Another application of restricted choice

[CSGibson]

[hv=n=s942hdc&w=shdc&e=shdc&s=saq653hdc]399|300|[/hv]

 

suppose that this is your trump suit, which you have to bring home for 1 loser. There is no bidding to help, you have plenty of entries to both hands, and no fear of a ruff.

 

you decide to play Ace from your hand first, to see what happens, and LHO drops the Jack or ten, while RHO plays small. When you cross to the board to lead another trump, RHO follows small again. Do you think it is now the percentage play to play LHO for the doubleton king? Is the described method of handling the suit the best way to play it?

[ArtK78]

My regular partner came up with exactly this problem, and tried to convince me and others that it was right to play for the bare K behind the Q in this position.

 

I am not convinced, although he seems to have convinced others that this makes some sense.

[fred]

Do you think it is now the percentage play to play LHO for the doubleton king? 

 

Is the described method of handling the suit the best way to play it?

Yes and yes.

 

Playing the Queen gains only if LHO started with J10 while playing low gains when LHO started with either KJ or K10. If LHO was dealt a singleton J or 10 your play doesn't matter.

 

A deeper question: Suppose you decide to make the (inferior) play of ducking the first round of the suit completely. LHO wins the 10 or Jack while RHO follows with a small card. RHO plays the remaining small card on the second round.

 

Is this situation any different? Why or why not?

 

Even if you think the situation is the same, it is easy to see why this line of play is inferior: it loses to J10 doubleton with RHO and never gains. Assuming all you care about is losing exactly 1 trick, the first round finesse of the Queen is equivalent to cashing the Ace and leading low to the Queen on the second round even if LHO plays the J or 10 on the first round (losing to KJ and K10 while gaining against J10).

 

Fred Gitelman

Bridge Base Inc.

www.bridgebase.com

[Lobowolf]

Do you think it is now the percentage play to play LHO for the doubleton king? 

 

Is the described method of handling the suit the best way to play it?

Yes and yes.

 

Playing the Queen gains only if LHO started with J10 while playing low gains when LHO started with either KJ or K10. If LHO was dealt a singleton J or 10 your play doesn't matter.

Is the 9 coming off dummy the second time?

[Finch]

Do you think it is now the percentage play to play LHO for the doubleton king? 

 

Is the described method of handling the suit the best way to play it?

Yes and yes.

 

Playing the Queen gains only if LHO started with J10 while playing low gains when LHO started with either KJ or K10. If LHO was dealt a singleton J or 10 your play doesn't matter.

I am confused. Why are you assuming that, after playing the Jack, LHO's only possibly holdings are J10 or KJ? Why can't LHO have J8, or J7 doubleton?

 

Surely it matters whether the defence have any idea what your holding in the suit looks like, or not?

[fred]

Do you think it is now the percentage play to play LHO for the doubleton king? 

 

Is the described method of handling the suit the best way to play it?

Yes and yes.

 

Playing the Queen gains only if LHO started with J10 while playing low gains when LHO started with either KJ or K10. If LHO was dealt a singleton J or 10 your play doesn't matter.

I am confused. Why are you assuming that, after playing the Jack, LHO's only possibly holdings are J10 or KJ? Why can't LHO have J8, or J7 doubleton?

Because RHO's 10 would show up on the 2nd round.

 

Surely it matters whether the defence have any idea what your holding in the suit looks like, or not?

 

In real life, yes of course, but the way these problems are usually analyzed is to assume that the defenders know what you have and defend optimally. In most cases it is difficult or impossible to arrive at a definitive conclusion unless you make that assumption.

 

Fred Gitelman

Bridge Base Inc.

www.bridgebase.com

[Trumpace]

Do you think it is now the percentage play to play LHO for the doubleton king? 

 

Is the described method of handling the suit the best way to play it?

Yes and yes.

 

Playing the Queen gains only if LHO started with J10 while playing low gains when LHO started with either KJ or K10. If LHO was dealt a singleton J or 10 your play doesn't matter.

 

<snip>

The above reasoning seems incorrect to me: you will always play LHO for KJ or KT (irrespective of LHO's habits).

 

Say LHO played the J under the A. Then isn't KT ruled out? of the relevant holdings, he either has KJ or JT. The question is, from which is he more likely to play the J and that would be KJ as from JT, he _could_ have played the T.

 

So against an unknown/good player, playing low instead of Q will be correct. If you knew LHO always plays J from JT, then playing the Q is correct.

 

What am I missing?

[fred]

Do you think it is now the percentage play to play LHO for the doubleton king? 

 

Is the described method of handling the suit the best way to play it?

Yes and yes.

 

Playing the Queen gains only if LHO started with J10 while playing low gains when LHO started with either KJ or K10. If LHO was dealt a singleton J or 10 your play doesn't matter.

 

<snip>

The above reasoning seems incorrect to me: you will always play LHO for KJ or KT.

 

Say LHO played the J under the A. Then isn't KT ruled out? of the relevant holdings, he either has KJ or JT. The question is, from which is he more likely to play the J and that would be KJ as from JT, he _could_ have played the T.

 

So against an unknown/good player, playing low instead of Q will be correct. If you knew LHO always plays J from JT, then playing the Q is correct.

 

What am I missing?

What you are missing is the same thing that most bridge players miss when it comes to restricted choice.

