# How to determine randomness of game

Is there a mathematical way to determine how much randomness determines the outcome of a game? Or a way to determine which of two(or) more games has a greater factor of luck affecting the outcome?

For example people agree that $$portes$$ (which is the usual Backgammon) has a greater factor of luck than plakoto (a variant of backgammon) and that Acey-deucey(another variant) has an even greater factor of lack. Is there a mathematical way to prove/disprove this opinion of most people and to generally compare games on "how random they are"?

I am looking for a general answer(not limited to the three games mentioned) since most people may not know the games I described and used for examples.

As a measure one could try to determine how much influence a player's strategy has on the outcome. E.g., if two players $$A,B$$ with different strategies play $$1000$$ games, we expect $$500\pm 16$$ wins for either player in a totally random game and $$1000$$ wins for the better strategy in a purely strategic game. Already observing more than $$600$$ wins for either player would be highly unusual ("six standard deviations") for a truly random game.
The problem with this is that in order to compare different games by their different levels of influence of randomness, one would need to somehow agree on what strategies to pick for the compared players $$A,B$$ -- a theoretical hard to find optimal strategy for $$A$$? Or the best human expert? But then what for $$B$$? Always pick a random valid move? Or a human player who learned about the game only last week? While probably any of these choices can be used to demonstrate that neither Backgammon nor Poker nor Chess are pure games of luck (whereas Roulette is), it seems hard to find a feasible way to compare and rank these according to the influence of strategy vs. luck