Re: Nutty and Non-Nutty Poker Variants
 

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It seems that a game which requires you to play more than one of your original cards will be allergic. Can you invent a variant which breaks this rule, or is it a sufficient condition?

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Why invent one, when five-card stud will suffice?

Re: Nutty and Non-Nutty Poker Variants
 

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It seems that a game which requires you to play more than one of your original cards will be allergic. Can you invent a variant which breaks this rule, or is it a sufficient condition?

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Why invent one, when five-card stud will suffice?

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Full marks for spotting this.

Re: Nutty and Non-Nutty Poker Variants
 

How about Pineapple?

It appears to me that Pineapple (or Crazy Pineapple) is an allergic game, but just barely. With 222 to start you can't make quads. You can make a straight flush but it is not the nut straight flush--- nor can you make a nut straight. But 333 and higher can make nut straights (A245x on board) and nut straight flushes... is 222 the only non-nutty hand in Pineapple?

(On the other hand, you can play the board in Pineapple so you can have the nuts on board. But let's look at non-board situations.)

Can we use this idea to create an allergic 5CS variant? Suppose you get 4 cards but have to discard two of them to make your hand. But even in this game you could catch three aces, which would be the nuts if your opponent's boards were unpaired, unflushed, and unstraightened. You just have too much information about the other players' hands.

But, we could play inverse 5CS in which you get three cards face down after your initial two. Would that be an allergic game? I think so. 22 couldn't make a lock hand; your opponents could always make hidden quads or a straight flush.

1 upcard, 1 downcard, + 3 cards dealt face up = nutty
1 upcard, 1 downcard, + 3 cards dealt face down = allergic

What about 1U1D + 2D1U? An opponent can make quads but at least one of his quad cards must be revealed: (x)y(xx)x. So, any starting hand can make quads and have the nuts so long as all his opponents' upcards are duplicated elsewhere, and nobody shows two to a straight flush. So 5CS is nutty as long as at least one additional card is dealt face up.

But, if we introduce a CP-style downcard, does the game becomes allergic again? Nope. Say you start with 222. Then the best you can make is AAA22. Note that anything that beats AAA22 also beats 2222, so the conditions above (all opponent upcards paired, no two to a SF) are sufficient to guarantee that aces-full is the nuts as well.

Summary:
Pineapple: allergic
5CS: nutty
5CS with discard: nutty
5CS with just one upcard: allergic
5CS with just two upcards: nutty
5CS with just two upcards and discard: nutty