Good lord this is still alive? I have written so much here.
Okay. Read the question, it says, “All things being as equal as possible regarding player skill, what percentage does luck influence the outcome of the game”.
The answer to this question really depends on whether there is any factor aside from luck and skill that affects the outcome. The question effectively defines a scenario where skill will not make any difference between the players, because the players are “as equal as possible” in that regard. So the game CANNOT be decided to any significant degree on the basis of skill, because it is equal.
I guess the other problem with the question is what is meant by luck. Obviously dice are part of luck, but there may be other factors in luck. If you miss something on the map, is that luck or is that skill? Are there other ways that luck can enter the game.
I think however that the question means dice when it says luck, and assumes that dice and skill are the only two factors. Logically, when you neutralize one of the two factors, the outcome will be decided 100% by the other factor.
Eg. suppose you are playing chess, or NO LUCK A&A (hits determined completely according to punch / 6, rounded). Then there is no element of luck, so skill makes 100% of the difference.
However, players of equal skill playing chess against each other will not always tie. Since there is no question of luck (or is there?) you have to say that the winner in each game played more skillfully than the loser. The fact is that we do not play with a 100% consistent level of skill. Some days you are on the ball, others you are not. So then are you lucky if you happen to be “on” on a given day, or are you “more skillful”?
The question is not sufficiently defined to be capable of a meaningful answer.