Talk:Principle of restricted choice

Clarity

I'm not sure that my description of the PRT is clear. Should I/someone else remove the combinaitons that don't matter?

Totally unclear.

Any suggestions to improve it then? Cambion 17:41, 5 April 2006 (UTC)

Jargon

This article is full of jargon that can't be understood just by referring the bridge glossary page. I have no idea what these terms mean; could someone in-the-know please clarify? Thanks for any help. --Doradus 19:05, 23 April 2006 (UTC)

• "an opponent unprovoked": "provoked" is not in the glossary.
  • Not jargon here; it just means the card was played without an apparent reason to (eg to force a higher one). This means that is was probably singleton or they hold another of equal rank.
• "AJT9x opposite xxxx": I don't know what this notation means, nor what "opposite" means.
  • One hand (eg dummy) has AJT9x and the hand oppsite (eg declarer) has xxxx. x means a small card who's value is not significant.
• "led to the Jack": the glossary entry on "lead" doesn't explain this phrase.
  • A card is lead from the hand opposite to the jack (in this case from declarer's hand towards dummy.
• "crush the Queen": no glossary entry for "crush".
  • Not jargon really; it just means that the queen is beaten by teh higher card.
• "lead towards the AT9x": what does it mean to "lead toward" something?
  • See above.

I've put in the answers above - can someone make the article clearer please? I'm used to all the jargon so maybe someone other than me should to it. Any thoughts on whether the above things should go in the glossary? Cambion 14:40, 25 April 2006 (UTC)

Ok, I have tried to do so. Not being a bridge player, I might have made the example incorrect, but I hope you see the sort of thing I'm looking for. --Doradus 17:51, 26 April 2006 (UTC)

No problem :-). As a non-bridge player, you might have chosen a wrong article to start with; many bridge players don't get the principle -- is it inavoidably difficult to explain to non-math geeks? Duja 23:30, 28 April 2006 (UTC)

The example is much clearer now. Thanks! --Doradus 16:28, 28 April 2006 (UTC)

List format

Is it just me or did it look better with a simpler list eg:

• abcde
• abcdef
• abc

rather than the spaced out thing that doesn't seem to line up horizontally?Cambion 12:47, 17 July 2006 (UTC)

The problem with simpler list is that doesn't line up vertically. I also see the slight misalignment horizontally. I'll give it a try with a straightforward table. Duja 15:25, 17 July 2006 (UTC)

Quack

I think we should try to avoid the term "quack" unless it's really awkward. We're not computers, so having a "declaration" of what the word means up in the article intro isn't sufficient to avoid confusion, as Ralian recently demonstrated. At least, the word "quack" itself should be a hyperlink to the appropriate definition; but my vote would be to reword the article without using "quack" at all. --Doradus 17:06, 31 July 2006 (UTC)

My apologies! I've been playing bridge for quite a while now and have amazingly never run into this -- rather hilarious -- terminology. I instantly grasped what it meant but thought it might have been either a typo or joke =P ralian 00:13, 2 August 2006 (UTC)

Ralian -- NP. My use of "who have played bridge" was not meant to refer to you. And Jeff Rubens, who appears to have invented the term quack, surely was being a little facetious at first, but the term turned out to be a valuable one. Xlmvp 00:29, 2 August 2006 (UTC)

I quite like 'quack' - It reminds me of quantum mechanics which this is related to. Heh - I always like the idea of a quantum queen which collapses into the wrong hand when you take a 2-way finesse.

I think that prior post is from Cambion. I agree: quack is conceptually useful and should be retained. However, I think that P3d0 is correct, that there should be a link to the contract bridge glossary and I'll make one. (As to quantum quacks -- I find the notion of one quack existing simultaneously in two different hands far too disconcerting. Am I supposed to go in search of Schrödinger's quack? Is that what happened to Billy Heisenberg?)

However, I completely disagree with P3d0's rewrite of the material at the beginning of the article, and I'm going to revert it. The changes that were made include errors of fact and diction, and are stylistically inferior (although the latter is a subjective judgment).

I disagree with the complaint about jargon. Were the article concerned with an elementary concept, there would be reason to go easy on the technical terminology: a neophyte could not be expected to understand, and its presence would be at least annoying. The Principle is not an elementary concept, however, but an advanced one, and the article cannot cater to all degrees of experience and knowledge. I can't be expected to write an article about Cox proportional hazards regression without mentioning relative risk, any more than a student in Statistics 101 could be expected to know what I was talking about.

