[han]

Certainly agree with Fred's analysis. Also frustrated with my own analysis, I missed AQ7 for my strategy 3.

[fred]

Stephen Tu, on Oct 18 2007, 10:22 PM, said:

Just because your reasoning leads you to correct conclusion about what to do when the 9 appears, and is "simpler", doesn't mean that it is also mathematically accurate & complete.

I think your reasoning doesn't adequately show what the proper thing to do is when the Q covers the J, for example. My reasoning does; it shows clearly that you play T if the covering percentage is >= 91.67%, and hook otherwise.

Just because your reasoning leads you to the correct conclusion about what to do when the 9 appears and is "more complicated" doesn't mean that it my reasoning is not mathemetically accurate and complete.

I think your reasoning tries to answer a question that was not asked and fails to take into account the assumption of best defense (which I admit I forgot to include in the original specification of the problem but added to a later post in this thread).

I think my reasoning demonstrates that you have to choose between A9+Q and Q9.

IMO that is sufficient for answering the question that was asked.

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

[cherdano]

I would just add one comment to Fred's reasoning: One might wonder whether there is a better line if RHO told us in advance how often he will cover from Q9 (but RHO will choose this percentage optimally, of course). It is quite easy to see that if RHO chooses to always plays the 9, we cannot improve on the correct line.


[Game theorists would say that Fred's line, plus RHO never covering from Q9, is a Nash equilibrium.]

[kenrexford]

My brain is about to explode here.

Lots of us worked out the you ride with the 7 showing but rise if the 9 appears. This is not all that magical. There are various ways of saying essentially the same thing. So, what difference does it make how you arrived at this conclusion?

I also have no idea what the approved mathematical defintion of "restricted choice" might be. However, in my layman's mind, I view the issue as one where the enemy in one situation has options but in the other does not, at least when coming up with the meaning for the term.

If you want weird analyses, or terms, I'd call this a sideways "V" center of gravity problem. I am considering two scenarios with one common point but two unrelated points. If I draw it out sideways, I have a point up high and left, crossing diagonally to a point low and right. crossing back to another point lower yet and left, creating a sideways V. I draw a line down the middle and notice that the same amount of lines are one both sides. However, if I fill in the space between the lines, the filled-in area left of the center line weighs more than the area to the right. So, I lean toward the left. Those two points to the left are then selected.

I can even analyze it quickly:

"I"ll play the low if the 7 is played but high if the 9 is played, because of the Sideways V principle."

[fred]

kenrexford, on Oct 19 2007, 12:11 AM, said:

Lots of us worked out the you ride with the 7 showing but rise if the 9 appears.  This is not all that magical.  There are various ways of saying essentially the same thing.  So, what difference does it make how you arrived at this conclusion?

Some people find simplicity to be elegant.

Also simpler solutions tend to be easier to comprehend and learn from than unnecessarily complex solutions.

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

[Cascade]

I am not sure that "restricted choice" is a mathematical term.

My understanding and recollection is that Terrence Reese coined the term restricted choice to explain the bridge situation.

"Restricted Choice" applies when we are considering a player who might have two different combinations - e.g. stiff queen (or jack) or queen-jack tight - and we reason that the combination in which there was a 'restricted choice' is the one that is most likely since with the other option the player had a choice and therefore the probabilities can be discounted since sometimes we will see the one choice and sometimes the other.

To me, as one who overlooked the defender having a choice of plays with Q9 I think this is a "restricted choice" problem. The defender with A9 has a "restricted choice" and with Q9 has a choice.

As Fred said normally "restricted choice" is from among equals. Here while the queen and the nine are not equals in the normal sense they are equal in the sense that either might take a trick if the other is played. In fact whatever you play with Q9 should get you a trick. As we have seen if you play the nine declarer should play the king thus promoting your queen. While if you play the queen declarer should be inclined to finesse for the nine on the second round.

[Apollo81]

fred, on Oct 18 2007, 08:19 PM, said:

Some people find simplicity to be elegant.

Best thing Ive heard all day

[matmat]

Cascade, on Oct 18 2007, 07:25 PM, said:

As Fred said normally "restricted choice" is from among equals. Here while the queen and the nine are not equals in the normal sense they are equal in the sense that either might take a trick if the other is played. In fact whatever you play with Q9 should get you a trick. As we have seen if you play the nine declarer should play the king thus promoting your queen. While if you play the queen declarer should be inclined to finesse for the nine on the second round.

that hurts my head.

[kenrexford]

fred, on Oct 18 2007, 04:34 PM, said:

Similarly, if East plays the 9 you have to choose between:

C: Q9
D: A9

Clearly these are equally likely which, at first glance, would suggest you have a complete guess when East plays the 9.

