At Sixes or Sevens

That we won our Silver Plate match against Anne Catchpole's team - Anne is the sister of Cambridge's Paul Fegarty - is due to a little luck and some solid declarer play by Victor Milman.

There was a little banter at the tea break regarding this slam deal which occurred in the first set.

In my room the contract was 6♠ by West and the lead was ♥Q. How would you plan the play?

♠AQ54		♠KJ83
♥AK1064		♥9
♦A6		♦KJ5
♣A6		♣K10754

Our table's auction was:

West	North	East	South
2♣ (1)	Pass	2♦ (2)	Pass
2NT (3)	Pass	3♣ (4)	Pass
3♦ (5)	Pass	3♥ (6)	Pass
3♠	Pass	4NT (7)	Pass
5♦ (8)	Pass	6♠	All Pass

(1) Benjimanised - showing various kinds of strong hand
(2) Forced
(3) Showing (ostensibly) 23-24 balanced
(4) Asking for majors
(5) Showing at lest one four card (or longer) major
(6) Showing spades
(7) Roman Key Card Blackwood
(8) Four keycards or one.

As dummy went down, Paul Lamford who was declarer said to his partner "Not tempted to try for seven?" Dummy muttered something about needing precise cards and then trailed off.

Paul won the opening lead in hand, ruffed a small heart on table and then cashed dummy's ♠KJ, both opponents following. A club to hand was followed by a second heart ruff with dummy's last trump - revealing the hearts to have started 4-3. Declarer now simply returned to hand with ♦A, drew the last trump and cashed his two heart winners and the minor suit kings for thirteen tricks.

As he took the last trick, Paul looked sternly at dummy, who quivered slightly.

This is undoubtedly a solid line of play at pairs where over tricks matter, but is it the best line in a small slam?

Hearts breaking 4-3 is a 62% chance and there are several additional chances even if they break 5-2 (assuming that spades break reasonably). One would be really unlucky to go down......

Victor Milman at the other table was also in 6♠ but this time played by East on ♣Q opening lead. Winning in dummy with the ace, he cashed ♠A, both opponents following, and continued with ♠Q. When trumps broke, he cashed ♣K and ruffed a club. In fact South had four clubs but also had the last trump, so dummy won this trick. Victor crossed back to his ♦K and ruffed another round of clubs successfully (establishing dummy' last club in the process). He followed with ♥AK, discarding the ♦J, ruffed a heart with his ♠J, drew the outstanding trump and claimed.

On this line of play, even if the third round of clubs had been over-ruffed, there was no way of preventing that ruff of the fourth round of clubs and establishing the suit for twelve tricks.

Now of course, there are distributions where Paul's line works better (notably in certain cases where clubs break worse than 4-2, and spades break 4-1) - but clubs breaking 3-3 or 4-2 is an 84% chance.

All much of a muchness, you may think - but Victor's line also seems to me have clear advantages if the spades prove to be 5-0 and the hearts 5-2 - certainly if the spade length is with South. Cashing the ♠A at trick two gives you more options of playing on cross-ruff lines if the bad break is revealed early, while ruffing a heart may prejudice your options.

Imagine the full deal had been:

	♠None
	♥QJ852
	♦10973
	♣QJ82
♠AQ54		♠KJ83
♥AK1064		♥9
♦A6		♦KJ5
♣A6		♣K10754
	♠109762
	♥73
	♦Q842
	♣93

 

After winning the opening lead with ♥K, you cash the ♠A and receive the bad news, North throwing a diamond. You next cash the three other aces in your hand (in true palooka fashion), discarding dummy's ♦J  - you are going to establish dummy's fifth club to play through South, so you must under no circumstances throw a club! You now follow with a club to dummy's king and a third round of clubs. What is South to do? Wriggle as he may, he cannot stop you from making five tricks from your remaining seven trumps. Say he discards a diamond, declarer ruffs and plays a diamond back to table; a fourth round of clubs follows. If he discards once more, declarer can again ruff small and take three top trumps. If South ruffs in, declarer overruffs with ♠Q, crosses back to table with a trump and cashes his now established fifth club. South can at last make a trump trick - but it is the last one for his side, and the slam makes.

Epilog

Thre are a lot of permutations on this deal - on most normal distributions of the opposing cards, the contract will make with either line. For the less usual distributions, sometimes it works better to winthe first trump trick in the East hand , sometimes in West. I'll let the reader judge.......

 

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: