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.

well, brian, what you wrote is not exactly what I was saying

the problem with your statement 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: is that I am not aware of any definite way to quantify the degree to which luck and skill contribute to the outcomes

People often assume that the most skillful the player need to be the higher the contribution of skill to the outcome is but this does not seem to be true

Very good. The conventional ways you propose to measure luck and skill ingredients are precisely the same as what I would use.So my notions are consistent with the usual ones. When you say that baseball involves more luck that basketball your notion depend on the entire scenario and reward systems and not just on the rules of the games precisely as I suggest the new ingredient in my analysis is that these measures may not be robust if we change the reward system.

Dear Orthonormal, You are partially correct. it may be true that the way I use game of skill/luck it is not the ususal one, but it is a reasonable way, more solid, in my opinion, from the point of view of game theory/economics, and more importantly, it is relevant to the usage in the relevant laws which was meant to define what gambling is, and to common wisdon regarding gambling

The conventional way does not give you a way to measure the ingredients of skill and luck, and it treats the bare game without taking into account the entire scenario, the game, the betting, the winners, the enterance fees, etc

When you try to determine what is a gambling activity and what is not, looking just at the bare game is insufficient the common wisdom regarding these 50 years old poker clubs in J-m is that what was going on there was a gambling activity Aumann proposed a loophole in the legal definition of gambling based on luck and skill ingredients However, if you examine the situation carefully you realize that the usual meaning about what is game of luck/skill is insufficient, and is not compatible with the usual meaning of what is a gambling activity. A more careful analysis based on the entire scenario is more appropriate

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

Yes, indeed i am talking about selection bias for players as stakes change. When the stakes are higher if players are rational then the selection bias will lead to them to have similar skills, and this means the game turning more into a game of luck, unless.. some players without adequete skills are playing just by gambling effect, and this also pushes the game into a game of luck ---of a different nature

Well, in hebrew the meaning is the same. Regarding the poker club in Jerusalem indeed Aumann felt that the judge did not follow the letter of the law but rather his own perception of right and wrong. I offered an explanation why the judge ruling is consistent with the law

I think the difference between our opinions is that you regard the part of poker that is luck and the part that is skill as intinsic property of poker, and perhaps also of how long is the game. In my opinion, just as longer games make the skill element higher there are other ingredients (such as high stakes; winner takes all, and more) that push the skill element down

"Most people can't do it"

This is precisely my point and probably the basis for the judge's rationale in the old case. The situation of those" most people" who cannot do it but still take parts in betting on poker is similar to those playing the roulete. if this accounts for a large percent of participants than it is justified to regard the activity as primarily - gambling (or game of luck) I think there are additional ingredients that will push the situation towards a game of luck when the stakes are high.

This is an interesting comment. I think people are aware that financial investment involves some elements of luck, but carries the benefit that it advances the economy a major difference with our case is that financial investment is not (at least not obiously) a negative expectation activity

Precisely, this is what I meant. Sorry for not being clearer.