The degree to which luck affects the game varies with the degree of skill of the players. The less the degree of skill of the players, the greater the degree luck affects their game.
But in the context above, “degree” is not used to describe a hard and fast direct or inverse relationship. “Degree” in this context refers to the overall tendency, the general probability.
Why do I say this?
I posit that the less skilled the players involved, the longer it will GENERALLY take for the game to end, because of the ineffectual strategies used by both sides. Over the course of a longer game, there should naturally be more dice rolls, so the cumulative effect of the luck variable will be considerable.
On the other hand, the more skilled the players involved, the sooner the game will find a crucial point or points beyond which victory may be decided. On that single or multiple battle will the outcome of the game be largely decided. So although the eventual outcome of that battle will be decided by chance, and thus the game could be said to be decided by chance, it is likely that the side that had the superior probability of winning will actually win.
Of course, that in turn asks the question of how it is that if both sides were equally balanced, how it could be that one side could have a superior probability of winning the crucial battle. The correct answer, given a starting bid option that is empirically fair, is that the side that has the superior position will have that superior position through chance.
Of course, if the starting bid is not empirically proven fair, it could simply be that both players are of insufficient skill to determine the game primarily based on skill, but must rely on luck to determine the victor.
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All in all, I would say that given the complexity of the game, it is unfair to say that the “better” player should always win, because the element of chance will make it so that the player that would win MOST of the games will lose SOME of the games, against a player of near equal skill.
So - short version. The worse the players are, the greater the element chance will play in determining the winner. However, even the best players will find that luck plays a considerable role in determining the victor.
If you want to determine a real percentage, I recommend taking down game results.