What's the Right Line

Put yourself as East in the following hand. Press next to follow the play to the first trick and the next lead. What is your plan?






You have lost 1 trick already. If spades behave, you have no losers there. If they don't, you have 1 loser there. Clubs seem fine. Diamonds are now fine. But hearts are problematic. You could lose 3 tricks in the suit if you have to lead. In any case, barring extremely good fortune, you have 2 heart losers. So, at most one spade loser, and three heart losers, which puts you down one.

Can you do anything about the hearts?

What if the opponents lead hearts? Then you have at most two losers in hearts.  That will work.  So if you lose to the QS, you want the opponents to lead hearts.  They of course will desperately try to not lead hearts, so you must force them, by ensuring that you will get a ruff sluff if they lead another suit.  So we need to run ourselves out of the other suits.  That means two diamond ruffs, and we need trumps left in both hands.  Can we do this?

Here's an effort:  Win the KD.  Lead a diamond and ruff it.  Cash the AS.  Then the AK of clubs.  Then lead to the KS.  If the QS hasn't fallen, lead the last diamond and ruff it.  Great!  We've eliminated all the suits.  Now we lead our last spade to put the opponents in and ...

We no longer have a spade left on the board.  They opponents simply lead back a minor and we are in even worse shape than if we hadn't schemed, since now we have to lead from our KH.

If an opponent has three trumps to the Q, if we put them in with the trump, dummy will be void in trumps.  If we manage to put them in with a heart, they will lead the QS, and dummy will be out of trumps.  Our one shot is that we can put South in with a heart, and North will have the QS to three.  Then this only gains on a few heart distributions anyway.

So maybe there is nothing we can do.  So we resign ourselves to hoping either North has the AH or South has the QH, and play the KD, or that spades split.  We still plan to win the KD and ruff a diamond.  Eliminating suits is still a good idea.  If spades split, there may still be a heart endplay for an overtrick.  So we play the KD and ...

Oops.  In all our plotting, we missed a very real possibility.  North had a singleton diamond, and ruffs.  So we have a spade loser after all.  Now we need a heart trick (and no more spade losers).  We can try an endplay (and there is one double dummy-but I think it is against the odds).  Playing for either the AH in North or the QH in the south, we go down, as both are offside.

 

Given South's bid, it is certainly plausible that North has a singleton diamond.  If we work that out, what should we do on the QD?

We could play as above.  Or we could duck the diamond!  North can ruff a winner or not.  Later, we will use the KD to discard the 2H guaranteeing only two heart losers, and only one if the AH is with North (unlikely given the opening bid, but possible).  It's a close call.  We need either spades to split (~41%) or the  AH onside (~50% in a vacuum, less here).  In a vacuum, that's 70%.  Somewhat worse given the bidding, but our other approach succeeds when the AH is onside too, so we should remove that.  If spades split, we succeed with this approach and fail with the next.  So ~41% of hands.

Is that better than playing the king and giving up the ruff?  Our play is AH onside (~50% in a vacuum, less here) or QH with South (~50%).  The advantage to above is QH with South.  But, ~18% of the time, South has 3 spades to the Q, and we still have a trump loser.  Then QH onside doesn't help.

These percentages are complicated, and probably the final decision is close.  If you aren't sure that North had a singleton diamond then, rising KD and continuing is almost certainly best.  If you are, think about ducking.  It would have paid off here.

The moral?  Stop and think when you see dummy.  You may or may not find a better line, but you give yourself that chance.