A Tale of Two's and Three's

My first session back at the table after several weeks away, produced a bit of a mixed bag of results. 

This hand caused a fair degree of hilarity around the room:

This was the “problem” from my side of the table. 

With both sides vulnerable and holding:  ♠A10965 ♥85 ♦10 ♣A10872, I passed as dealer and was slightly taken aback to hear partner open with 6♦, third in hand. What (if anything) should I bid?

Well, if you assume that partner is bidding sanely, the only reasonable explanation must be that he has two two black suit voids. He presumably holds thirteen red cards but has a gap (or perhaps gaps) which cause him to hesitate to contract for thirteen tricks – he might also be worried that a more scientific approach could result in allowing the opponents to find a black suit sacrifice. Perhaps he is missing ♦K or, more likely, ♦Q and some number of small diamonds. Missing either of these key cards, it seems clear to pass.

But in fact, before you have a chance to get the green card out of your bidding box, your left hand opponent doubles!

At teams, I might have considered a redouble – the opportunity for gain (an additional 240 points, for the contract making – assuming no overtrick – against a potential additional loss of 200, would certainly be in my favour, possibly offset by the risk of the opponents running). Playing  pairs, however,  I essayed a smooth pass.

Now look at the full deal:

East’s double had little to recommend it – except that - as confirmed by Deep Finesse - the contract can be defeated. How?

Clearly a black suit lead allows declarer to ditch his two low hearts and simply concede one diamond trick. A diamond lead away from the queen leads the defence to suffer a similar fate - but consider:

a.       ♦Q lead

Close – but not good enough! Declarer wins in hand and cashes two more top diamonds and one top heart, then throws East in by leading his diamond deuce. East perforce wins the trick and now has to give the lead to dummy, allowing the pitch of the losing hearts. (If the ♦2 and ♦3 were switched between the North and East hands, East could avoid the endplay by unblocking his trumps from the top, but North could then draw all the trumps and get off lead with a small heart).

b.      ♥J lead

This is the killer! In fact declarer has to be careful not to go two down! If he wins in hand and cashes his top two trumps, for example, East unblocks with ♦9 and ♦7. He wins the third round of diamonds with ♦Q and plays back the ♦3. If declarer “carelessly” wins this, he is stranded in hand again and must lose two hearts at the end. So he must underplay his deuce!

Alternatively declarer can simply duck the opening lead of ♥J and East has no good lead to the second trick; he can always be endplayed to give dummy the lead for a pitch of the second losing heart.

Thank you to Jon Cooke for pointing this out to me. (I see from the travellers however that he and David Kendrick defended 5♦ and their opponents made twelve tricks, so sadly he did not have a chance to produce this brilliance at the table)

The Paradox of Percentages

This hand from the weekly pairs session provoked a bit of lively discussion between Mike Seaver and myself.

First, the bidding:

West	North	East	South
Pass	1♠	Pass	1NT(1)
Pass	Pass(2)	Pass

(1) In our system two over one responses are forcing to 2NT, so are usually based on a minimum of eleven HCP

(2) Conservative. Partner figures to hold at most two spades most of the time and ♥KQ may well not be pulling their full weight

A non-forcing 1NT response to one of a major opening is a definite weakness in Acol-type systems. On a (very) good day, you avoid getting too high with misfits - on a bad day, you play in a totally unsuitable contract. I think on my actual hand, passing was too unilateral and it would have been better to rebid 2♣ to keep my options open. Of course, if we would then have stayed out of 5♣ is  different question......

Anyway, how should Mike have played the hand on the lead of a the diamond deuce (fourth best) to the queen and ace?

In isolation the best way of playing this combination, according to the percentages, is to finesse twice, so he led the ♣10 and West played low.

Mike felt that the correct play now is to win with ♣A and lead a second club, making the contract whenever clubs were evenly split and also for those 3-1 breaks when the singleton was an honour.

I didn't agree: I favoured an initial finesse;

(1) If the ten holds but East follows suit, you can follow with a second round to the ace and then a third round of the suit. West will win and play a heart which you must win in hand, overtaking one of dummy's honours. You can then cash your three club winners, discarding dummy's small spades and play a diamond (or a spade), generating a ninth trick.

(2) But if the ten loses, say to the queen, the defence will come back a heart or a diamond and you lack the two entries necessary both to take the second club finesse and enjoy the long clubs.  You therefore have no choice but to cash the club ace and if clubs were originally 3-1, making only eight tricks. If the clubs started 2-2, you make your contract easily.

(3) The third possibility is that the ten holds but East shows out. You follow with a second club and West plays low. You can win with the knave and play a diamond on the (fairly safe) assumption that each opponent started with four. The opponents can generate a second diamond trick (by playing back a diamond) or a club trick (by playing a club) but not both.- you thus have time to generate two spade tricks before the defence have five tricks.

(4) The final option is again that the ten holds and East shows out. This time when you follow with a second club, West puts in a an honour card.and you win with the ace. You then follow with a third club and if West takes this, the hand reduces to hand (1) above. If  West ducks, again you have time to develop a second diamond trick and two spade tricks.

In summary, this line works when clubs are 4-0 onside, 3-1 when the singleton is not an honour, and all the two-two breaks. It therefore seems to gain approximately 5.0% of the time over the alternative of simply cashing the ♣A (but see below).

