The Law of Symmetrie

[xx1943]

Hi all

 

Terence Reese writes in his "On Play" page 12/13:

 

"....if you have yourself a unbalanced hand pattern, such as 6-5-1-1, then you are likely to find that your long suits break badly against you. It must be stated, that this argument has no support among mathematicians"

 

Some of my partners swear, that the likelyhood of a singleton in opponents hand is much greater, if you are looking at a singleton in your hand or dummy.

 

Imo this is pure superstition.

 

What do you think?

 

Regards

 

Al

[EricK]

You have asked two separate questions.

 

The odds of a suit breaking badly are not affected by the presence or absence of a singleton in your hand. eg if you are missing 5 cards you will still get a 3-2 break 68% of the time.

 

The odds of an opponent holding a singleton are affected by the presence of a singleton in your hand. This is because the presence of a singleton will tend to increase the length of your best fit with partner which in turn increases the chances that one of the opponents will be short in that suit.

 

Eric

[hotShot]

The nasty distributions are just more memorable ......

[spwdo]

The nasty distributions are just more memorable ......

agree:) so many memories:D

[xx1943]

The odds of an opponent holding a singleton are affected by the presence of a singleton in your hand. This is because the presence of a singleton will tend to increase the length of your best fit with partner which in turn increases the chances that one of the opponents will be short in that suit.

 

Eric

Hi Eric,

 

Compare these two: The singles in the second distribution make it not more probable, that an opponent has an single.

 

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[hv=n=sakjxxhaqxxdxckxx&s=sxxxxhxdakxxcaqxx]133|200|[/hv]

 

Sincerly

 

Al

[EricK]

The odds of an opponent holding a singleton are affected by the presence of a singleton in your hand. This is because the presence of a singleton will tend to increase the length of your best fit with partner which in turn increases the chances that one of the opponents will be short in that suit.

 

Eric

Hi Eric,

 

Compare these two: The singles in the second distribution make it not more probable, that an opponent has an single.

 

[hv=n=sakjxxhaqxxdxckxx&s=sxxxxhxdakxxcaqxx]133|200|[/hv]

 

 

[hv=n=sakjxxhaqxxdxckxx&s=sxxxxhxdakxxcaqxx]133|200|[/hv]

 

Sincerly

 

Al

I agree with you, but this is not a counterexample to what I said.

 

It doesn't matter how the cards are distributed between you and your partner's hand, the chances of a singleton are unaffected. This is what I meant when I said that the chance of a bad break doesn't change.

 

But, if you have just seen your hand, then the presence of a singleton does affect the chances of a singleton in any other hand (in fact any distributional information about one hand affects various distributional likelihoods in the other hands). This isn't a useful piece of information from a bridge perspective, but I believe it is true nonetheless.

 

Eric

[MickyB]

For computer dealt hands, I agree with Eric. Manually dealt hands, however, are a different matter - IMO some shuffles (and previous orders of the cards) are more likely to produce shapely hands than others, so if you are dealt a shapely hand, it increases the chances that the deal was such that shapely hands are more likely.

[pclayton]

I've seen too many singleton Kings in different hands on the same deal to not believe in this. People think its an anomaly; I don't.

[han]

A partner of mine thinks that the chance that trumps split 5-1 is more than 50% when playing in a 4-3 fit. He doesn't think that there is any explantion for this, it's just true in his experience. He won't say anything when they split 3-3, but anytime they split badly, he says "You see, I told you!".

[xx1943]

A partner of mine thinks that the chance that trumps split 5-1 is more than 50% when playing in a 4-3 fit. He doesn't think that there is any explantion for this, it's just true in his experience. He won't say anything when they split 3-3, but anytime they split badly, he says "You see, I told you!".

Hi Hannie

 

That is just my experience and the reason why I posted thid poll here.

 

Al

[the hog]

"A partner of mine thinks that the chance that trumps split 5-1 is more than 50% when playing in a 4-3 fit. He doesn't think that there is any explantion for this, it's just true in his experience. He won't say anything when they split 3-3, but anytime they split badly, he says "You see, I told you!".

 

That is clearly at odds with mathematics, Hannie. He probably is scared of 4-3 fits.

[nickf]

I've seen too many singleton Kings in different hands on the same deal to not believe in this. People think its an anomaly; I don't.

Interesting comment.

 

what about singleton 3s in different hands on the same deal?

 

Phil - what's your sample size and how rigidly have you been keeping records of all the hands you've played?

 

nickf

sydney

[Free]

I've heard a lot that it just isn't correct, but I still follow it. If I have a singleton, then I usually play trumps for 4-1 split, especially with computer dealt hands!

 

This is just a rule like "The Q is behind the J if you can finesse both sides".

 

I should actually run a simulation about this singleton stuff, but I haven't had the time...

[hotShot]

This is just a rule like "The Q is behind the J if you can finesse both sides".

Well those rubber-bridge-rules were right, when tricks were thrown together and people shuffled themselfs. If a finesse did not work last hand, it is very likely that the two cards had been glued together and the finesse will not work this hand too.

 

If they apply to computer dealt hands, there is something wrong with the programm.

[pclayton]

I've seen too many singleton Kings in different hands on the same deal to not believe in this. People think its an anomaly; I don't.

Interesting comment.

 

what about singleton 3s in different hands on the same deal?

 

Phil - what's your sample size and how rigidly have you been keeping records of all the hands you've played?

 

nickf

sydney

Of course I don't keep 'records' on this; but it seems more common than one might think. Never thought about other singletons; that would seem to counter the whole symmetry belief.

