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But is it like, a 50% chance to show the finale player, then randomize which finale player is shown, otherwise randomize which non-finale player is shown?

Because if does not feel it works as that.

Exempt, if it iterates through all players, and any player with an active finale does its own 50% roll.
Because for 3 players with finales that would be like 87.5% chance to show the finale, and only 12.5% to not show it.

And with 4 players with finales and the rest replaced players would give even less chance for others to appear (around 6.25%).

(+1)

50% chance to choose a finale player at random.  If not, then it picks a player at random from the whole list.   

So if half the players have active finales, they effectively have a 75% chance of appearing, which seems like a lot, until you remember they'd have a 50% chance of appearing anyway.

If you have 4 finale players and 1 replaced player, then the replaced player goes from having a 20% chance of appearing to 10%.