[MarkGritter]

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Can you think of any true-inversion or second-best game that can be nutty?


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Yes!

Play Hold'em but eliminate all difference between ranks. There are still straights, flushes, etc., but any pair ranks as a tie with any other pair, both ends of the straight have equal value, top set splits the pot with bottom set, etc. Call this variant "Discrete Hold'em." Discrete Hold'em is nutty, although it produces a lot of split pots. (I invented it to find a variant in which holding 67 was better than AK.)

Now play the true inversion version of this game. (That is, each player must make the best possible hand from their hole cards + the board; the lowest of these hands wins the pot.) This game is also nutty. AA is the nuts with quads on board--- but then, so is every other hand! (Perhaps I should have named it "degenerate hold'em" rather than "discrete hold'em.")

I'm not sure how to define the nuts in a second-best game...

I think nuttiness has more to do with how much of your hand you get at once than anything else. Omaha's 2-card requirement means that 2/5 of your showdown hand is known at the start, while in other variants only 1/5 or 0/5 of your starting hand might play at the river. (While in Guts you get 3/3 of your hand!)

So, if we want an allergic Stud variant, perhaps we should try introducing a rule that two of your first three cards must play. Or that you are dealt two downcards and two upcards (instead of 2:1), since that also ensures that 2/5 of your showdown hand is known. (I can't believe that either of these are novel--- maybe I should troll through the poker variants site and see if I can find a reference.)

(However, Omaha-with-revealed-pairs is nutty. Additional information can thus turn an allergic game into a nutty one. So it may be hard to make an allergic stud variant because of the additional information provided by board cards.)