Problem # 23

From                   14th June, 2006, Board 13

Theme                Counting the Distribution

Difficulty            * *

Dlr North            Both Vul

 ♠ KJ95 ♥ K7 ♦ 9872 ♣ 654

 North West             East           South

 West     North   East      South              Pass    Pass      1♥ Pass     1♠        Pass      2♥ Pass     Pass    Pass

 ♠ AT6 ♥ AQ9843 ♦ A5 ♣ 83

The opening lead is the K (E-W play Ace from Ace-King), then the Q, East following with the 7 and the 2.  West now shifts to the 4, East plays the King, and you win the Ace.  Now you play three rounds of trumps, East following once, then pitching the 3 and the J.

Clearly, on the play of this hand, the only remaining item on the agenda is to find the Q, if we misguess that card we'll end up with just 8 tricks.  But it's not quite that simple ... for example, if West started with Qxx in Spades, you can get that Diamond loser away (if you guess right) and score 10 tricks  ... on the other hand, if East started with Qxx, that upside does not exist, and the correct Spade guess is worth just 9 tricks.

Which do you choose?

SOLUTION

Unless there has been some clever false-carding, we can deduce the following:

- Clubs are 4-4, West having started with KQxx and East with AJxx

- Diamonds are 4-3 either way, West with the Queen and East with the King-Jack ... how do we know that?

Well, at Trick 3, East played the K, denying the Queen ... and East had led a low one, surely not a

sensible play holding QJx(x).

- And, Hearts are 4-1, of course.

In other words, it looks as if East started with 5-1-3-4 shape or 4-1-4-4 shape.  Either way, we can forget about West starting with Qxx of Spades, and getting the Diamond away on the Spades is therefore just a pipe-dream.  So, we'll just play East for the length in Spades, which means that the odds are that East has the Queen.

 ♠ KJ95 ♥ K7 ♦ 9872 ♣ 654

 ♠ 32 ♥ JT62 ♦ Q64 ♣ KQT9

 North West             East            South

 ♠ Q874 ♥ 5 ♦ KJT3 ♣ AJ72

 ♠ AT6 ♥ AQ9843 ♦ A5 ♣ 83

Before we make the fateful Spade guess, we should also do some HCP-counting.  East appears to have 9 points in the minors, so there is room (but only just!) for another 2 points in Spades.

Keys to Success

- Deducing from the Club play and East's Club discard that the suit is probably 4-4

- Deducing that the Diamonds are 4-3 (either way)

- Concluding that East has 4 or 5 Spades and playing the suit accordingly