"The Miner's Adventures"

If the order of places is important, then there should be criteria for this. In many sports, luck plays a role (for example, in Euro 2008, some scenarios could have led to a coin toss). No one forces anyone to maximize all three criteria. Those who find it difficult can simply ignore one of them (especially since it rarely comes down to it). You can simply change the third criterion (for example, whoever sent the save file first – an analogy to weightlifting, where the lighter weight wins in case of a tie). And in the Champions League, the fifth or sixth criterion is the country ranking. So, you could use the player ranking as a criterion (for example, in chess, if the world champion draws with a challenger, the champion is declared the winner of the match).