[bluecalm]

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1st trick: 7♠, 6♠, A♠, 4♠
2nd trick: 2♠, ????

Opponents are sound 1 level openers. The play perfect mixed strategy from AKxxx so don't read into that.
7♠ is either from K97 or J97.

Your play ?
Your math ?

(This is real hand, and two world class declarers faced it. This is bidding from one table, it was similar in other room)

[gszes]

bluecalm, on 2012-January-10, 10:47, said:

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1st trick: 7♠, 6♠, A♠, 4♠
2nd trick: 2♠, ????

Opponents are sound 1 level openers. The play perfect mixed strategy from AKxxx so don't read into that.
7♠ is either from K97 or J97.

Your play ?
Your math ?

(This is real hand, and two world class declarers faced it. This is bidding from one table, it was similar in other room)

if W has the AK of clubs there is a fair probability they would have led the
Club K at trick 2 to tell p how to get back to their hand after the spades were set up. The absence of that play leads me to assume E has one top club honor and
since no 2s raise with 3 to an honor it seems far more likely E has J97 vs (K97 or KJ7) and I will guess to insert the Q.

[bluecalm]

This is very weak reason imo. There is no chance what so over that world class defender plays K♣ showing AK. I mean, he tries to defeat the contract, not give free info to declarer. There will be plenty opportunities to show entry later if declarer plays some suit, especially that the only possible entry from someone holding 12hcp there is in diamonds so the only suit we could have entry in is clubs without any signal needed.

[JLOGIC]

What is perfect mixed strategy with AKxxx? Would your answer change if our hand was QTx KT AKQTx Kxx? In that case they better play the ace 100 % of the time with AKxxx to give us a problem (depending on their opening bid style).

[JLOGIC]

Likewise if they opened AKxxx xx Jxx Kxx, our hand might be QTx Kx AKxxx Axx, in which case they should probably always play the ace every single time and definitely if we added a red jack to that.

[JLOGIC]

I would definitely play the queen.

Here are some possible scenarios:

1) West has all of the AK, AK in blacks.
2) West has AK of spades and the CA
3) West has AK of spades and the CK AND either or both the HJ or DJ (needed for his opening bid).

OR

4) West has AJxxx of spades and AK of clubs.
5) West has KJxxx of spades and AK of clubs. (Included to show restricted choice element in the spades if you want it to be...you can just take this one out and divide the first 3 by two if you prefer looking at it like that).

You see that if we play west for for only one spade honor, we are also playing him for both the AK of clubs at the same time. If we play west for one spade honor, we are catering to him having either club honor, OR BOTH (a little more complicated than that because if he has the AK of spades and the CK he will probably need another jack to open the bidding). Case 1 may or may not be slightly discounted depending on their NT range and if they open 1N with a 5 card major and a pure hand if he's balanced. It seems to me our edge in playing the Q is that we pick up AK AK. All other plays are about equal playing the other hand for one honor.

This hand is also a little more complicated since we are not cold if we get spades right, but I don't think one "guess" working significantly increases our chances of the side suits coming in (except that if west has AK of spades and the CK and a red jack, that makes it more likely the diamonds will come in), so I'm basically ignoring this.

Now, as I alluded to, I think that most people will either always or almost always play the ace from AKxxx when they are an opening bidder, and the opps seem to have at least 24 and maybe 25 or 26 HCP. This is because you are dangerously close to being counted out, there is not much room for partner to have an ace...there is much more room for patner to have a king. This makes playing the queen even better. Perfect mixed strategy, that seems really rich, given that he does not know that we have only 14 HCP and that we cannot count anything out. Not to mention some people would think that partner would raise to 2S with Axx of spades...I agree that r/w partner should not raise with Axx but some people might, and that might affect declarer. To me it would be a really bold/ballsy play to play the king with AKxxx. Considering it just a restricted choice situation would be really wrong.

[mfa1010]

If we reasonably give west at least 3 of the 4 black tops, then playing him for spade AKxxx will allow three times as many club holdings than AJxxx would.
He could then have any spot card club holding in combination with A, K or AK.
So even if we think the spade situation is restricted choice then this is trumped by the degree of freedom with club holdings.

[bluecalm]

Quote

Perfect mixed strategy, that seems really rich, given that he does not know that we have only 14 HCP and that we cannot count anything out. Not to mention some people would think that partner would raise to 2S with Axx of spades...I agree that r/w partner should not raise with Axx but some people might, and that might affect declarer. To me it would be a really bold/ballsy play to play the king with AKxxx. Considering it just a restricted choice situation would be really wrong.

Yeah, this is good point about Axx and raising, at least some hands are eliminated because of it.
As to playing the king, you need to play K from AK some smallish % of the time to "cover" the cases you have KJxxx
So for example if the distribution of our range from our point of view is:
70% for AK
20% for AJ
10% for KJ

We need 1/7 of our AK to play a king to make declarer indifferent in case he sees a king. So yeah, only slight mixing is needed.

As to actual hand:
It was during 2010 Champions Cup. Both Drijver and Bocchi played the queen. Both lost

It seemed extremely close to me but I made a mistake of assuming defender is playing 50-50 with AK.
A priori probabilities are more or less 66-33 to AK comparing to AJ (and probably even more if we add that other defender didn't raise). Anyway, I am now convinced playing the queen is right and probably playing the ten is right if we see the king instead of ace as most opponent probably won't mix enough (ie, they will always play the A from AK).

[gnasher]

Here's one reason for playing the ten: if it works, there is a greater chance that opener is balanced, so a greater chance that a red suit will come in. If LHO has AK AK, he's more likely to be unbalanced, because he didn't open 1NT.

That's probably not a sufficient reason, because you have good chances in the red suits even when opener is unbalanced. I like the idea though.

[TWO4BRIDGE]

bluecalm, on 2012-January-10, 10:47, said:

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Side issue: What was East's 3♦-jump advance ? ( preemptive invitational transfer ? )