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Proposed quantitative definition of skill
Posted By: Timothy Chow In Response To: Proposed quantitative definition of skill (Bob Koca)
Date: Tuesday, 19 June 2012, at 5:28 p.m.
Bob Koca wrote:
Now suppose that there is a single person who develops the skill to do this correctly within 10 seconds. That demonstrates super tremendous skill. Yet your measure still shows no skill in the game.
No, this is incorrect. Re-read comment one. The definition of skill depends not only on the game, but on the population of players. If the single person in question is brought into the population, then the skill goes up. If he's left out, then there's no skill.
Suppose there is a game which has a clear mathematical strategy such as nim. One could imagine a large population of math students with half knowing the strategy and half not knowing it. In games of a knower vs a non knower p is close to 1 for the knower and close to 0 for the non knower. In other games it is close to 0.5. Your definition gives a rating of close to 1 skill for this game (and population).
Right. This sounds like what I would want. Does it not sound like what you would want? If there are some perfectly skilled players who can almost always beat unskilled players, then there's a lot of skill involved, right?
Did you consider taking the average over the possible choices for inter-nth%-ile (What is a good way to say that idea?) ranges?
As I said, you can pick anything you want, but in general I think that we want to explore close to the extreme ends of the skill spectrum, rather than "smooth" over the big in-between region. This will provide more discriminating power across different games.
As a concrete example the game might be to see who has the greater height.
Yes, that's one of my friend's favorite examples. Something at this extreme is close to being a "measurement" rather than a "game."
What would the population be? Would it be tournament players or all persons who know the rules of the game?
On a note that is not related to the math, why should the level of skill and or luck matter to legality in the first place?
Why it should matter, I don't know. I don't think that this particular "why" question is the relevant question in the realm of law. The fact of the matter is that it does matter in legal discourse, as you will quickly find if you examine court records. Gambling is typically defined as something where there is (1) consideration in, (2) consideration out, and (3) some element (or a predominant element) of chance/luck/randomness. Skill is usually seen as something that counterbalances luck. Successful exemptions to gambling bans have often been based on a skill argument.
The choice of population would necessarily depend on the context of the court case. If someone is proposing outlawing venues X, Y, and Z, then the relevant population would be the population of players who frequent X, Y, and Z.
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