Nutty and Non-Nutty Poker Variants
 

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?

Re: Nutty and Non-Nutty Poker Variants
 

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 scoops against any quads on board, such as (xx)8888(x), since the latter can make only a pair of eights for low at best.

I need some help with your terms. In the hold 'em example, I assumed that the nuts was a hand that would win <u>regardless</u> of what its opponent's hand was. In the above hi-lo example, this is not the case--the nuts is opponent-dependent.

Re: Nutty and Non-Nutty Poker Variants
 

Maybe there should be another distinction between games in which you can have the nuts and be assured a win (hold em, omaha, stud i guess) and games in which the nuts merely means that you cant be beaten (draw).

Re: Nutty and Non-Nutty Poker Variants
 

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Maybe there should be another distinction between games in which you can have the nuts and be assured a win (hold em, omaha, stud i guess) and games in which the nuts merely means that you cant be beaten (draw).

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In flop games where some of the board cards must be used, it may be possible to freeze out an opponent; for example, if you have 9s7s, and the board is 8s6s5s4s3s. But it seems in stud, or stud hi-lo for that matter, the best you can be guaranteed is a tie.

OP asks: [ QUOTE ]
If we eliminate straight flushes, do the high and high-low stud variants become allergic?

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I think the opposite may happen. If AAAAx becomes the best hand in stud, stud hi would go from allergic to nutty.

Re: Nutty and Non-Nutty Poker Variants
 

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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 scoops against any quads on board, such as (xx)8888(x), since the latter can make only a pair of eights for low at best.

I need some help with your terms. In the hold 'em example, I assumed that the nuts was a hand that would win <u>regardless</u> of what its opponent's hand was. In the above hi-lo example, this is not the case--the nuts is opponent-dependent.

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I am assuming that nuts = best hand given the information available to you. In board games, this is your hand + the board, but in stud games this is your hand + all your opponents' boards.

The question in either case is "is there some board (some boards) that will guarantee a win (or tie) for a given starting hand". If the answer is always yes (any starting hand can develop into a lock) then the game is nutty. If the answer is no (there is at least one starting hand that cannot lock up the pot no matter what falls) then the game is allergic.

Re: Nutty and Non-Nutty Poker Variants
 

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Maybe there should be another distinction between games in which you can have the nuts and be assured a win (hold em, omaha, stud i guess) and games in which the nuts merely means that you cant be beaten (draw).

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In flop games where some of the board cards must be used, it may be possible to freeze out an opponent; for example, if you have 9s7s, and the board is 8s6s5s4s3s. But it seems in stud, or stud hi-lo for that matter, the best you can be guaranteed is a tie.

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Yes, I consider a lock for the pot to be the nuts, even if it is possible that you are tied.

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OP asks: [ QUOTE ]
If we eliminate straight flushes, do the high and high-low stud variants become allergic?

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I think the opposite may happen. If AAAAx becomes the best hand in stud, stud hi would go from allergic to nutty.

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Hm, I had been trying too hard with normal Stud Hi. It is not necessary to catch four cards to a straight flush, just runner-runner-runner-runner quad aces. [img]/images/graemlins/smile.gif[/img] In order for this to be a lock, your opponents' boards must make a straight flush impossible.

Or, to put it another way, if you start with any three cards, and make (xx)xAAA(A), you will have a lock for high as long as your opponents' boards contain no two cards to a straight flush. That makes stud hi "nutty", with or without straight flushes.

You can also make a lock with (sx)xsss(s) where sssss makes a straight flush, as long as your opponents' boards again lack any two cards to a (higher) straight flush.

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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Phat Mack's question led me to a counterexample. Suppose you are playing Omaha (high) but with the additional rule that everybody must reveal, preflop, any pairs they hold in their hand. Then even the lowly 2222 can make the nuts because on an AAAAx board you will know whether or not anybody can make a better full house. I can't find an example of a hand that can't make the nuts in this variant. (Any paired hand can make the best full house; any unpaired hand can make quads on a non-straight flush board.)

Re: Nutty and Non-Nutty Poker Variants
 

This is a fine post and has generated a good discussion. Can anyone think of play implications for nutty and non-nutty games? Obviously, you can play a touch loosely in nutty games and make plays based on hand reading. Should players choose nutty games over non-nutty games because they are potentially playing for the nuts and if they play well their opposition may well be drawing dead or should good players choose non-nutty games because the chasers are doomed not to end up with the nuts no matter how lucky they get?

Re: Nutty and Non-Nutty Poker Variants
 

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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 scoops against any quads on board, such as (xx)8888(x), since the latter can make only a pair of eights for low at best.

I need some help with your terms. In the hold 'em example, I assumed that the nuts was a hand that would win <u>regardless</u> of what its opponent's hand was. In the above hi-lo example, this is not the case--the nuts is opponent-dependent.

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I am assuming that nuts = best hand given the information available to you. In board games, this is your hand + the board, but in stud games this is your hand + all your opponents' boards.

The question in either case is "is there some board (some boards) that will guarantee a win (or tie) for a given starting hand". If the answer is always yes (any starting hand can develop into a lock) then the game is nutty. If the answer is no (there is at least one starting hand that cannot lock up the pot no matter what falls) then the game is allergic.

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OK, this definition is helpful.

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

Is there a relationship between the nuttiness or alergicity of a game and its popularity or its ability to generate action?

Re: Nutty and Non-Nutty Poker Variants
 

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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.)

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