[sceptic]

if the small card is the 9, then east does not have 4 cards or he would play the 7 as he can see the 810J, so the splits you can have are 2/2 or 3/1, if west has AQ or AQx or AQxx you are stuffed anyway

I think to make 5 tricks you need to finese the jack, beacuse if east has 79Q you have no second shot at the finese also if east has xQA it works

[Gerben42]

I would just like to say I enjoyed this suit combination.

[benlessard]

Quote

You play the A and RHO pitch the J

This is the wrong example. 2nd round either the K or T is played, you don't really have any guessing to do. The one you are looking for is:

I just didnt put the high spot in LHO hand but its almost the same example as the 1 you show.

---

After the J from (J8) or (JT) or (J9) or (KJ) .Declarer will play have a guess between playing low to the Q or ducking all around. I think the correct solution is to play low to the Q unless RHO rarely falsecard.



But i agree for the rest of Stephen post.

[Stephen Tu]

Quote

It's a little embarasing for me as a mathematician, with specialization in probability theory and operational analysis, to admit this, but I feel rather helpless when confronted with this kind of problems. The complexity just makes me dizzy,

You know, it's really not that complex a problem, if looking only at the question of whether to play K if RHO plays the 9, ignoring the question of what to do if RHO plays the Q (which is more complex IMO).

If the 9 shows, there are only 2 relevant possibilities where you can pick up the suit, A9 and Q9 with RHO, because with all other combos you can see that the defender can always force the loss of 2 tricks. These are equal only if RHO plays 9 from Q9 100% of the time as he would with A9. But he won't (since covering can generate a 2nd trick vs. declarers who don't know the optimal play and might take a 1st rd hook, and can't ever hurt him unless he does it too often), so rising with the K is better, Q.E.D.

All you really have to do is convince yourself that it's stupid to play anything but the 9 from A9 (if pop ace, declarer can't go wrong), and that RHO will want to play Q from Q9 some non-zero amount.

[fred]

It would be nice if one of the math stars out there would say something about the restricted choice issue.

Besides Helene, I seem to recall that both Cherdano and Hannie are graduate students in math. I have no idea about Stephen's credentials, but at least he seems to take himself seriously - for all I know he has a right to.

It sounds to me like a lot of people are confused about this in the sense that I believe that this problem has nothing to do with what bridge players normally mean when they refer to "restricted choice". This has managed to confuse me too - I thought I knew what restricted choice meant and I thought it was a concept that could be defined/explained using mathematics (Bayes theorem if I recall correctly).

But it is not like I think I really know what I am talking about. Maybe one of you who does seem to know what you are talking about can enlighten the rest of us

If so please try to keep it simple!

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

[kenrexford]

The issue with the refusal to accept this as a restricted choice problem is that folks want to define "equal" with reference to some arbitrary standard.

A Queen and a Jack are "equal" in the sense that, when together, they both are less than all outstanding honors above them and both are greater than all outstanding cards below them. They are not truly equal, they are simply equally positioned for the person holding them. If one person did not hold both, they would not be equal.

In this situation, the Queen and 9 are "equal" in the sense that the play of either card at the critical moment will yeild what appears to be a 50-50 guess for Declarer. If Declarer guesses wrong in either situation, the other will take a trick. If the Declarer guesses right, neither will take a trick. So, each has equal trick-taking power.

The other problem is that either card creates its own artificial image of alternative layouts, and those layouts are not the same. Playing the 9 creates an artificial image of having A9, whereas playing the Q creates an artificial image of just the Queen.

So, you end up with three possibilities, when RHO plays the [Q/9]:

1. [Q/9][Q/9]
2. A9
3. Q

Two of three times, the [Q/9] is resolved as one or the other. So, restricted choice applies.

This sort of looks like a cat-in-the-box situation. In a manner of speaking, the three options are:

1. [Q/9][Q/9]
2. A[Q/9]
3. [Q/9]

However, 2 and 3 will manifest the nature of the [Q/9], whereas 1 will not. That does not change the odds a priori.

[helene_t]

Restricted choice applies whenever one assumes that a defender, if he held two equivalent cards, would chose either with 50% probability. One could generalize this to cases where the probabilities are something else, or one could generalize it to three equivalent cards with each 33.3% probability etc.

This is indeed a special case of Bayes' theorem.

I don't think it's correct to apply restricted choice here. Even if 9 and 7 are equivalent DD and RHO knows that, we cannot a priori assume that RHO will chose either with 50% probability, because he knows that we do not know that 9 and 7 are equivalent. He knows that we will make different inference from 9 and 7 and he may exploit that.

(Or substitute 9+Q or whatever for 9+7).