 

I'm sure my 'evidence' is more or less anecdotal.

 

To me; things like "Law" of symmetry and Crane's rule about 2-way finesses for queens might be superstition based, but they make the game interesting.

 

Perhaps someone can give some mathmatical proof for the law of symmetry. I still don't have any myself; but it seems the raw odds of two stiff kings on one hand is rather high, don't you think?

[xx1943]

Perhaps someone can give some mathmatical proof for the law of symmetry. I still don't have any myself; but it seems the raw odds of two stiff kings on one hand is rather high, don't you think?

Hi

 

I can give you a mathematical proof, that the so called "law" of symmetrie is wrong, if the cards are randomly shuffled.

Shuffling maybe the point.

 

1) Shuffling by hand could be but in reality never is random.

 

2) "Random" dealt hands by PC cannot be mathematical random at all. PC's can only produce "pseudo-random-numbers"

 

 

Sincerly

 

 

Al

[hrothgar]

2) "Random" dealt hands by PC cannot be mathematical random at all. PC's can only produce "pseudo-random-numbers"

Pseudo-random number generation is considered insufficient for for serious cryptography. The "random" number generators implemented in most operating systems are more than sufficient for generating bridge deals.

[jikl]

There is a book that sort of covers this written by mathematicians. I am sorry to say I don't remember the name of it. It is something like "A Mathematical Treatise of Bridge", it was written about 30 years ago or so by I think either french or swiss authors. (I am not referring to the Roudinesco book on combinations about 10 years ago)

 

Sean

 

PS: It would definitely be out of print and would only be able to be picked up secondhand.

[Gerben47]

It's all pure superstition.

 

A mathematician

[Gerben47]

Let me make this more precise.

 

If you have an unbalanced hand pattern, say 6♠ 5♥ 1♦ 1♣ exactly, then it is more likely that your opponents also have an unbalanced hand pattern. This is because there are 24 minor suit cards missing, people tend to have a lot of them and have a shortness somewhere. So far the reasoning is okay.

 

Now the big mistake is made. Suppose I find partner with 2 ♠. Now the 5 remaining spades are divided as predicted by the 1-suit distribution we all know, regardless of previous observations on the unbalanced nature of the opponent's hands. So the chance of a 3-2 split is still the same 68% as always.

 

As for singleton Kings. I remember a deal where all 4 Kings were singleton. The reason you notice is that if a King is singleton people always say 'If only I had cashed the Ace' even though that would be a silly plan percentagewise, so people tend to notice those more. I might have seen a deal with all 9s singleton and not have noticed. The cards cannot tell a King from a 9, so the odds of a singleton 9 and King are equal. This should also be true for manual shuffling except if magicians are involved. I can imagine that there might be some obscure explanation for this which has to do that people cover an honor with an honor and so cards are connected in some way, I will do a simulation of hand-shuffled deals that keep track of different singletons. I have already used this program to show that hand shuffling causes fewer extreme distributions (as others have).

 

Just to uncover another myth: Computer based random generators can normally generate only 2 billion deals unless you have a special program like Big Deal, that actually uses a random seed larger than the number of possible deals. However if the shuffling mechanism is unbiased (and most are as it takes some effort to make a biased shuffling mechanism) statistics generated from such programs is valid until duplication sets in (after said 2 billion deals).

 

The REAL problem with the 2 billion deal limit is to avoid making the same set again and that someone who knows the algorithm can calculate the next hand from the current one.

[slothy]

Its rubbish....

 

the likelihood of opponents hand containing singletons is totally independent of the circumstance of you having a singleton...

 

the other hands may be (more) distributional by virtue of yours being so ( in the sense that there are more cards in the suit(s) that you are short in and less cards in the one(s) you are long in)

 

but the probabililty of them having singletons still abides by the same probabilities (with regards to the number of cards available in a suit to be divided between remaining hands)

 

 

of course if you got

 

AKQxxxxxxxx

x

-

x

 

naturally at least two hands have a singleton or void in the spade suit....:D)

but how the remaining 39 cards, and especially for this argument, 37 cards in the non-spade suits, are distrtibuted RANDOMLY in the other hands makes all card permutations EQUALLY LIKELY and thus follow the same principles as when we are talking about the frequency distributions of the suit-cards in 4 hands...only thing that has changed is the number of hands and the number of cards..

 

in other words...the probability of balanced hands is more likely than unbalanced hands

[Chamaco]

I thought that the Law of Symmetry worked: usually when one player yells at his/her pard, he/she gets yelled back ! B)

[slothy]

I thought that the Law of Symmetry worked: usually when one player yells at his/her pard, he/she gets yelled back ! B)

My dear Mauro,

 

Good principle...however if we are talking about 'probability' and 'frequency' WHY HAVE YOU written his/her he/she????

 

writing she and her is perfectly adequate (yet again talking statistically)

 

Your Local MCP

 

Slothy

[DrTodd13]

 

2) "Random" dealt hands by PC cannot be mathematical random at all. PC's can only produce "pseudo-random-numbers"

While that used to be the case, it is not necessarily the case anymore. There are now true hardware random number generators on many processors and it is just a question of whether your library is getting its random numbers from the hardware or doing it the old way. Anyway, I'll predict that soon the default will be truly random but that pseudo-random will be retained under different names because it is still useful as a debugging tool. You can trust me on this since I work for Intel. B)

 

Todd

[slothy]

You can trust me on this since I work for Intel. B)

 

Todd

Todd, you couldnt ship me a Pentium 4 motherboard on the QT could oyu?

 

PS Promise i wont grass