the sex of an individual customer doesn't help predict whether s/he will visit the site or not.) This is the best strategy because if each individual visit is like a random selection of a customer from the population, the chance is greater that the selected customer will be a man. The analogy with seawater is problematic. After all, if I pick one customer, that customer won't be 55% male and 45% female. The salinity of small samples of seawater closely approximates the salinity of the sea (unless we get down to really small samples of a few molecules, and then your principle breaks down.) The make-up of a small sample from a population may depart markedly from the make-up of the populations. What's interesting is that once our samples get to be of even a moderate size, things...

Games typically involve a blend of things that a player can control and things s/he can't. A golfer can work on her backswing; she can't do anything about the moment-by-moment shifts in the wind and the fine-grained condition of the greens. Things like the winds and the lay of the greens or the outcome of a dice-roll are what we might call externalities. It's not that they have no explanations and it's certainly not that they have no bearing on who wins and who loses. But the players don't deserve any blame or credit for how they turned out. In that sense, they're matters of luck. Depending on the game, skilled players may have ways of compensating for them to some extent, but they can produce advantages and disadvantages that are outside the players' control. With that in mind, I don't take Kahneman's appeal to "luck" to be an explanation. An explanation would call for specifics about conditions and causes, and the mere appeal to luck doesn't provide any of those. I take the appeal to luck to be a...

Statistics could give evidence that something about one of the casinos makes it more likely that your gambler will win there. Feng shui could be the explanation, though it would be a funny sort of feng shui that only worked for some of the gamblers, and so if it is feng shui, the casino may not be in business long! The more general question is whether there could be serious evidence that the gambler is more likely to win in one casino than the other, and the answer to that is yes. It might be feng shui, but other explanations, weird and mundane, would also be possible. (Maybe he's an unwitting participant in a psychology experiment; and the experimenters load the dice in his favor in one of the casinos.) Careful observation and experiment might even hone in on the explanation, if there really is a stable phenomenon to be explained. As for the pragmatic question, why not? If the evidence suggests that he's more likely to win in one casino than the other, he could go with the evidence without...