I think I do detect an argument.

Most people would say that the difference between a game of luck and a game of skill is the degree to which luck and skill contribute to the outcome, proportionally. If more than half of it is luck, it's a game of luck.

Gil Kalai seems to be saying that it's really a matter of risk exposure. If the chance of losing multiplied by the dollars lost is high even for skilled players, it's gambling.

ETA: I guess I was seeing faces in the clouds.

Considering the number of things he didn't mention that he's since endorsed as exactly what he meant, I've joined your consensus.

In any case, the difference is not between tennis and poker, and it is not based on ethical boundaries (I do not have strong opinions about whether gambling should be legal). The difference is between high stakes negative- expected-rewards games and high stakes games where players expect positive rewards

That's absolutely fine. Just don't call it skill versus luck. Come up with new words to express the concepts you think are important; these names are taken.

The conventional way does not give you a way to measure the ingredients of skill and luck

Yes it does; one piece of evidence that tennis involves less luck than golf is that in match-play tournaments of about the same size, you're much more likely for a golfer outside the top 10 to win than for a tennis player outside the top 10 to win.

Or that baseball involves more luck than basketball, because a streak of (say) 27 wins in 30 games is much more common for a top team in basketball than baseball.

(Yes, there are differences in how level various playing fields are, but these phenomena seem to be robust across competition in high school, college and professional levels (AFAICT), so it seems like strong evidence to me. If it were important to me, I could start finding more and more objective metrics of skill versus luck in various games.)

Well, as someone else has noted here, this still doesn't correspond to our usual meanings of skill and luck. I mean, I'm equally likely to beat or lose to you in a game of Candyland, and Federer and Nadal are (very roughly) equally likely to win at tennis, but the two situations aren't equivalent, since you could replace me with your 4-year-old niece at Candyland and have the same probabilities, but not so much with the tennis example. This is why most of us call Candyland a game of luck and tennis a game of skill (with a small amount of luck involved); the degree of skill is determined by how much the probabilities of outcomes depend on certain measurable and robust characteristics of the players.

I don't know, but I suspect that you have some strong ethical boundaries regarding the "skill/luck" line, so that you've identified it with a "good/bad" line; tennis is "good" because few people lose their livelihood trying to succeed at it, so it must be "skill", while poker is "bad" because a large number of people lose their savings playing it, so it must be "luck". But you need to be aware that there's a rather uncontroversial way that most of us use the terms "skill" and "luck", and that your usage violates it.

It's not a matter of being clearer; you didn't say anything like the paragraph cousin_it wrote above. You have to show some intermediate steps here, because it looked to me that you were claiming that the same two opponents would have different probabilities of outcomes depending on the stakes of the game, without any explanation of why this should be so.

If you're indeed talking about the selection bias for players as stakes change (and more or less an "efficient market" hypothesis near the top), you needed to say something in that direction.

But what do you mean by "luck"? I am wondering if there is a translation problem here, and a Hebrew word that does not quite map onto the English one. In English it simply means random factors outside the control of the participants. (It is often accompanied by a superstition that it isn't random but a fickle force that can be attracted or repelled by suitable behaviours.) In that case roulette is entirely luck, poker is partly luck and partly skill (but less luck and more skill the better you are at it and the longer you play), and chess has very little luck. All regardless of the stakes.

The case of the poker club in Jerusalem was presumably conducted in Hebrew. Did the judge simply decide that the activity in question was a social evil that had to be found illegal whatever the letter of the law, or did the law allow itself to be read as supporting the ruling?

I think the argument is that if the stakes are high enough people's betting patterns create a zero expectation on the bit itself. This seems wrong on the face of it. It assumes that the bettors on the chess match are perfectly evaluating their skills at making perfect bets with expectation of zero, that there is no skill in determining the bet. Thus with an expectation of zero, the winner of the bet is determined by luck.

This becomes more absurd in the poker game. The difference in skill of betting for action is a large part of the game. Most poker books try to teach it. Most people can't do it.

The judge did not base his argument on an abstract mathematical modeling of the entire setting but rather on the consequences. If such clubs indeed cause people to lose everything leaving their families destitute we must conclude that the overall setting makes this activity mainly a gambling activity and that this game is mainly a game of luck (in the same way playing the roulette is).

By this "argument", financial investing is mainly a gambling activity and mainly a game of luck, since it's just as obviously the case that such markets "indeed cause people to lose everything leaving their families destitute."

Folks, I got Gil's argument at last. Woohoo!

A chess tournament produces bits of information: who won which game. If most of those bits can be causally linked to skill differentials between players, rather than chance, Gil calls it a game of skill. Otherwise, luck. If stakes are high and zero-sum, players start trying to find weaker opponents. This means each game will be between players of roughly equal ability, so skill differentials cease to contribute bits to the bottom line.

Gil, is that right? If so, I apologize for misunderstanding at first. This sounds interesting.