Ultimatively, Bayes' theorem should be applied when responding to any mixed strategy, even if the parameters are not known apriori but change during itteration while one is looking for the Nash equilibrium. I don't think the term "restricted choice" is used that broadly, but I might be wrong.

[hotShot]

We don't know much about defenders hands, but what do the defenders know about our cards?
Does defender know that Q and 9 are equivalent?
He won't know that his partner holds the Ace. His partner could hold the single K or only small cards.

I don't think that this situation is equivalent to holding touching honors in your own hand.

But knowing that he would never play A from A9 and sometimes Q from Q9 makes playing the K a little more attractive.

[fred]

hotShot, on Oct 19 2007, 03:20 PM, said:

We don't know much about defenders hands, but what do the defenders know about our cards?
Does defender know that Q and 9 are equivalent?
He won't know that his partner holds the Ace. His partner could hold the single K or only small cards.

I don't think that this situation is equivalent to holding touching honors in your own hand.

But knowing that he would never play A from A9 and sometimes Q from Q9 makes playing the K a little more attractive.

There is a big difference between real life problems and problems like the one that was presented here.

Many suit combination problems are "solvable" only if you assume that the defenders can see your cards and never make a mistake.

Of course this is not realistic, but it makes it possible to solve these problems. If you do not make this assumption you have to make other (subjective) assumptions like how often a defender who is in the dark will think you have what you actually have, how often he will think you have various other things...

Obviously such things vary greatly from defender to defender and from hand to hand.

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

[ralph23]

cherdano, on Oct 19 2007, 03:57 AM, said:

fred, on Oct 18 2007, 09:55 PM, said:

Sorry guys. I have had enough of this.

Me too
Thanks for a very funny post and a suit combination that reminds me why I play bridge...

Thanks Fred, I thought it was a very interesting combination also. I didn't mean to start a firestorm of controversy. But --Remember, no good deed goes unpunished. C'est la vie.

It is certainly not a "textbook" case of RC -- i.e. one that you would show to a beginner to explain the concept of RC. There, I would use a singleton Jack or Queen, and compare it to a doubleton QJ. In that textbook case, the play of the singleton J is "restricted" by law; any other play is a revoke.

In the A9 case, the choice is "restricted" because the defender knows how to play. He could legally play the Ace; but he won't. His choice is "restricted" it seems as much as the defender holding the singleton Jack in the paradigm case.

Likewise, the Q9 are certainly not "equal" in the sense of QJ's being equal. But the play of either one could be "right"!

Playing the 9 from Q9 may persuade South to rise with the King, and lose to the Ace. This strategy will, in our case, defeat the "wise" declarer.

Playing the Queen may persuade South to finesse the 8 on the next round of the suit, having induced the false belief that East originally held a stiff Queen, and West started with A97. I must admit, the play of the Queen from Q9 would certainly fool me!!

I don't know but it seems like at least an analogue to RC, if not an actual example of the same mathematical principle that RC is based upon. Whether one CALLS it "RC" or not -- well, that is a matter of semantics, I think.

Whether the same logical or mathematical principle that underlies RC, also underlies this situation, is IMHO an interesting question -- and frankly one that I have never seen before in the literature.

Thanks again for a very thought-provoking problem.

This post has been edited by ralph23: 2007-October-19, 10:31

[ralph23]

Stephen Tu, on Oct 19 2007, 09:13 AM, said:

All you really have to do is convince yourself that . . . . RHO will want to play Q from Q9 some non-zero amount.

That really sums it up for me. If all defenders always play 9 from Q9, 100% of the time, then (and only then) ex hypothesi A9 and Q9 are equivalent. Since all defenders don't play that way, 9 is more likely to be from A9 than Q9, because the Q9 defender had a "choice" -- he was not "restricted" by law or by simple common sense -- of plays.

Whether it's an apt opportunity to apply the nomenclature "Restricted Choice" to this or not, I don't know. It seems to exemplify the same principle as does RC to me, that's all.

This post has been edited by ralph23: 2007-October-19, 10:32

[ralph23]

benlessard, on Oct 19 2007, 01:17 AM, said:

So the fact that with Q9 the 9 and the Q arent played with the same frequency doesnt say its isnt a RC.

This seems exactly right. Is it stated somewhere in the definition of "Restricted Choice" (whoever the hell defines these things!!) that it must be exactly a 50-50 chance that defender will discard either Q (50%) or J (50%) from QJ?

All that seems to matter (to paraphrase Stephen) is that it is not 100-0, i.e. that one term is non-zero.

[whereagles]

fred, on Oct 19 2007, 03:41 PM, said:

Many suit combination problems are "solvable" only if you assume that the defenders can see your cards and never make a mistake.

Which is why I look at their faces instead of the book

[Stephen Tu]

Quote

It would be nice if one of the math stars out there would say something about the restricted choice issue.

