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Restricted Choice Fallacies

#1 User is offline   Spisu 

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Posted 2016-July-14, 05:43

The "rule of restricted choice" claims that play of one equal by an opponent decreases the chances the other equal is in that same hand.

But 2 equals (say K-Q) divide between 2 opponents hands in only 4 ways, West K-Q, K, Q, zip, and East the same in matching hands. Each of the 4 is a 25% possibility. So 50% of cases will see both honors (or any equals) in the same hand and being led or otherwise played from half of all hands.

So half of all first plays of an equal come from combined honors.

So restricted choice is a fallacy. Any questions?

Edit to add: I'm surprised to see comments below talking about singletons and cards already played. Perhaps I overestimated the concept of "expert". This post very simply shows that 2 equals (regardless of any accompanying cards) must eventually be played, and when one is played, it will come 50% from combined honors and 50% from divided honors. And that disputes restricted choice claims. If that's not clear, at least I tried.

Edit to add: I thought it would also be obvious that a "first play" of a suit does not "follow" or otherwise come subsequent to that first play of a suit but, for the bewildered, that is indisputable fact.
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#2 User is offline   1eyedjack 

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Posted 2016-July-14, 05:50

Nope. And no, no questions.
Psych (pron. saik): A gross and deliberate misstatement of honour strength and/or suit length. Expressly permitted under Law 73E but forbidden contrary to that law by Acol club tourneys.

Psyche (pron. sahy-kee): The human soul, spirit or mind (derived, personification thereof, beloved of Eros, Greek myth).
Masterminding (pron. mPosted ImagesPosted ImagetPosted Imager-mPosted ImagendPosted Imageing) tr. v. - Any bid made by bridge player with which partner disagrees.

"Gentlemen, when the barrage lifts." 9th battalion, King's own Yorkshire light infantry,
2000 years earlier: "morituri te salutant"

"I will be with you, whatever". Blair to Bush, precursor to invasion of Iraq
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#3 User is offline   1eyedjack 

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Posted 2016-July-14, 05:55

Leaving aside the small mathematical error as trivial to the basic point (being that the four scenarios are not equally likely, albeit close), you need to exclude "zip" from the population as, having already followed with an honour on the first round, he cannot have played that honour from an a priori holding of "zip". You should only be comparing the likelihood of "HH" against the likelihood of "H" singleton, the latter of which is (about) twice as likely because as you have pointed out there are two possible singletons to be dealt, each of which is (approximately) as likely as HH doubleton.

"Expert" bridge subforum? Seriously?
Psych (pron. saik): A gross and deliberate misstatement of honour strength and/or suit length. Expressly permitted under Law 73E but forbidden contrary to that law by Acol club tourneys.

Psyche (pron. sahy-kee): The human soul, spirit or mind (derived, personification thereof, beloved of Eros, Greek myth).
Masterminding (pron. mPosted ImagesPosted ImagetPosted Imager-mPosted ImagendPosted Imageing) tr. v. - Any bid made by bridge player with which partner disagrees.

"Gentlemen, when the barrage lifts." 9th battalion, King's own Yorkshire light infantry,
2000 years earlier: "morituri te salutant"

"I will be with you, whatever". Blair to Bush, precursor to invasion of Iraq
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#4 User is offline   eagles123 

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Posted 2016-July-14, 06:01

great to see we have an expert poster here at last.
"definitely that's what I like to play when I'm playing standard - I want to be able to bid diamonds because bidding good suits is important in bridge" - Meckstroth's opinion on weak 2 diamond
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#5 User is offline   Fluffy 

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Posted 2016-July-14, 06:34

Mind blown!, why have you been so silent past 7 years? we could had improved our bridge so much more if you contributed more.
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#6 User is offline   billw55 

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Posted 2016-July-14, 07:02

View Post1eyedjack, on 2016-July-14, 05:55, said:

you need to exclude "zip" from the population as, having already followed with an honour on the first round, he cannot have played that honour from an a priori holding of "zip".

Oddly, he stated this quite clearly himself, in the other recent thread on restricted choice.

I suspect he is trolling, and the forum choice is part of the joke.


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#7 User is offline   Phil 

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Posted 2016-July-14, 07:42

View PostSpisu, on 2016-July-14, 05:43, said:

The "rule of restricted choice" claims that play of one equal by an opponent decreases the chances the other equal is in that same hand.

