In case you are playing on two boards identical sequence of rolls for both sides means that both sides are ABSOLUTELY equal according the dice sequencies and now the question: who is win MORE????
It should be demonstrate that with the equal identical sequence of rolls the best player must be a winner!
Must? No, that's not true. And the duplicate dice don't eliminate luck. An example -- below, on the left our "Professional" has rolled 2-1 and slotted. On the right our "Amateur" has rolled 2-1 and split. It could have been the opposite; that doesn't matter:
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Amateur (White) on roll
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Professional (Blue) on roll
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Of course there is a question of who is more likely to win -- the professional, presumably. But what does having duplicate dice add to the contest? How they make the contest more "fair"? The dice sequences on the two boards "are ABSOLUTELY equal" only in that they will be the same dice sequences. But already on the second turn, which numbers will be good or bad, or lucky or unlucky, or easier or harder to play, or more or less likely to lead to victory, have diverged on the two boards. The mere fact that the sequences will be the same on both boards has nothing to do with the professional's presumed advantage or his probability of winning.