Ed Scerri gave an excellent seminar on Saturday in Richmond Bridge Club on Winning Pairs Tactics.  There was something there for everyone but one deal caught my interest in particular.

Ignoring the 6-2 break for the moment the issue is whether to try for the contract or to play passively for one down.  By playing on clubs declarer can ensure eight tricks if hearts break 5-3 by playing on clubs.  If the hearts are 4-4 he will make the contract with three clubs, three diamonds, two hearts and one spade.  There is an alternative line – play on spades.  If East holds both honours nine tricks will trundle in but if West holds either honour only eight are available (three spades, three diamonds and two hearts).  And if West holds both honours declarer will scramble only seven tricks for two off.

So, playing pairs, what is the “best” line?

Unless hearts are 4-4 some declarers will be going one off by playing on clubs.  Others will make 7-9 tricks by playing on spades.

Now the bidding comes into the picture.  If it was 1NT – 3NT West might lead a spade with 4-4 in the majors.  That tends to indicate five hearts.  But if it went 1ª - 2§ - 2NT – 3NT West would lead hearts with four or even three.  It’s probably not a very important point but the lack of a spade lead does seem to indicate 5-3 hearts.

Finally the issue of how you are doing in the session comes into play.  If you need a top you might play on the spades but of course you will be joined by all the pairs who did not attend Ed’s seminar and try for the contract whatever the odds. 

If hearts are 5-3 and you go two off (18.3%), you will score badly, possibly a bottom.  If you go one off (52.3%) you will get a fairly average result shared with those who played on clubs.  But if you succeed (29.4%) you will get a good result, possibly a top.

If hearts are 4-4 and you play on spades you will get essentially the same results since you have no time to set up a club trick if both spades are wrong unless the long diamond has no entry.  The revised percentages are: two off 23.5%, one off 53.0% and making 23.5%.  But you have given up the certainty of making however the spades lie.

A priori (the mathematician’s equivalent of a doctor saying “you have a virus but I don’t know which”) the chance of a 4-4 split in hearts is 32.7% while the chance that West had precisely five is 23.6%.  But if West had 4-4 in the majors the odds change – he would be equally likely to lead a spade unless they had been bid.  Or a diamond if held five, not so wildly unlikely.  So by the principle of “restricted choice” the odds are reduced that West has four hearts.  There is also the possibility that West led from ©K x x.  In that case the suit is blocked for the defence and they can only cash one trick quickly while if he led from ©x x x they can take three but in that case East will probably win the first trick.  Since it is otiose to calculate the odds exactly I’m going to assume the 4-4 break is equally likely as a 5-3 break.

Results:

Playing clubs produces eight tricks 50% of the time and nine tricks 50% of the time.

Playing spades (winning ¨K in dummy unless East wins the first trick and returns a heart) and finessing ª10 produces nine tricks 26.4% of the time, eight tricks 52.7% and seven tricks 20.9%.

For my money that is a clear winner for playing clubs first.  Unless West led the heart extremely quickly.

Ed subsequently pointed out to me that another reason for playing clubs immediately is that the defence might duck and then declarer could turn to spades with a 75% chance of making nine tricks.  That raised a possibility in my mind – what if West held both ªK and ªJ but the hearts break 4-4?  Now two expert defenders might duck the club, seeing that there was no hope of beating the contract by hearts alone.  Declarer then switches to spades and loses two spades, two hearts and two clubs for a bottom.  If that happens both defenders will be tall and one will have a Swedish accent! (I’m tall but I wouldn’t find that defence at the table).  Of course West might be a Pakistani resident in USA and win first with ªK (he did that to me once).