You can resolve this guess by considering what you will do if East plays the Queen. Now you have to choose between:

E: Q9
F: Q

It is now easy to see that you should resolve the C/D guess by picking D since that allows you to get F as well. If instead you pick C, you also get E, but you already had that in the form of C

Not to nit-pick, but I don't understand how this way of putting it is simplicity that is elegant.

Paraphrasing what you said:

I'm resolving what to do if one thing happens by deciding what I will do if another thing happens and doing the same thing in the first situation that I did in the second situation because this allows me to get something in that other situation. Furthermore, if I opt to do something else in the first situation that would work to help me get something else in the second situation, but I'd already have that because that's the same thing.

That's simpler than what I and others said?

Paraphrasing what I and others said:

How do I decide whether the 9 is from A9 or Q9? With A9, he has to play the 9 to give me a guess. With Q9, he wins no matter what he plays, because the 9 gives me a guess and the Queen gives me a guess. So, I decide that he played the 9 because he had to.

I must not understand what "simplistic" means.

[fred]

Maybe "simple" is partly a function of perception. I thought my solution was simpler than most of the others because:

- I used less space
- I did not use any % symbols
- I did not consider irrelevant holdings
- Everything I said was on the path between the question and the answer
- I did not need to mention "restricted choice" (a concept that is not well-understood and may not even apply here)
- I explictly stated the key point (if you play for A9 you can also play for stiff Q)

If you like your solution better I am happy for you

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

[kenrexford]

fred, on Oct 18 2007, 09:20 PM, said:

Maybe "simple" is partly a function of perception. I thought my solution was simpler than most of the others because:

- I used less space
- I did not use any % symbols
- I did not consider irrelevant holdings
- Everything I said was on the path between the question and the answer
- I did not need to mention "restricted choice" (a concept that is not well-understood and may not even apply here)
- I explictly stated the key point (if you play for A9 you can also play for stiff Q)

If you like your solution better I am happy for you

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

You used less space because you skipped a hell of a lot of explanation.

I have no idea why anyone would use % symbols. I did not.

Although you claim to have not considered irrelevant holdings, you actually did. You considered them, recognized why they were ireelevant, and discarded them. You just did not include your reasons in your explanation. (See "saved space" above.)

I have no idea what you mean by a path.

You are correct that you did not need to mention the term "restricted choice." However, that concept is actually quite simple, and elegantly so, for many of us. Plus, it does absolutely apply and is the reason why you play the King.

Although you did state what you believe to be the "key point," I still don't get the manner of thought here. You are bouncing back and forth between a posteriori's and a priori's in a manner that works out right, but I cannot follow what your argument is enough to determine if it makes sense or if your just get to the answer by lucky happenstance.

Finally, the reason why I mention all of this, and mentioned similar things earlier, is that you dangled before many of us who figured this thing out a while ago a "hint" of some great mysterious manner of analyzing this, gave a bizarre way of analyzing it, and claim that weird ACDC but for's and otherwhich's is a simpler way to look at something than what others suggested.

What I was expecting is something like this:

Fred: "Very well done! I'm sure many would agree that this is quite a sublime and rare anomaly, eh?"

Us: "Quite!"

Some: "Still don't get it... "

Fred: "Well, try this way of looking at it..."

Instead, it read more like...

Fred: "Y'all got it, but you did it a weird way. My way is much simpler and more elegant."

Us: "What do you mean?"

Fred: "Well, take an albatross, let it fly backwards ten yards, count the wing strokes, subtract that from the wingspan, and you will know that grass is clearly green."

Us: "Uh, OK."

[Stephen Tu]

Quote

think your reasoning tries to answer a question that was not asked and fails to take into account the assumption of best defense (which I admit I forgot to include in the original specification of the problem but added to a later post in this thread).

I think my reasoning demonstrates that you have to choose between A9+Q and Q9.

Fred, your reasoning may be "simpler", but frankly it's just incomplete.

Using your terminology for C, D, E, F,
(C = Q9, 9 played,
D = A9
E = Q9, Q played
F = Q)
, you essentially argued that the choice was between
C+E and D+F.

But those aren't the only choices one can make!

One can also play for combos D+E, and C+F.

Since you didn't demonstrate that D+F is also greater than those other options, then your reasoning must be considered incomplete.

And my more complete explanation showed the conditions where D+E > D+F, and that this only applied vs. perfect defense where RHO knows you have 6 cds rather than 5, and knows that you will choose the right play. Do you not agree that a non-omniscient defender with Q9 will want to cover if 5 cd suit is a possibility?