Whether to call it "restricted choice" IMO is a bridge terminology semantics issue, not a math question, since RC only appears as a term in bridge articles AFAIK. This problem certainly falls under the general category where you have to apply Bayes theorem so it is related subset if not the same subset.

In any case, I think it should be clear that the crux of the specific problem of what to play on the 9 is that defender has a choice of plays from Q9 and doesn't really have much to do with "picking up stiff Q" as your original argument stated. A declarer could choose a line of always picking up the stiff Q, yet still ducking if the 9 appeared. This would just fail more & more often vs. playing the K as the defender increased the frequency of choosing to cover with the Q from Q9, thus decreasing the probability that the 9 represented a holding of Q9 instead of A9.

Quote

Besides Helene, I seem to recall that both Cherdano and Hannie are graduate students in math. I have no idea about Stephen's credentials

I don't see what credentials should have anything to do with it. To me, for a real mathematician, math/logic arguments should stand on their own intrinsic merit, not what credentials the person holds. Credential evaluation is only a (poor) substitute for evaluating the argument itself if you have insufficient knowledge/training to do so.

I personally put only a little faith in credentials since I have both met college dropouts who are simply brilliant, & also people with graduate degrees who are mostly incompetent. I will give people with the paper credentials the presumption of competence at first, but once they start their discourse their arguments must make sense to me.

In any case, my degree is in computer science not math so perhaps that disqualifies me in your view, but to me this is not an advanced math problem, and as someone who started taking university math at 13 I like to think I am at least better than most. If one of the math majors wants to start a topic on topology or something like that I would keep my yap shut as I know nothing, but this was a simple problem.

[fred]

Stephen - let's just agree to disagree!

The last word is all yours...

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

[kenrexford]

Restricted options?

[ralph23]

kenrexford, on Oct 19 2007, 04:16 PM, said:

Restricted options?

Restricted strawberry shortcake ????

[djehuti]

Wow grosvenor: someone to play the 9 with Q9x

[ceeb]

Stephen Tu, on Oct 19 2007, 02:40 PM, said:

Quote

It would be nice if one of the math stars out there would say something about the restricted choice issue.

Whether to call it "restricted choice" IMO is a bridge terminology semantics issue, not a math question, since RC only appears as a term in bridge articles AFAIK.

In one view "restricted choice" is a single term and as such it's meaning is inferred from the usage as a phrase with no attempt to interpret the individual words. The classical examples involve defender's play from touching cards. Since that's the overwhelming usage, that's the meaning. There are even some people who further limit usage of RC to cases where you really should finesse. Thus, if RHO drops the Q or J but LHO has such a long side suit that a finesse into RHO is nonetheless not percentage, they would say "It's NOT a restricted choice situation." Perhaps they would say the same even if the percentage play in the suit is to finesse but the sensible play overall is not to.

Another view -- more authentic in my opinion but it really comes down to taste -- is to interpret "restricted choice" as a phrase in which the two words retain their individual significance. With respect to the present problem a defender with A9 has only one sensible choice, whereas the defender with Q9 has more latitude. The fact that the hypothetical A9 defender has a more restricted choice of plays is -- or may be -- a relevant consideration in deciding declarer's strategy.

Furthermore, the pattern of mathematical reasoning for analyzing the A9/Q9 and the QorJ/QJ situations are the same.

Incidentally I'm a mathematician (http://dna-view.com/math.htm), which in this case is perhaps more a disclaimer than a credential. No doubt it colors my preference of definition.

Charles Brenner

[kenrexford]

You are declaring a grand slam. You have AJ10 in a side suit, opposite Kxx in hand. The whole slam turns on the decision in this suit.

This is a bad slam, as it turns out, but you were lucky to find out on the opening lead of another suit that the other suit behaved. You held xxx on dummy and AQJ in hand. That King was well-placed.

So, you assume restricted choice analysis.

LHO could have held Kxx(x) in the one suit and Qxx(x) in the other suit. He would have made another lead.

LHO could have held xxx in both. In that event, he might have selected either suit.

LHO would have held an honor in one but not in the other. In that event, he would have selected the no-honor suit.

So, Hxxx/xxx, xxx/Hxx, or xxx/xxx.

Two of the three have "Hxx," so you place the missing Queen with LHO. Restricted Choice.

However, Kxx and Qxx, especially in different suits, are no "equals" from one way of analyzing "equals." From a relevant perspective, however, they are. The relevant perspective is options.

So, this was a Restricted Choice problem.

The really interesting "rest of the story" is that this situation illustrates a very strange type of restricted choice analysis. I wonder if there are others that we have not thought of, where someone has one restrained situation, a completely different and unrelated constrained situation, and an option that somehow attaches itself to each.