Symmetry definition

[Danlo]

Hi all,

 

Symmetry is quite often used in the description of bidding systems, especially relay oriented systems.

 

To be able to discuss symmetry, I'd like to hear some definitions (if possible: generally accepted definitions) of the symmetry concept. This will probably result in multiple definitions for related uses of symmetry, but that's OK with me.

 

Thanks in advance!

[hrothgar]

Good question! I've seen lots of discussion about "Symmetric Relay", however, I have never seen a really good definition of the term. Here is what I settled on when working on my MOSCITO notes:

 

[Please note: It is entirely possible that there is some kind of standard definition to the term that has escaped me so far... If so, I am happy to be corrected]

 

Here is the quote from my notes:

 

Symmetric relay gets its name because the entire relay structure is “symmetric” in nature. Symmetric is an adjective that means, “having similarity in size, shape, and relative position of corresponding parts”. Within the context of relay bidding, "symmetric relay" refers to a relay structure designed such that specific hand shapes are typically resolved with the same bid.

 

For example, any 5431 shape is always resolved with a 3D bid. Regardless of whether you open with a strong club or a limited opening bid, regardless whether you open 1C or 1S, if you have a 5431 shape, you will always resolve a 5431 shape with a 3D bid. In a similar fashion, any 7330 shape is always resolved with a 3S bid.

 

If we apply this criteria to MOSCITO's relay modules, its quickly apparant that two of the modules are reasonably symmetric.

 

The module showing two suited hand patterns is almost complete symmetric.

All shapes other than 6520 and 6511 are resolved with the same bid.

 

The module showing single suited hand patterns is also very symmetric.

All shapes other than 6322 shapes are resolved with the same bid.

 

However, the relay structures designed to show balanced hand patterns and three suited hand patterns are not Symmetric. In some cases, there are standardized approach sequences and junction bids. For example, 2NT is often used as a junction to show 5332 hand patterns. 2H is often used as a junction to show 3 suited hand patterns. However, I don't believe that these relay structures qualify as Symmetric.

[Rhutobello]

uhmmm, and I who only wanted to have some relax time among friends :rolleyes:

(just kidding)

I can see there still are tons to learn :D

thx

Have a nice day all :D

Edvin

[the hog]

Richard has defined Symmetry in relay terms. Terrence Reese also discussed the "rule of symmetry" in hand shapes. eg if one hand holds a 4333, there are high odds that another hand will have the same hand shape, and the two remaining hands will be symmetrically unbalanced.

 

Ron

[1eyedjack]

Bit of trivia thread drift:

 

As I am sure you are all aware, there are precisely 17 different symmetrical ways to map plane (ie 2-dimensional) repeating wallpaper patterns. And they are all to be found at the Alhambra palace.

[Danlo]

Thank you all for your comments. I've been thinking a lot about symmetry the last few days.

 

The definition of Richard looks right to me, for a certain kind of symmetry. If I could coin a term, it would be 'absolute symmetry'. Referring to the fact that the symmetry stems from using the exact same bid for all instances of a shape.

 

In my musings I have identified a second kind of symmetry, that I call 'relative symmetry'. Not very surprising of course, after introducing absolute symmetry.

 

Relative symmetry means that the same bids have the same meaning, relative to X. Where X can be several things: the opening bid, the primary suit, the agreed trump suit and probably some other things.

 

Relative symmetry is used quite a lot in natural systems, and somewhat less in relay systems, I suppose.

 

Examples: simple raises of the opening suit. 1H-2H is symmetrical with 1S-2S, since the bid and the meaning are the same, relative to the opening suit. 2X means support in X and 6-9 HCP, where X can be subsituted by the opening suit.

 

Relative symmetry is a little more complex then absolute symmetry, because you have to identify the kind of X needed and the actual X.

 

Both kinds of symmetry have advantages and disadvantages. The most noteable disadvantages of absolute symmetry: if 3S shows 7330, the distance to 4H and 4S differs. This influences the possibilities for slam investigation. Also, depending on the opening bid, the distance from the opening bid to 3S differs. This will make it difficult to devise (relative?) symmetrical sequences ending in 3S. Furthermore, the ability to rightside the contract is probably depending on the seven card suit. If you have seven spades, the contract will probably be in the hands of the relay puppet, whereas a seven card heart suit will probably be played by the relay captain.

 

Relative symmetry does not have these disadvantages. Because it is for example relative to the longest suit, it is easier to design a system where the contract is rightsided automatically in important cases. Relative symmetry also makes it easier to incorporate nonforcing bids. Relative symmetry has problems, however, when the envisioned trump suit is not the same as the suit where the symmetry is based upon, or when the prospective contract is 3NT. When you have relative sequences, 3NT will pop up in all kinds of places of all kinds of sequences, making it more difficult to devise a possibility for a last minute 3NT signoff. And if the long suit is diamonds, but you want to end in hearts, you may just be too high to do any kind of slam investigation.

 

There are areas of the bidding where the advantages of each kind of symmetry are noticeable: relative symmetry is probably good in the start of the bidding, mostly because it keeps bidding straightforward and effective in non forcing situations. Relative symmetry is probably also effective in one suited scenarios. Since a six card suit is a likely trump suit candidate, centering the bidding around this suit seems a reasonable strategy.

 

Absolute symmetry lends itself to situations where there are several trump suit candidates, or the result may be a no trump contract.

 

But if you want to use these forms of symmetry in the same system (as of course we all do one way or the other), you'll have to fix the transition problem. To get from different opening bids into an absolute symmetrical structure, most systems use the 'big bang' option: the same (hence absolute symmetrical) bid is used to start the absolute symmetrical relay scheme. For example use 2C over any 1 level opening bid as a game forcing relay.

 

Another strategy is to load the opening bids differently: put a little more into the 1H bid then the 1S bid. After 1H-1S(relay) the little more is bid with 1NT, the 2C and higher bids are used in the same way as after 1S-1NT(relay). This way you slide from different opening bids into an abolute symmetrical structure. I would call this something like 'slicing', since the difference in meaning between the next higher or next lower bid is the addition or removal of a slice.

 

Relative symmetrical structures do not have the need foor big bang or slicing, they flow quite naturally, but only to a certain final contract.

 

One of the problems I encounter in system design is that when reusing structures, the result is often not as expected. In one situation the structure works, but in another it doesn't. The problems I identified above are some of the reasons. At the moment (but insight change over time) I feel that using relative symmetry is the best approach when a five card or longer major suit is identified. Absolute symmetry is the best in most other situations, especially for (semi)balanced hands, but even with the most extreme minor suit oriented hand 3NT stays a good option.

 

But in this approach full absolute symmetry is discarded for one suited hands and some two suited hands, because it is replaced by a hybrid approach (absolute when minor suit oriented, relative when major suit oriented).

 

Anyone out there still with me ;) ?

 

============

Bert Beentjes

Nijkerk (Gld.)

The Netherlands

 

"Give your partner easy decisions, not difficult puzzles."