But 2 equals (say K-Q) divide between 2 opponents hands in only 4 ways, West K-Q, K, Q, zip, and East the same in matching hands. Each of the 4 is a 25% possibility. So 50% of cases will see both honors (or any equals) in the same hand and being led or otherwise played from half of all hands.

So half of all first plays of an equal come from combined honors.

So restricted choice is a fallacy. Any questions?


PhilG007 welcome back..
Winner - BBO Challenge bracket #6 - February, 2017.
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#8 User is offline   Spisu 

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Posted 2016-July-14, 08:45

View Post1eyedjack, on 2016-July-14, 05:55, said:

Leaving aside the small mathematical error as trivial to the basic point (being that the four scenarios are not equally likely, albeit close), you need to exclude "zip" from the population as, having already followed with an honour on the first round, he cannot have played that honour from an a priori holding of "zip". You should only be comparing the likelihood of "HH" against the likelihood of "H" singleton, the latter of which is (about) twice as likely because as you have pointed out there are two possible singletons to be dealt, each of which is (approximately) as likely as HH doubleton.

"Expert" bridge subforum? Seriously?

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#9 User is offline   Spisu 

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Posted 2016-July-14, 09:02

Seriously? You cannot recognize 4 a priori possible holdings showing how 2 cards divide between 2 hands? There is no other way two cards divide.

Did you think the King could divide by mitosis and have 2 in one hand and a Queen or 2 in the other?

Get this please: Two cards divided between 2 hands can only be 2 in either or 1 in each, in 2 ways. That is 4 possibilities

Funny that you show up insulting but utterly clueless.
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#10 User is offline   1eyedjack 

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Posted 2016-July-14, 09:40

You cannot recognise that the odds change as the play of the hand progresses. The 4 holdings are indeed (approximately) equally likely before any cards are played (assuming that nothing is revealed by the bidding).

But after a round of the suit has been played, some of those possibilities are eliminated, but the remaining holdings that have not been eliminated retain their proportionate likelihood relative to each other.

So yes, the a priori odds are not far off what you quote. But decision time is not a priori.

Get this please: Restricted choice is not some random old wives tale dreamt up by clueless individuals. Highly qualified mathematicians have proven the theory, which theory has also been borne out in practice by countless expert and world class players who unanimously abide by the principle and who would, by now, have reneged on it if there was the slightest evidence that it was flawed.

You stand alone, unique in challenging a theory that is so simple to grasp that had your conclusions held water it would have been blindingly obvious a hundred years ago when the principle became settled accepted doctrine.

Forgive me, but I do not feel threatened by your assessment that I am clueless, presumably along with the hundreds of thousands of players of similar persuasion.

Anyway, if you fancy a bit of a read, this is a good starting point:

http://tinyurl.com/gunwte3
Psych (pron. saik): A gross and deliberate misstatement of honour strength and/or suit length. Expressly permitted under Law 73E but forbidden contrary to that law by Acol club tourneys.

Psyche (pron. sahy-kee): The human soul, spirit or mind (derived, personification thereof, beloved of Eros, Greek myth).
Masterminding (pron. mPosted ImagesPosted ImagetPosted Imager-mPosted ImagendPosted Imageing) tr. v. - Any bid made by bridge player with which partner disagrees.

"Gentlemen, when the barrage lifts." 9th battalion, King's own Yorkshire light infantry,
2000 years earlier: "morituri te salutant"

"I will be with you, whatever". Blair to Bush, precursor to invasion of Iraq
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#11 User is offline   Jinksy 

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Posted 2016-July-14, 10:30

Also helps to consult a Monty Hall simulator: http://www.stayorswitch.com/
The "4 is a transfer to 4" award goes to Jinksy - PhilKing
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#12 User is offline   nige1 

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Posted 2016-July-14, 10:31

View PostSpisu, on 2016-July-14, 05:43, said:

