Our mathematical models make the following assumptions:
(a) we do not take into account action cards nor the draw pile; (b) all the cards dealt to and
in the hand of any player are open during the game (i.e., perfect-information);
Well, that's unfortunate, i.e. it's about UNO variants, not the actual game. UNO without action cards?!
Yeah, and that doesn't actually reflect the game-as-played. I have never played an Uno game with perfect information, or without action cards. I can't imagine it would even be fun! Also, try playing Hot Death Uno, which for me ups the strategy so it becomes a worthwhile game.
Reducing the non-cooperative version to a variant of GEOGRAPHY implicitly assumes perfect information -- basically that both people know each others' hands. I wonder what the complexity of optimal play is if you don't know your opponent's hand.
Well, that's unfortunate, i.e. it's about UNO variants, not the actual game. UNO without action cards?!