In Hold'em, "any two cards can win". In fact, any two-card hand can become the nuts (the best possible hand given the cards that are out) by the river. Even 32o or 72o can make quads or a straight flush. Let's call such a poker variant, where any hand can make the nuts, a "nutty" poker variant.
In
Lomaha (Omaha played for low with true-inversion ranking), however, there are only 150 hands that can make the nuts. Other hands are not the best on any possible board. Let's call games with this property "allergic".
What poker variants are nutty? Which ones are allergic?
Omaha and Omaha/8 are allergic. Quads less than aces or kings cannot be the nuts on any board. AAAA can be the nuts on a KKKKx board (kings full of aces beats any other hand, nobody can make quads) and KKKK is the nuts on AAAAx. But 2222 can't make quads and can't make a nut full house; in fact in only wins when the board shows trips and nobody else has a pair in hand.
Draw games are somewhat of a special case. Certainly anybody can discard their entire hand and draw for the nuts. So I'd place Badugi, Triple Draw, California Lowball, and Draw (high) in the "nutty" category as well, though often players will choose to make non-nut draws.
We could invent a draw variant that restricted the number of cards you could draw. For example, triple draw restricted to one-card discards is allergic since a hand such as KKKQQ can only make a KQ-low at best.
Stud hi/lo without a qualifier appears to be nutty! There are not many cases where a starting hand such as KKK can be assured of a scoop, but there are a few. (KxKx)KsQsJsTs(9s) is a straight flush and a KQJT9-low, and sccops against any quads on board, such as (xx)8888(x), since the latter can make only a pair of eights for low at best.
Razz is nutty. KKK is obviously a poor starting hand, but against quads on board it can make a lock low, as in the Stud hi/lo example. Stud hi is nutty due to the straight flush possibilities possible with every hand. In Stud/8, it is certainly impossible for some hands to be the nuts for low, but the qualifier means that any hand, even a high-only one, can scoop (and know it--- if all your opponents show three paint cards they cannot qualify for low). So all the stud variants appear to be nutty games (as long as you don't specify what the opponent upcards are along with the starting hand.)
If we eliminate straight flushes, do the high and high-low stud variants become allergic? I don't think so. A hand like 2222 needs to worry about higher quads (a rolled-up hand could hit the river) but in a three-person game the quads could be up against two identical boards and thus be assured that neither of his opponents could make higher quads.
Games without draws or boards, such as Guts, are hyper-allergenic! Only the dealt nuts counts.
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? (Note that it is not necessary; Badugi with the one-discard-only rule requires only one of the original cards to play but still is allergic. The high-card "game" is another counterexample.)
What other variants are nutty or allergic?