Furthermore, the example is neither redundant nor "extraneous." The introduction needs a relatively quick -- in this case, three-sentence -- overview of the principle, whereas the body of the article requires a fuller explanation. (And BTW, the article could go much further than it does, covering cases that give even better odds, such as AKQ10 opposite 432). So, because people who have played bridge spent a fair amount of time crafting the introduction, I'll put it back the way it was. Xlmvp 21:54, 31 July 2006 (UTC)

The comment was mine - I messed up signing it somehow. One thing that should probably be noted is that PoRC has links with maths (Baysian stats) and the Monty Hall problem (which was a FA a while ago) bringing in people who are not bridge players. It might be a good idea to make this article more approachable for that reason. Cambion 12:46, 2 August 2006 (UTC)

Fundamentally, I think what it comes down to is that we're not writing a bridge text here, so it doesn't matter how necessary the jargon is: if it won't be understood, it doesn't belong; and if that means this article isn't appropriate for Wikipedia, then, well, I'm not sure what we would do. Fortunately I don't think that's the case here. This is primarily a mathematical concept -- the fact that it arises in bridge is almost secondary -- and I think we can achieve the required level of clarity if we keep polishing the article. I'll continue to offer my services as the bridge ignoramous and spot the parts that are incomprehensible if you folks will agree to keep reverting me when I botch things. I think we're on the right track; let's just keep on progressing toward an article that we're all satisfied with.

Xlmvp - thanks for reverting me. I think I got a little too bold. I'm intrigued by your AKQT and 432 case; can you add that to the article? --Doradus 19:40, 2 August 2006 (UTC)

Doradus -- I apologize for not having responded before now. I had this page on my watch list but I don't think I saw your query when you posted it. I just now came across it in the process of making some corrections at the end of the article.

As to AKQT opposite 432, that was careless, and again I apologize: the odds in favor of dropping the J on the third round are 51-49. The dramatic setup, one that the Principle really does bear on, is AKQ8 opposite 432. Suppose you play off the AK from North, and East follows with the 9 and then the 10. You come to hand and lead your last small card, and West follows low. Now the principle offers odds of not just 2:1 but close to 3:1. If East started out with JT9, he had six ways to play two of his minor honors, and he chose one of them from his extended quack. (Six ways: JT, TJ, J9, 9J, T9, 9T.) A priori, a 3-3 split occurs 35.5%, and there are 20 ways for that to occur, so specifically JT9 is 35.5% / 20, or 1.78%. Dividing that 1.78% by the one-sixth chance of selecting the 9, then the T, from JT9 is 1.78% / 6, or 0.3%.

In contrast, a 4-2 split is 48.45% a priori and there are 30 combinations, so 48.45 / 30 = 1.62% for the T9 doubleton. There were two ways to play those two cards, so 1.62% / 2 = 0.81%.

0.81% vs. 0.3% is slightly less than 3:1 (actually, 2.7:1).

Two questions: (1) Are you sure you want that in the main article? (2) Frank Loesser could never have woven "... It's a probable 2.7 to 1" into Guys and Dolls, so I just think of it as 3:1. Xlmvp 20:56, 25 September 2006 (UTC)

Play of a card from a sequence

Don’t most partnerships have an agreement as to what to play from a sequence, as opposed to playing at random which is what the article seems to suggest? For example, lead the K from KQx but play the Q if splitting honours? Roman V. Odaisky 14:49, 10 October 2007 (UTC)

That's not quite the same situation. If someone finesses into your KQ almost no partnerships would have an agreement on what to play. If for example you always played the Q at that point then this can be used by declarer. If he sees the K first round he knows it is 100% to finesse. (Interestingly if he sees the Q the probability remains 50% - the 'total probability' is conserved). People try always winning low then always 'falsecarding' and soon realise that the best thing to do is pick at random.

You do have a point though - there are situations where a person's cards are all equal _but he doesn't know it_ (i.e. his partner has the other card). This can then be used against him. Though I can't think of this applying to PRT it can apply to break probabilities.

eg

      AK8xx
 JTx          Q9x
      xx

Declarer plays the AK from dummy. On the K how many Easts will realise that the Q & 9 are equal and pick randomly? Therefore if the Q _is_ played on the 2nd round the odds of it being doubleton are increased (it could still be from QJx or East may be sharp enough) and so declarer might fall back on whatever other plan he had in other suits. If the queen is not seen then the chances of a 3-3 break are higher than what might have been expected (6 cards missing ignoring the 6-0 & 5-1 splits has a just over 40% chance of being 3-3 but in this case it is a bit higher. Not certain how much as I don't have the time to calculate it is there are many possibilities where E/W _will_ be able to tell - I'd say about 50%). Cambion 09:52, 11 October 2007 (UTC)

Could someone else give another example or clarify? It seems very interesting but I'm having trouble following. —Preceding unsigned comment added by 220.239.234.163 (talk) 03:46, 1 June 2008 (UTC)

I don't wonder that you're having trouble following the discussion. It's tricky stuff and often counterintuitive. Forty years ago a player named Sam Fry, a winner of the Vanderbilt, the Spingold and the Reisinger, among many other national titles, and a contributing editor to The Bridge World, wrote letters to that magazine disputing the Principle's validity. It is valid, of course, but the explanation almost has to be tailored to the way a particular person's mind works.