The "rule of restricted choice" claims that play of one equal by an opponent decreases the chances the other equal is in that same hand.But 2 equals (say K-Q) divide between 2 opponents hands in only 4 ways, West K-Q, K, Q, zip, and East the same in matching hands. Each of the 4 is a 25% possibility. So 50% of cases will see both honors (or any equals) in the same hand and being led or otherwise played from half of all hands.So half of all first plays of an equal come from combined honors.So restricted choice is a fallacy. Any questions?Edit to add: I'm surprised to see comments below talking about singletons and cards already played. Perhaps I overestimated the concept of "expert". This post very simply shows that 2 equals (regardless of any accompanying cards) must eventually be played, and when one is played, it will come 50% from combined honors and 50% from divided honors. And that disputes restricted choice claims. If that's not clear, at least I tried.
An intelligent player at Reading Bridge Club claimed that the rule of restricted choice was bunkum. We offered to set up a typical matrix, then shuffle the remaining cards and back our respective judgements at £10 per deal. After some homework, our friend declined our challenge :)
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#13 User is offline   shyams 

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Posted 2016-July-14, 10:39

View PostSpisu, on 2016-July-14, 05:43, said:

Edit to add: I'm surprised to see comments below talking about singletons and cards already played. Perhaps I overestimated the concept of "expert". This post very simply shows that 2 equals (regardless of any accompanying cards) must eventually be played, and when one is played, it will come 50% from combined honors and 50% from divided honors. And that disputes restricted choice claims. If that's not clear, at least I tried.

Two puzzles for spisu (and spisu alone) to answer:

1. You run into a familiar person one day. The only think you know about this person is that he has two children (but you have no idea how many of them are boys vs. girls).
....So this person says "Hello" etc, and then points to the child walking with him saying "This is my son".
....What is the probability that his other child is also a boy?
Spoiler


2. If #1 was hard, here is an easier one. Why is cow's poop usually in the form of a "patty", goat's poop usually tiny spheres, and human poop usually somewhat cylindrical?
Spoiler

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#14 User is offline   SteveMoe 

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Posted 2016-July-14, 13:31

View Post1eyedjack, on 2016-July-14, 05:50, said:

Nope. And no, no questions.

Methinks "Nope" is an UNDERBID!!
Be the partner you want to play with.
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#15 User is offline   Stephen Tu 

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Posted 2016-July-14, 13:42

Spisu:
Say you have akt98 opposite xxxx in dummy. You bang down the ace and an honor falls on the left. Do you play for the drop or the finesse? This is one of the basic restricted choice combinations.

1. Do you agree that out of all possible original holdings, LHO will be dealt QJ tight 6.78% of the time, the stiff Q 6.22% of the time, and the stiff J 6.22% of the time?

2. If you agree with 1, does it not make sense that playing the drop works 6.78% of the time, compared to 12.44% of the time for the finesse? Or basically 64.7% advantage to finesse, close to but not quite 2:1, counting only deals where an honor falls on the left?

If you do not agree with these statements, please explain why.

3. Do you agree that holding the stiff J, LHO will play the J 100% of the time from that holding?

4. Do you agree that holding the QJ tight, most LHO will play the J much less than 100% of the time from that holding?

Non-restricted choice (fallacious) reasoning:
LHO dropped the J. He either had QJ or J tight. The chances of these are about the same. Actually QJ slightly more common. So play the drop for a slight edge.

Restricted choice reasoning:
Wait a minute, from the stiff J he always has to play the J. From the QJ he might have played the Q half the time. So it's actually more likely that he had the stiff J and was forced to play it, than that he BOTH was dealt the QJ AND randomly picked the J to play. Finesse for a big edge.
Or simply go by the original deals, stiff Q + stiff J (finesse line) is almost twice as common as QJ tight (drop line).
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#16 User is offline   jogs 

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Posted 2016-July-14, 15:49

View PostStephen Tu, on 2016-July-14, 13:42, said:

Spisu:
Say you have akt98 opposite xxxx in dummy. You bang down the ace and an honor falls on the left. Do you play for the drop or the finesse? This is one of the basic restricted choice combinations.

1. Do you agree that out of all possible original holdings, LHO will be dealt QJ tight 6.78% of the time, the stiff Q 6.22% of the time, and the stiff J 6.22% of the time?

2. If you agree with 1, does it not make sense that playing the drop works 6.78% of the time, compared to 12.44% of the time for the finesse? Or basically 64.7% advantage to finesse, close to but not quite 2:1, counting only deals where an honor falls on the left?

If you do not agree with these statements, please explain why.

