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BGonline.org Forums
Proposed quantitative definition of skill
Posted By: Bob Koca In Response To: Proposed quantitative definition of skill (Timothy Chow)
Date: Tuesday, 19 June 2012, at 4:29 p.m.
Suppose that the game is "given an integer n chosen at random from the interval 1,000,000,000,000,000,000,000 to 2,000,000,000,000,000,000,000 give the nth digit of pi without computational aids within ten seconds. If one player gets it correct and the other incorrect then that player gets a win otherwise it is a draw. Supposing that the population is of players who at least know to shout out a digit. I beleive that currently all of the entries will be extremely close to 0.5 (Some players could get a very small advantage by memorizing a few of the digits). Your measure shows there is no skill in this game.
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. Is that desirable?
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). Is it desirable that it has a skill rating equivalent to ""At the other extreme, suppose that pi,j = 1 for all i < j; then the skill is 1 as long as n is big enough". This may be related to my next question.
"There's nothing magical about the interdecile range; some other measure of statistical dispersion might do just as well or better, but I pick this one for concreteness"
Did you consider taking the average over the possible choices for inter-nth%-ile (What is a good way to say that idea?) ranges?
"At the other extreme, suppose that pi,j = 1 for all i < j; then the skill is 1 as long as n is big enough"
As a concrete example the game might be to see who has the greater height.
"What is the point of the definition? The main application I can see is in the legal realm"
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?
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