First, though, consider that the situation that Mr. Odaisky originally cited at the top of this section. Leading the top of a sequence is quite different from choosing which card to follow suit with. Your purpose in leading K from KQ, say, is to build up a trick and to inform your partner that you have the Q. But when you're following suit, your purpose in choosing the card to play is normally different: to avoid giving away information unnecessarily, while preserving your trick-taking potential in the suit. So the situations are different, and partnerships normally do have agreements as to leads and signals (e.g. upside down signals), but normally not in situations where declarer is playing the suit.

Roughly 30 years ago, Frank Vine wrote a humorous article for The Bridge World titled How I Abolished the Principle of Restricted Choice. The first lead came from South, the K bringing down the Q from East:

      A109xx
            
       Kxxx

Per restricted choice, South was preparing to finesse on the second round of the suit when West alerted: "We always play Q from QJ tight." This announcement blew South's mind and made for a very funny followup. But the situation can be analyzed. Whether there's an actual agreement to that effect (and such an agreement would be deranged) or East just always chooses the same card, declarer should play for the drop next.

That's because carding at random from QJ makes it 12.44% to 6.78% in favor of the (losing) finesse: 6.22% for the singleton J, 6.22% for the singleton Q, 6.78% for specifically QJ in East. But if (whether by agreement or through laziness) East always plays the same card from QJ tight, he will play (say) the J from QJ 6.78% of the time and the singleton J 6.22% of the time (note that South has a sure thing when East plays the Q). So when South believes that East won't randomize, he should play for the drop.

Actually, the analysis should go farther. If East randomizes only one time in 15, South should still finesse, because in that case the odds on the doubleton are still lower than the odds on the singleton quack. (But in this particular situation, he must randomize at least that often.)

It can get hairier when full-hand, single-dummy situations arise, involving tactical and strategic matters in other suits. Suppose that E-W together have KQJ6, and S leads small toward dummy's Axx. S must assume that the KQJ are split somehow and not in the same hand. West needs to take the trick if possible, because if East wins he will be endplayed in another suit. Now what is normally the defenders' ally, random selection from equals, becomes the worst thing they could do. It's the reverse of what Cambion noted in his layout: in this case, cards that appear to be equals aren't.

Suppose W holds KJ6 and E holds Q. West must play the K to keep S from ducking to East's Q.

But W might also play the K from K6, E holding QJ, again to hold the lead. W, then, will always play the K from KJ6 or K6. If E then randomly selects from his QJ, S will always see the Q when it is singleton but only half the time when it is doubleton QJ, so it's 2:1 that the played Q is blank. If E always plays Q from QJ, declarer is back to even odds.

When East does play the J, declarer does not have a sure thing, because then W won't have played the K. Suppose that W has the Q6 and E has the KJ. W plays the Q, trying to hold the lead, and E plays the J. Declarer now has a pure guess as to W holding Q6 or KQ6. Notice that if W chose at random between K and Q when he holds KQ6, S will see the Q only half the time, vs. all the time when W holds Q6. Again, to give S a pure guess, W must always play Q from KQ, and not select randomly from equals.

And if the K and the J appear on the same trick, all S knows is that either E or W has mistakenly selected at random. If S knows his opponents, he may be able to infer who it was and play accordingly.

TurnerHodges (talk) 00:57, 25 August 2008 (UTC)

Interesting stuff. :-) Perhaps you could put it into the article somehow? I reckon we could put some more advanced bits in for people that get the basics - eg PRC with _small_ cards. Something like J765 opposite AQ98. (Finesse the Q losing to the K. Now what should you do to protect yourself from the 4-1 break? PRC says cash the ace as KTxx x is 3 times more likely than K Txxx.) Wanna do that too Turner? Cambion (talk) 10:08, 26 August 2008 (UTC)

I think the percentages in the "a priori" section are wrong. There are 16 cases, so the relevant probabilities are 8/16 = 50.0%, 6/16 = 37.5%, and 2/16 = 12.5%.

