BBO Discussion Forums: Law of Similarity? - BBO Discussion Forums

I recall an empirical "law" that said that if you had a long suit then maybe that was the same pattern in other hands.

I have looked for more info without success.

Any ideas please?

I believe it wasn,t true.

This is a weird claim from 60+ years ago, back before computer dealt hands.

It has absolutely no validity (assuming fair shuffling)

It's a great urban myth though.
I used to believe that if the cards were new then I was more likely to get a distributional hand. I got flamed for that thought.

Perhaps we should have a Bridge Urban Myths Section? (BUMS).

pljr, on 2020-November-26, 10:12, said:

Most postulates proposed as "laws" are unreliable at best and this one (the "law of similarity") was clearly nonsense even in its time.
The originator was of course Ely Culbertson, somewhere between bridge genius and con-man.

It was Culbertson's "Law" of Symmetry.
e.g. Singleton kings

hrothgar, on 2020-November-26, 10:58, said:

The fair shuffling comment matters, I recall a deal with new cards where all 4 hands were (6421) with identical pips within each suit.

Suppose you have a 7-2-2-2 hand vs a 4-3-3-3 hand

Surely the distribution of the remaining cards is such to shift the chance of others having a long suit - who knows how much by - I doubt you could assume much about others having similar distributions, but come on it seems obviousl, albeit hard to calculate.

It was always a bit depressing when a night seemed to become defined by a boring pack of cards - time to try another one sometimes

But then again I imagine boring distributions are the bulk of the bridge deal space with occasional bright interesting patches - much like life, the universe and everything really In fact come to think of it, when I watched a video of John Conway discussing surreal numbers he seemed to have a similar philosophy towards infinity, that only a relatively small part of it was interesting - sorry for the paraphrase - apologies, it was more along the lines of levels or types of interestingness of different parts so he concentrated on the most interesting bit

There may be something useful in this page by Pavileck on Freakness

I heard once that if you had a 13-0-0-0 hand it was likely someone else had a void somewhere


Has anyone written anything interesting on shuffling theory Maybe an idea (not serious) for bridge software would be to have different shuffling algorithms to make it more interesting (has it been done)

pljr, on 2020-November-26, 10:12, said:

You are correct


Culbertson, one of the pioneers of the game, believed in what he called the Law of Symmetry

I dont believe any good player believes in it these days.

According to P.E.I. Bonewits, the Law of Similarity is one of the laws that govern the creation of magical spells. Bonewits was the only person who had a degree in Magic from a major Western university (B.A., U.C. Berkeley, ca. 1970).

thepossum, on 2020-November-26, 18:06, said:

As this hand has a generic frequency of 6 x 10 to the power of -10, it seems somewhat academic

Ah, it's more common than that - it's shown up in at least 4 books that I own.

Almost always when it's shown up, of course, it's because a new deck was put in a board by suits (or, back in the day, when we suited boards on last play to be able to create the hands from handouts) and not shuffled/made/dealt.

mycroft, on 2020-November-27, 16:24, said:

Back in the day? We still do that.
Indeed my alternative reply was that it was even likely that each other hand had 3 voids.

pescetom, on 2020-November-27, 14:20, said:

I know but some people may want a special convention to cover it

Would a transfer work

It would be sad to get excited and bid no trumps

I do imagine a lot of people would pass in case they were accused of psyching

But seriously getting back to the OP have there been attempts at analysing or proving such things. Could you not prove it on a simplified game

The "law" I had heard of postulated that hand patterns repeated in the suits. So if you have a 5332 hand, there will be a suit that is 5332. I heard of it about 30 years ago as hearsay and have never heard it again. It was in conjunction with the idea that if you have a void, there will be another hand with a void out there.

I reckon you could try something by induction

Consider a simple game. 2 players. 2 cards each, 2 suits etc

thepossum, on 2020-November-27, 20:00, said:

Yes

It is trivial to demonstrate that this is complete nonsense for either

A. Computer dealt hands or
B. Hands that a hand shuffled in "good" manner

It is possible that there is some truth for this for hands that are manually shuffled using some "poor" technique. The problem here is that almost any claim is consistent with bad shuffling.

The only way to really analyze this is to collect all sorts of data about hands that are manually shuffled in bridge clubs and use this to test the hypothesis. There was a data set that got posted a few months back from one bridge club in the Netherlands. As I recall, it didn't show anything particularly interesting.

Quote

The issue here is not the complexity of the game, but rather the availability of the data

HardVector, on 2020-November-28, 01:03, said:

You are right. To quote from a 1933 newspaper article by Ely Culbertson:
"It was original with me, and I have long recommended it to all bridge players because I know how valuable it has been to me, and thus can be to them. The player must simply remember that whatever the pattern of any hand of 13 cards dealt, there will probably be a suit pattern which corresponds to it. Thus if a player's hand is divided five-four-three-two-one(sic), the distribution of some suit in the four hands will probably be five-four-three-one also. This varies, of course, but only to the extent of one card. That is, the equivalent suit may be divided five-four-two-two."

Almost one hand in four is either 5431 or 5422, so allow space for "exceptions" and this "law" might be seen to work.

hrothgar, on 2020-November-28, 07:09, said:

Come on Richard, until now I gave you credit for a fair bit of understanding of maths and the concept of proof..it's nothing to do with shuffling at all. It's a mathematical proofs, whether possible analytically or not I don't know

Unless of course by shuffling we are discussing complete randomness with any hand equally likely etc

And in terms of data you would need however many times 10^28 hands and a large database. Sorry the number of hands has been reduced considerably by the OPs hand

But it's obviously and selfevidently true. But I don't know if it's provable


Just by way of an aside I read something about a law of similarity in Gestalt psychology. It seemed to me a statement of the obvious too

thepossum, on 2020-November-28, 14:31, said:

Nothing to do with it? The shuffling is the entire point and premise of the 'law of symmetry' - the first paragraph of Culbertson's article:

Quote

With perfect shuffling it's trivial to prove mathematically. If you fix North and South's hands, for example, you can swap cards between them without affecting any frequencies of East + West's - so the shape of one cannot influence the shape of another.

smerriman, on 2020-November-28, 17:13, said:

I'd frame it slightly differently

With perfect shuffling the odds of being dealt any given deal are equal.

Lets filter down the set of hands by fixing the North hand and the South hand.
The odds of being dealt any given pair of East West hands are still equal.