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I had never heard of that. Having looked it up, all I can say is, “Ewww.”
It does seem to exactly fit what I was after, though.
You need the first half to explore (randomize) the house, distribute items/tools, etc. The exploration phase is a great randomizer and assures that even the same haunt will be completely different each time.
The coin game Spoof fits the bill.
Karma/Shithead also has players play until they are out of cards and the last player remaining is the loser.
To explain a bit more, there are things that can happen in the exploration phase that can give you useful items and help/harm your stats. So no matter what side you are on in the reveal, this phase can help or harm you as a player.
Are those the same game? I’m familiar with Asshole, but I call it “President” when playing with children. In Asshole, the first one out is the president, the next is VP, [insert other titles], down to the last one out being the asshole.
If what oft wears hats is talking about what I think they’re talking about Asshole/President/Hand of Caesar/(or as I would call it, the Great Dalmuti) has each player taking turns to throw the same number of cards of decreasing value until no player can go lower or everyone passes and the last player to play starts a new hand. That is, one player throws 3 10s, the next player must throw 3 9s or lower or else pass and so on.
Karma/Shithead is sort of the inverse. One player starts by throwing a card in the center and players take turns playing higher cards. If you can’t play a higher card, you must take the entire center pile into your hand. Certain cards are given special abilities. Usually 10s burn the center pile and any cards in it are removed from play and 2s reset the pile to 0 and so on.