Quote

I explictly stated the key point (if you play for A9 you can also play for stiff Q)

That's not the key point. If the guy with Q9 never covers, you can also play for stiff Q, and hook on the 9 for the exact same percentage result. The key point is that in practice Q9 will cover sometime, so Q9 is less likely than A9 when the 9 is played.

[fred]

Stephen - the assumption was best defense.

Ken - apparently we do not live in the same universe.

Sorry guys. I have had enough of this.

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

[helene_t]

Don't worry Fred, we will set up a committee with a mandate to define the meaning of the term "simple". You don't have to bother about it.

[fred]

helene_t, on Oct 19 2007, 04:37 AM, said:

Don't worry Fred, we will set up a committee with a mandate to define the meaning of the term "simple". You don't have to bother about it.

Thank you my dear, but I was actually hoping you would weigh in on the math

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

[benlessard]

Quote

3 playing LOW (the 8) to the king is inferior because of (9----AQ7)

Oups my mistake since low to the k win when (Q---A97) its equal. In practice leading the 8 to the K is probably better because RHO might rise with AQ7 (not likely but its possible)

I liked Fred very simple explication.

For me the interesting part of the problem is that an option by the defense on another holding (A97---Q) or (A7----Q9 with the play of the Q or the 9) is the key to understand why going up with the K is better.

But i still think solving it with the restricted choice is still a simple and sound solution.

When similar problems will come up it will be simpler for me to understand it in RC term then a "duplication of holding" method.

Anyone here who doesnt understand RC should devote some time to it because its quite important and its not that hard to understand.

The 'classic' definition of RC is between card of equal values (that are assumed to be played with even frequency) but the RC method also applies when equal arent played with even frequency or when they are not quite equals.


ATxxx

K98x

playing low from hand and LHO play the J.

its a (QJ) VS (J---Qxx) case

Even if LHO (a beginner who doesnt mixed his play) with (QJ) play the J 80% and the Q 20% its still a restricted choice. Just that finessing for the Q become a small winner instead or a big winner.

However the day LHO will drop the Q on first round now the finesse for the J is going to be a big winner. So the fact that with Q9 the 9 and the Q arent played with the same frequency doesnt say its isnt a RC.

---

you play the A and RHO pitch the J

here we have a falsecard that is a RC problem for declarer (between KJ, Jx) (assuming declared is dead anyway if the J is stiff).

IMHO its a RC without equals cards

but some will say that since the J is worthless then the J and the spot are equal.

[Stephen Tu]

Quote

But i still think solving it with the restricted choice is still a simple and sound solution.

I don't think I would really call the original problem a restricted choice problem since it doesn't involve equals. Restricted choice is a specific application of Bayesian reasoning, the complete reasoning behind playing the K is similar, also Bayesian, but I wouldn't necessarily call it RC.

The principle to learn is that if a defender has a choice of plays from a holding, you should assign a probability to each choice, and calculate accordingly. Figure out why a defender ought to do something, and how often. Often you find a range of values for the choice where declarer should do one thing, but if the defender strays outside those ranges declarer should do something else. This can affect practical play of combinations such as the original, e.g. best play after the Q covers, which is different between omniscient "perfect" defenders who know declarer has 6, and non-omniscient "perfect" defenders who also have to cater to declarer having 5 (where you should cover with Q9 doubleton).

---

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:

---

And the idea is you have a choice between playing RHO for JT or KJ after the J falls. RC will show that you should cater to KJ.

[Codo]

fred, on Oct 19 2007, 12:55 PM, said:

Stephen - the assumption was best defense.

Ken - apparently we do not live in the same universe.

Sorry guys. I have had enough of this.

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

Sometimes you open a can of worms and you find? Worms.

I had waved my "I did not vote the worms" sign to warn you, but it was forbidden.

Thx for this threat, it made me a better bridge player. Just a little bit better, but it helped.

[cherdano]

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...

[helene_t]

fred, on Oct 19 2007, 07:14 AM, said:

I was actually hoping you would weigh in on the math

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, since the only way for me to analyze it would be to spell out the entire game matrix, decision tree or whatever. Shortcuts such as probability tables (I don't know them by heart) and restricted choice can help, but often I'm unable to decide if those shortcuts apply.

Intuitively, it is expected that playing the king has more merrit when RHO plays the 9, since if he played the 7 there is a case for saving the king as a guard against the nine. Also, it feels like RHO would be more likely to play the 9 without the queen since the 9 and the queen are equally expensive, so the 9 would tend to deny the queen and thus making it necesary to play the king, hoping for Q or Q7 by LHO. This is not a proof to me because I still wonder if RHO may nullify said effect by sometimes false-carding the 9 when he wants us to cover. Maybe this false-carding argument is irrelevant for this analysis, but that is the kind of things that are not obvious to me.