Can chess be a game of luck?

Consensus so far (to which I add my voice) is that none of us can even detect an argument there, let alone agree or disagree with it. Solved!

"We can suppose that the higher the stakes are, the higher the ingredient of luck of the combined game."

That's called "assuming what you are trying to prove"!

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.

It seems that Kalai's argument is that high stakes can transform a game of luck through its effects on the "incentives and motives of players", though he never explains what those effects are, or describes what he thinks the "incentives and motives of players" are in any situation. In short, I don't think he presented an actual argument to be followed.

Perhaps a better way to put the argument in the post is as follows: High-stake chess is either a game of luck (which is in tension with no-gambling laws) or a fraud (which is also in conflict with the law). The same holds (even more so) for high-stake poker.

Another example: If people bet on the outcome of a fair coin this is a 'game of chance' (and this in conflict with the no-gambling laws). If people bet (evenly) on the outcome of a biased coin this is fraud (and also in conflict with law). High stake chess and high-stake poker are either a  'game of chance' or fraud.

I'm glad you brought this to discuss here. I read that article earlier this morning before I saw this post and was similarly confused.

People are risk averse, so a zero-sum bet (in money) would have negative utility for the weaker player, unless the player causes the probability of winning to increase given a fixed bet (this is "application of skill", that is performance with exceptionally good concentration/preparation/etc. that makes the a priori estimation of player's skill inaccurate in the particular game). The amount on which this probability must be increased in order to make the expected utility of the bet positive, depends on the absolute values of bets. The bigger the bets, the more the weaker player must increase the probability of winning in order to cross over into positive expected utility.

A game can then be called "a game of skill" if effort can sufficiently increase player's probability of winning, and "a game of luck" if an impossible increase in this probability is necessary. Normal lotteries can't be turned to positive expected utility, so they are always games of luck. Poker can't be turned to positive expected utility by weak players, so for them it's game of luck, while for stronger players it's game of skill. Chess for smaller bets is game of skill, and for bigger bets game of luck for the weaker player.

The picture at the top of the article is of a chess board that has been set up incorrectly (the white queen and king are swapped). The rest of the article is just concentrated confusion; he switches unexpectedly from talking about chess to talking about betting on games in general, then rambles about luck for a bit without ever nailing down a definition of it.

I've always though that the difference was the frequency that skilled players win.

Incidentally, Richard Garfield, designer of Magic, once wrote on the topic of luck in games. He said that there is, in fact, luck in chess, because we cannot predict the outcome with certainty. He went on to explain that if he sat down to play chess against Kasparov or some other world-class chess champion, he'd expect to lose, but there's still a possibility (however small) that he could happen to stumble upon a superior line of play, perhaps without even realizing it, and end up winning.

Fails to define what it means to be a "Game of Luck" - AFAICS. In practice, human chess is a game of skill with a small element of luck.

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."