3. Do you agree that holding the stiff J, LHO will play the J 100% of the time from that holding?

4. Do you agree that holding the QJ tight, most LHO will play the J much less than 100% of the time from that holding?

Non-restricted choice (fallacious) reasoning:
LHO dropped the J. He either had QJ or J tight. The chances of these are about the same. Actually QJ slightly more common. So play the drop for a slight edge.

Restricted choice reasoning:
Wait a minute, from the stiff J he always has to play the J. From the QJ he might have played the Q half the time. So it's actually more likely that he had the stiff J and was forced to play it, than that he BOTH was dealt the QJ AND randomly picked the J to play. Finesse for a big edge.
Or simply go by the original deals, stiff Q + stiff J (finesse line) is almost twice as common as QJ tight (drop line).

View PostSpisu, on 2016-July-14, 05:43, said:

The "rule of restricted choice" claims that play of one equal by an opponent decreases the chances the other equal is in that same hand.

But 2 equals (say K-Q) divide between 2 opponents hands in only 4 ways, West K-Q, K, Q, zip, and East the same in matching hands. Each of the 4 is a 25% possibility. So 50% of cases will see both honors (or any equals) in the same hand and being led or otherwise played from half of all hands.

Stephen, Spisu doesn't know squat about statistics. Spisu thinks each of the four outcomes are equally likely.
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#17 User is offline   1eyedjack 

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Posted 2016-July-14, 20:10

View Postjogs, on 2016-July-14, 15:49, said:

Stephen, Spisu doesn't know squat about statistics. Spisu thinks each of the four outcomes are equally likely.

Your point is valid but a distracting irrelevance. BUT FOR restricted choice an equal likelihood is a sufficiently close approximation that, had the principle to which he objects been flawed, his conclusions would have been close to reality. The point is that the validity of the principle has so significant an impact that such approximations end up utterly irrelevant.
Psych (pron. saik): A gross and deliberate misstatement of honour strength and/or suit length. Expressly permitted under Law 73E but forbidden contrary to that law by Acol club tourneys.

Psyche (pron. sahy-kee): The human soul, spirit or mind (derived, personification thereof, beloved of Eros, Greek myth).
Masterminding (pron. mPosted ImagesPosted ImagetPosted Imager-mPosted ImagendPosted Imageing) tr. v. - Any bid made by bridge player with which partner disagrees.

"Gentlemen, when the barrage lifts." 9th battalion, King's own Yorkshire light infantry,
2000 years earlier: "morituri te salutant"

"I will be with you, whatever". Blair to Bush, precursor to invasion of Iraq
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#18 User is offline   Spisu 

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Posted 2016-July-15, 05:45

View Postnige1, on 2016-July-14, 10:31, said:

Am intelligent player at Reading Bridge Club claimed that the rule of restricted choice was bunkum. We offered to set up a typical matrix, then shuffle the remaining cards and back our respective judgements at £10 per deal. After some homework, our friend declined our challenge :)


Your is a non-sequitur because I have not even mentioned the wisdom of plays. Restricted choice has probably endured because the "finesse twice" is valid but arises elsewhere. It is the rationale of RC that is error, and the fact is that it piggy-backs on the actual valid basis for that strategy which is an a priori stategy.
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#19 User is offline   Spisu 

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Posted 2016-July-15, 05:55

View Postshyams, on 2016-July-14, 10:39, said:

Two puzzles for spisu (and spisu alone) to answer:

1. You run into a familiar person one day. The only think you know about this person is that he has two children (but you have no idea how many of them are boys vs. girls).
....So this person says "Hello" etc, and then points to the child walking with him saying "This is my son".
....What is the probability that his other child is also a boy?
Spoiler


2. If #1 was hard, here is an easier one. Why is cow's poop usually in the form of a "patty", goat's poop usually tiny spheres, and human poop usually somewhat cylindrical?
Spoiler


0

#20 User is offline   Spisu 

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Posted 2016-July-15, 06:01

I may be more familiar with the 2 kids/ boy girl puzzle issue than you. Many might say that actually seeing the boy would be random discovery and make odds 50-50...So I try to use more easily perceived sources of non-random data such as meeting your new neighbor you know has two kids and you see a pink girl's bike. Then you would have justification that you very likely had learned indirectly (non-randomly) that one was a girl, which makes the odds 2:1 for a boy and girl to be the 2 kids.
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