A measurement of skill versus chance in games.
Overview
I present here what I believe to be a novel approach to measuring the amount of skill versus luck in various types of games.
The method gives each game considered a rating between 0 and 1 inclusive. 0 means there is no skill involved, everything is down to chance. 1 means there is no chance involved and it is all skill.
Here are a few games on this scale:
Skill/Chance rating, Example game
0, Snakes and Ladders, Roulette
(bewteen 0 and 1), Backgammon, Gin, Poker, Yahtzee
1, Chess, noughts and crosses
Method
In an extensive form representation of a game at each node use backward induction to calculate the payoffs (but do not discard them). Then "normalise" them by making sure all payoffs are between 0 and 1. Then calculate the largest difference in payoffs for each player at each node. Then take the average of these differences for each player (moves by nature aka moves by chance are to be considered a player). Then use the below equation.
B = The average of all largest differences in payoffs for moves by nature
A = The average of all largest differences in payoff for all other players
Measure of Skill (S) = A/(A+B)
Examples
Chess: A=0.5 (i think)
B=0 (no moves by nature hence no difference in payoffs).
S=0.5/(0.5+0)
therefore S=1
Snakes and Ladders.
A = 0 (all moves are by nature)
B = I'm not sure but its positive and finite.
As A=0 A/(A+B) is 0 therefore S=0
Worked example of intermediate skill/chancegame
skill verses chance worked example http://cleerline.com/images/skillmeasure.png
A=0.21
B=0.28
S=0.43
Tagging this as game theory is actually inappropriate. Game theory is a branch of economics that studies decision-making.
That aside, this is an interesting idea. However, I think that this measurement is flawed: can you justify your equation S = A/(A+B)? Why would you define it as such? What tells you that the proper measure of skill isn't, for example, computed by subtraction?
I haven't seen anything like this before (though I haven't looked extensively), so yes, this computation is (probably) novel. However, as I explicated above, there are some flaws: specifically, you have to be able to support your measurement with evidence. You must be able to justify your conclusions.
So, again, this is a neat idea, and it is certainly a question worth exploring. However, I think you need to work on it by providing some thorough evidence for your theory. Good Luck!
EDIT: Also, what about $(A/(A+B))$ when $A+B =0$? ;)