[nigel_k]

Scoring: IMP

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Opponents reach 6♦ after East opened a 12-14 1NT. The auction was science fiction so I won't repeat it but the essence is that East has one ace and preferred 6♦ to 6♥ (he would have been declarer in either). Therefore they are off two aces.

You lead the ace of hearts, partner plays the seven and declarer the two. Partner's card will be suit preference or a singleton (not that this helps much given the eight and four are still out there).

What next?

[cherdanno]

Well I would still like to know what declarer implied to have in the auction, but I would most likely lead a club.

[Fluffy]

Agree with Arend.

[ONEferBRID]

Partner's 7 can't be from 3 cards if he has an outside Ace.
He would have played the 8 or the 4 .
Thus, the 7 is either stiff or from 2 cards.
EDIT: duh, surely Opener didn't open 1NT with a stiff, as has been pointed out.
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Declarer sees your partner's 7 too.
He knows which suit your partner is signalling for.
If he held the EIGHT, he would have played that to make it
look like the 7 was partner's highest card from two.
EDIT: duh, Declarer never would falsecard the 8, as has been pointed out.
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I suspect partner holds the 8, so switch to a Club.
EDIT: duh, just amounts to a guess.
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ps. I suspect West transfered to Hts, and East never raised later, so East started with only two Hts; hence two for partner.
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[aguahombre]

of course there is always the possibility that the 7 was neutral from 874, if declarer is like some contributors here who would open weak NT with a singleton heart.

In that case Partner's key card is the diamond king, and nothing matters. However, If Declarer had the 8, the 7 by partner WOULD be his highest of two, so playing the 8 would just confirm that. Therefore, A spade seems the better choice.
If Declarer has any options he is trying to coax a club.

[nigel_k]

Just to clarify, they played some strange system where West started with 2♣ (not Stayman), East bid 2♦ which just indicated a balanced hand (no 5 major or 6 minor or 5422), West then transferred to hearts, asked for aces and bid 6♦ (yes, he knew they were off two aces when he bid it). It was keycard for hearts so the diamond king wasn't included.

Opening 1NT with a small singleton might not be beyond these guys, but for the purposes of this problem you can assume East has two or three hearts and partner one or two.

If partner has two hearts, they are either:
i) 87 and the ace of clubs
ii) 74 and the ace of spades

In ii) declarer should not falsecard with the 8 because it makes partner's 7 high
In i) declarer might have falsecarded with the four but it's not certain how often he would do this.

If anything, the falsecard possibility points slightly towards spades not clubs.

[655321]

ONEferBRID, on Aug 5 2009, 05:41 PM, said:

Partner's 7 can't be from 3 cards if he has an outside Ace.
He would have played the 8 or the 4 .
Thus, the 7 is either stiff or from 2 cards.

Declarer sees your partner's 7 too.
He knows which suit your partner is signalling for.
If he held the EIGHT, he would have played that to make it
look like the 7 was partner's highest card from two.

I suspect partner holds the 8, so switch to a Club.

ps.  I suspect West transfered to Hts, and East never raised later, so East started with only two Hts; hence two for partner.

No, the one card declarer will never play is the 8.

If we assume that hearts are 2-2 (declarer chose not to play in hearts) then the only possibilities are 87-42, and 74-82.
If partner has 87, he is signalling for a club, and declarer has a choice of the 4 and the 2.
If partner has 74, he is signalling for a spade, and declarer is forced to play the 2.

So, from the signals alone it seems to me that partner is twice as likely to have the ♠A, and I probably play a spade for that reason. But it should perhaps also depend on the chances of which black suit is less likely to run away if we don't switch to it. That is too tricky for me, but it does seem likely if we guess wrong that the losers can be discarded.

[y66]

spade per 65's reasoning. nice.

[655321]

(On the assumption that declarer has exactly 2 hearts)

If partner has the ♣A we can safely switch to a spade when:

• Declarer has 4 clubs, and
  
• Declarer doesn't have Qx(x) or Jx(x) of spades along with the A.

If partner has the ♠A we can safely switch to a club when

• Declarer has 4 spades, and
  
• Declarer doesn't have KQ of clubs along with the A.

On the one hand it is more likely that declarer has short spades, on the other hand it must be very unlikely for declarer (4243 12-14) to hold exactly AKQ of clubs along with top diamonds. So it could be that the club switch is significantly safer than the spade switch. Perhaps a simulation would come up with some percentages.

[Edit after seeing cherdanno's post to add the possibility of AJx(x) of spades]

This post has been edited by 655321: 2009-August-05, 20:09

[cherdanno]

655321, on Aug 5 2009, 06:11 PM, said:

ONEferBRID, on Aug 5 2009, 05:41 PM, said:

Partner's 7 can't be from 3 cards if he has an outside Ace.
He would have played the 8 or the 4 .
Thus, the 7 is either stiff or from 2 cards.

Declarer sees your partner's 7 too.
He knows which suit your partner is signalling for.
If he held the EIGHT, he would have played that to make it
look like the 7 was partner's highest card from two.

I suspect partner holds the 8, so switch to a Club.

ps.  I suspect West transfered to Hts, and East never raised later, so East started with only two Hts; hence two for partner.

No, the one card declarer will never play is the 8.

If we assume that hearts are 2-2 (declarer chose not to play in hearts) then the only possibilities are 87-42, and 74-82.
If partner has 87, he is signalling for a club, and declarer has a choice of the 4 and the 2.
If partner has 74, he is signalling for a spade, and declarer is forced to play the 2.

So, from the signals alone it seems to me that partner is twice as likely to have the ♠A, and I probably play a spade for that reason.

I agree with your odds - if partner has a doubleton. But I assume (and cannot tell as we aren't told the auction) that it is quite likely that he has a singleton, so the signaling odds are more like 55%-60%.

Quote

But it should perhaps also depend on the chances of which black suit is less likely to run away if we don't switch to it. That is too tricky for me, but it does seem likely if we guess wrong that the losers can be discarded.

I figured the spades are less likely to go away then the club - declarer needs AKQ to pitch spades on clubs, but only AJx or AQx to pitch a a club on a spade.

[pooltuna]

looks like pretty much a guess. Declarer probably has the ♠A and ♣K so I would try the ♣