 

Probably you have seen the standard arguments for why one should believe in restricted choice (if not I am sure you can find this by searching through Forums or by doing a web search). I tend to think about these situations somewhat differently - maybe this will help:

 

In trying to evaluate a given line of play, make a list of all of the possible holdings for which the line in question will win. Once you decide to adopt a given line of play, do not let the specific cards played by the defenders talk you out of your original plan (they are not on your side!). Make sure that, no matter what happens, you will always succeed in those cases for which you originally planned to succeed.

 

So try to use this sort of reasoning to compare these 2 lines of play:

 

1) Cash the Ace, if LHO plays the 10 or Jack, play low to the Queen the second time.

 

2) Cash the Ace, if LHO plays the 10 or Jack, duck the second round.

 

It is easy to see that 2) is better than 1). 2) gains over 1) when LHO has KJ or K10 and 1) gains over 2) when LHO has J10.

 

Line 2) is better so adopt it and stick with it regardless of whether LHO plays the Jack or the 10 under your Ace.

 

I am not sure I could offer a compelling argument as to why this approach to solving suit combinations tends to work (ie why your statement "once West plays the Jack he can't have K10" is not relevant). It might be easier for you if you just take my word for it, but I can understand how that might not be satisfying. If that is the case, speak up, and I am sure someone out there (not me) will offer a real mathematical argument for why I am right (though I am guessing that you won't find that particularly satisfying either).

 

You are correct that things would be different if your LHO always played either the Jack or the 10 from J10, but a strong LHO should mix things up when he has that holding. As I said in a previous post in this thread, the only practical way to solve most of these problems is to assume that the defenders play perfectly.

 

Fred Gitelman

Bridge Base Inc.

www.bridgebase.com

[Trumpace]

As a general practical approach, I agree, opponents spots can be ignored, but for this specific case, that reasoning does not apply, IMO.

 

I don't think you will be able to prove this mathematically, as your reasoning seems to ignore restricted choice (or Bayes principle) which (I think) needs to be applied here. If you/someone can mathematically prove what you say, I would be very interested to see it.

 

In the current problem, if LHO is always known to play J from JT, it seems it is a guess whether to play low or Q on the second round (so my earlier statement of always playing Q seems incorrect to me now). In fact, one extra factor for playing low is that RHO _might_ have risen with the K on the second round if he had it...

[MFA]

I agree with fred's analysis. This is a restricted choice situation, since the presence of the 9 in dummy effectively prevents the opponents falsecarding options.

 

A deeper question: Suppose you decide to make the (inferior) play of ducking the first round of the suit completely. LHO wins the 10 or Jack while RHO follows with a small card. RHO plays the remaining small card on the second round.

 

Is this situation any different? Why or why not?

Yes, it's different but very complicated.

 

Now east has the option of falsecarding with the T from Txx on the second round, and west has the option of falsecarding with the J from Jx on the first round.

 

So we'll need to evaluate our opponents' tendency to falsecard.

[fred]

I don't think you will be able to prove this mathematically, as your reasoning seems to ignore restricted choice (or Bayes principle) which (I think) needs to be applied here. If you/someone can mathematically prove what you say, I would be very interested to see it.

No - I am saying that this is a restricted choice situation and, even though I am not using a conventional restricted choice argument to come to my conclusion as to how one should play, my conclusion is the same as that which would fall out of such an argument.

 

In other words, I guess it is accurate when you say I am "ignoring restricted choice", but only in the sense that I am able to come to the same conclusion in a different way.

 

Of course it is possible that I have made a mistake, but I don't think so.

 

Fred Gitelman

Bridge Base Inc.

www.bridgebase.com

 

PS You right that *I* might not be able to prove this mathematically, but I have no doubt that someone else could do this in their sleep :)

[Trumpace]

I don't think you will be able to prove this mathematically, as your reasoning seems to ignore restricted choice (or Bayes principle) which (I think) needs to be applied here. If you/someone can mathematically prove what you say, I would be very interested to see it.

No - I am saying that this is a restricted choice situation and, even though I am not using a conventional restricted choice argument to come to my conclusion as to how one should play, my conclusion is the same as that which would fall out of such an argument.

 

In other words, I guess it is accurate when you say I am "ignoring restricted choice", but only in the sense that I am able to come to the same conclusion in a different way.

 

Of course it is possible that I have made a mistake, but I don't think so.

 

Fred Gitelman

Bridge Base Inc.

www.bridgebase.com

Ok. Now I understand. I misread your post as going with a-priori probabilities.

 

In fact, your reasoning looks correct to me now!, the key point (for me) being "does it really matter (make you change your line) if LHO played the J as compared to the T"? Since it does not really matter, you can assume you don't know exactly what it was, and reason assuming that it is one or the other, which is what you seem to have done.

 

(For the more mathematically inclined, I suppose it is same as the claim P(LHO holds King| he played Jack) = P(King|Ten) = P(King | Jack or Ten))

 

PS: By "you" i didn't mean specifically you, it was just a generic word... Perhaps I should have used "one"...

[kenberg]

If I can suggest a way of thinking, maybe not grossly different. As always, count the ten and the Jack as indistinguishable (both are tacks) since either he would play them randomly holding both or what comes to the same thing practically you don't know his tendencies if they are not random.

 

So: At the time you play from hand to the second trump trick you know with certainty that the two spots were dealt to your right and at least one tack was dealt to your left. If lho was dealt all three honors your play is irrelevant. The same is true if the tack was stiff although you will take your tricks in a different order depending on your play. So the only issue is two honors originally dealt to your left. These could be tack tack (one way) or tack King (two ways).

 

So yes you should play low and yes it is the same argument that usually appears for Restricted Choice.

 

I don't mind at all saying this had never occurred to me before, so thanks.