Chien-Hwa Wang, on pp38-9 of his book "The Squeeze at Bridge", discusses this end position. South is on lead in a NT contract and needs the remaining three tricks. There are four spades outstanding, including the Q, together with A and Q.

What is the chance that South will make the contract from this position, using his best line (which begins with play of the 9), if:

• (a) he knows nothing about the lie of the 6 outstanding cards;
• (b) he knows only that West has the A;
• (c) he knows only that East has the A;
• (c) he knows that West has the A and that East has the Q, but has no other knowledge?

North-South bid to 7NT with the cards shown in diagram (a), using an auction which marks South with a 3334 shape and 17-18 HCP (including one ace and two kings). West leads the J. South plays off winners to reach the 3-card ending shown in (b), noting that both opponents followed suit to each trick. He also noted that West played 10 and  9 on the second and third round of diamonds (as one would do if dealt J109, J109x or J109xx -- using the principle of playing what one is known to hold). He also noted that neither the Q nor J fell.

What is the chance, given the information to date, of making 7NT from situation (b) using the best line (which obviously starts by cashing the Q, pitching the 4 and observing both discards)? 

You'll have to consider all possible discards for the opponents. As an example, what is your best line and chance of success once (c) is reached if both discard a diamond on trick 11 and West plays x when you lead the 7?

Deal (a) occurred during the 2005 Bermuda Bowl. The Australian Open team was playing Brazil. The contract at both tables was 7H.

In attempting to understand better the issues entailed in such a hand, I posed a somewhat simplified version, deal (b). My “generic” form of the deal has solid trumps (having no risk of over-ruff) and no lower honours nor high pips in the side-suits. So your resources are limited to the 9 trumps, the 5 outside high tricks and potential long tricks in the minor suits.

 Suppose, on deal (b), that West leads the 3 and East follows. What is the best line of play?

Thanks to Len Dixon for drawing my attention to the deal.

After the auction 1D-1H <> 2NT-3NT, South received the  5 lead. The leading convention was "4th highest from length". East played the  K.

There appear to be two distinct lines of play. One of these, Line A, is the play of the diamond suit, hoping to derive 4 tricks from the suit. The other line, Line B, tackles the heart suit first – low toward KQ2  –  with  a  fall-back  on  the finesse against the Q should West have the A. This line relies on the clubs breaking 4-4 and West not having both the Q and A. In both lines, sensible management of the spades to provide entries to dummy, without blocking the suit, is achievable.

How should one play the hand?       Thanks to Les Varadi for providing  the deal.

   North
AQJ
9876
J86
874

  South
K932
KQ2
AKT5
AJ

You pick up a balanced hand of 16 HCP and plan to open a 15-17 1NT. Partner, however, opens before you, with 1NT.

I saw such a hand recently; the responder bid 6NT directly. Was it wise, do you think, for him to bypass the ace-asking convention?  What do you think the chances of the partnership missing two aces would be -- given responder's 16 HCP and the information that opener's range is 15-17?

As  dealer  sitting South, in  a  tournament  with  IMPs scoring, you open 1S showing 5+ spades. LHO passes, partner bids 1NT (the usual 6-9 with at most 2 spades) and RHO passes. What do you bid? 2H or Pass? EW are vulnerable. Take a view before reading the analysis.

 
  South
AT542
J752
K42
A
 

All of the CHANCES columns to date have focussed on problems of card play. Yet considerations of the probabilities also arise in bidding; a recent hand from Thursday-night bridge at Lindfield illustrates this.

As South you must decide where to place the contract. Your partner has shown 25+ HCP, with no 5-card suit and no singleton. Upon enquiry you learn that he has 3 aces and 3 kings. Do you bid 7NT or subside in 6NT?

   North
AKJ9
KQ94
AJ
AKT

  South
QT6
AT2
Q2
QJ954

On (a), a trump is led to East's K. He leads a trump back to West's A and a 3rd round of trumps is led. How to proceed?

On (b), West leads the K, which you duck. He then leads a trump. East wins and plays the T. You win, noting that both have followed and the 9 is still out. Should you now try to ruff two diamonds in hand or rely on a 3-3 club break? Or is there something better than these two choices?

   North
K76
QT52
A732
K5

  South
A95
J643
K4
A762

(b)

   North
J6
KQJ5
K732
K63

  South
A75
8432
A4
A742