71.191.38.150 (talk) 18:36, 6 December 2009 (UTC)James

No, that's a pretty serious oversimplification. See Wikipedia's Vacant Places article for a good and pertinent discussion. TurnerHodges (talk) 02:51, 7 December 2009 (UTC)

Jim323436 (talk) 23:39, 9 December 2009 (UTC)

This is an important bridge topic and very interesting to study. Some suggestions for improvment:

The first example "declarer leads small toward dummy’s ♠AJ10" and left hand opponent plays K or Q, is not a true example of restricted choice. A good bridge player will ALWAYS play the K or Q in this position, with any holding including the KQ. This is to prevent the declarer from scoiring a free trick with the Jack. This is called "splitting your honours".

Also, the American Contract Bridge League website has a link to a glossary that defines "quack" as a queen or a jack. See http://www.bridgeworld.com/default.asp?d=bridge_glossary&f=glossq.html

This article should not invent a new meaning for Quack.

Well, I disagree that the article invents a new meaning for quack. Although Jeff Rubens coined the term as a portmanteau for queen and jack (and that it is a contraction of those terms is mentioned in the article), over the 30+ years that the term has been in use it has been extended, through that usage, to refer to any two cards that are considered equals in the context of the Principle.

You should probably give some more thought to the Principle (and most people need to give it considerable thought before they grasp it). The statements, first, that the KQ hand you cite is not a true example of restricted choice, and second, that the K or Q would be played, are mutually contradictory.

As to always splitting honors, all I can say is that I hope to play against you someday at rubber bridge. And Jim -- bring money. TurnerHodges (talk) 21:37, 11 December 2009 (UTC)

withdrawn comment

Rewrite

After a major rewrite today, this article includes two hidden comments that may be useful or interesting to some who do not examine the code; who do not read in edit mode.

Uniform randomization may not be best in theory. Where best in theory it may be useless in practice, both because repeated play against the same opponents is limited and because humans cannot recognize or remember non-randomness very well; and also because randomization interferes with signaling between partners. Any randomization is difficult to implement and the rules of bridge forbid use of external aids such as the "seconds" displayed on a wristwatch. (on the last see [1])

(The principle of restricted choice pertains to cards of different suits and hence to the choice of suits but it is much more difficult to recognize the relevant "equivalent" alternatives and the bridge literature is poorly developed. For one example see Martin (1989).) At Talk:Monty Hall problem, editor Secondfoxbat recently challenged Martin's article harshly. Evidently the application to other non-standard situations is challenging to understand, not to mention explain.

--P64 (talk) 03:54, 12 March 2010 (UTC)

There is an excellent reference that explains restricted choice for 2-card, 3-card, 2-suit and other scenarios. In their book "Bridge Odds for Practical Players", Kelsey & Glauert (1980) devote chapters 8 & 9 to "Freedom of Choice" (they give a humorous account of why they don't like the term "Restricted Choice" --- I don't like the term either for a different reason: restricted choice trys to explain the problem confronting declarer in terms of defender's choices or lack of choices. Every beginning probability text on the planet describes the basic conditional probability problem facing the problem solver (declarer) from the problem solver's point of view, but bridge players perversely have to "do things their own way", even if it makes the explaination almost incomprehensible.)

In contrast, Martin (1989) is an extraordinarily poor reference for almost everything. The brief reference to restricted choice is made in passing, with no attempt to explain.

My vote is for replacing Martin(1989) with Kelsey & Glauert (1980). Secondfoxbat (talk) 05:12, 13 March 2010 (UTC)

I had not seen the March 2010 rewrite of this article before today. I must say that it's pointless and ill-written, adds nothing to what had been the existing version, and removes useful material. It's almost as though someone wrote it in an attempt to organize his own understanding of the topic. Too bad. TurnerHodges (talk) 19:29, 17 January 2011 (UTC)

It does look a little cluttered. I'm pretty busy these days and have let my bridge slip enormously so one of you guys will have to tidy it up. I do agree that 'Bridge Odds for Practical Players' is a great book. :-) Cambion (talk) 19:58, 17 January 2011 (UTC)

Example

Does the example go against the rules of contract bridge? If East wins the first set then East would lead for the second set. — Preceding unsigned comment added by 220.255.1.52 (talk) 00:27, 13 January 2014 (UTC)

It does say "Later, South..." but may deserve more emphasis. Will copy edit. Newwhist (talk) 11:19, 13 January 2014 (UTC)

 Done

Odds in "Better Calculation of Odds" section

I do not understand this section. What is the derivation of the odds shown in the table? How was it determined that the lies are not each equally likely? Intuitively, it seems they should be, given a random distribution of cards. 12.31.111.76 (talk) 04:23, 13 May 2017 (UTC)