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
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.