This got me thinking.

Under normal circumstances, finessing the first round - losing to an offside queen - and then playing for a 2-2 break after all is against the odds. The play of the queen affords an increased likelihood that the player does not hold the king-queen doubleton (this is the principle of restricted choice). Indeed, once East has produced the queen, the odds are two to one that he does not have the king.

However if you don't have the opportunity to lead a second round of the suit and see West follow, surely the odds favouring a finesse do not apply? When you are in dummy considering the likely division of the remaining two cards, the odds are just better than evens that cashing the ace will draw the remaining cards. It is only in crossing to hand and leading a club to take the finesse that the odds change.

One final thought: if you have determined to play the clubs by cashing the ace and then playing another club, are you not maximising your chances of an overtrick to lead a spade at trick two in case West has the spade ace and cannot afford to rise with it?

By the way, I may have won the argument, but I would have lost the war for the full deal was:

 
 

"Respect" or "A thing of beauty is a joy forever"

Reputations can be a dangerous thing....

Declarer, fresh from his success at the Pachabo,  played this hand well against my partner, Roger Salmon and myself, up to a point. Unfortunately a more mundane line would have worked rather better.

Holding: ♠K9 ♥A1094 ♦K109 ♣A972, North heard the bidding unfoold;

Dealer E

N- S Vulnerable

East	South	West	North
1♣	1♦	Dbl	2♣(1)
Pass	2♦	2♥	3NT(2)
Pass	Pass	Pass(3)

 

(1) Unassuming cue-bid

(2) Practical shot, can almost count nine tricks before dummy is tabled

(3) Disciplined. Shows respect for opponents - there seem to be a lot of points in this pack!

East, a sometime bridge blogger, led ♣K (king for count) and this is what declarer could see.

When declarer ducked the first trick, East followed by ♣Q, his partner following upwards to show an odd number of clubs, while North held off again, East paused for thought and then exited with a small diamond.

Opponents' hand pattern was pretty clear to declarer. West surely had five hearts and four spades for his double followed by his bid of 2H, leaving East with a likely 4-2-3-4 shape. Declarer has eight top tricks via six diamonds and two aces but needs to decide where to go for his ninth trick? A weak player might simply play a spade towards the king (having first cashed his diamonds), a slightly better player might win the diamond switch with dummy's queen and play for the defending heart honours to be split by leading ♥J from table.  However declarer looked more deeply into the hand and saw that he could still make the contract if West had started with ♥KQ and East ♠A. Either of the two earlier lines would fail if that were the case - which seemed a distinct possibility from the bidding.

Winning the diamond in hand he cashed six rounds of diamonds, West following for one round only and then discarding one club, two hearts and two spades, while East discarded two spades and a heart. Declarer could be pretty sure that this was the end situation.

                   ♠K9

                   ♥A

                   ♦None

                   ♣A9

♠??                                 ♠??

♥???                               ♥?

♦None                            ♦None

♣None                            ♣J8

                  ♠654

                  ♥J5

                  ♦None

                  ♣None

Declarer knew that East had started with ♣KQJ and ♦J - so where were his remaining points to justify the opening bid? Did he have the queens in both majors or ♠A?

If the former, he needed simply to lead a spade form the table towards his king; if the latter, he had executed a neat strip squeeze. With chances evenly balanced, he went for the "prettier" option. After  crossing to his ♥A, he cashed ♣A and threw East in by playing ♣9 to lead away from his ♠A for his ninth trick.

Except that I didn't have ♠A.

After winning ♣J, I simply played a spade to my partner's ace. His heart king won the setting trick.

The full deal:

A little unlucky perhaps - but declarer was effectively playing for me to have misdefended. Going back to trick three when I led a passive diamond - had I held neither heart honour, a heart switch from me would have been "automatic" - it could not cost the contract and it might be the only way to get partner in to lead a spade through declarer's presumed ♠K.

As it was, it seemed pretty clear to me that declarer had six diamond tricks and the club ace, together with stops in both hearts and spades. If he had held ♠A and ♥K, he would not have left me on lead to trick three, risking me playing a spade and thus generating three spade tricks to go with our two clubs and HA. True, partner might have held ♥K10, in which case a heart lead would generate tricks for the defence before declarer had established a spade trick by leading from table to his presumed ♠K. But how likely was it that declarer had bid 3NT with a  heart stop of A98x? If declarer had ♥A108x instead, leading a heart might easily result in North South making overtricks.

Moral of the story: while it is frustrating to go down in a contract when you had a chance to make it (due entirely to an opponent's misdefence), this is an occupational hazard. When working out why opponents have played the was they have, show them some respect - sometimes they even deserve it.

PS Just a small throwaway comment. When I was discarding spades on the run of the diamonds, I played the eight followed  by the two, signalling my length. In diffferent cirumstances with a spade holding headed by J108 or J109, I might have played the knave initially, to show the ten and deny the queen. Can you see how dangerous that would been on this hand? Knowing that I did not hold ♠Q, declarer would have been sure to place me with a top heart honour to justify my opening bid. And if I held a top heart honour, my partner must hold the ♠A to justify his bidding. When signalling, it is vital to recognise that you are not only signalling to partner but also to declarer.