Silver Plate

Our luck finally ran out in another tight match against a team from Sussex, when we lost by 5 imp. After a close loss there are numerous hands where all of us could have done something different and reversed the result, but the potential for the largest swing was on this hand where we lost 9 imp but might have gained 8.

I can see three ways to bid the West hand, given that the auction will be at the 4 level for your second bid.
(1) Bid 2♦ and then 5♣
(2) bid 2NT and pass
(3) bid 2NT and then double to show extra values.

Nothing is ideal. The first option is a bit too unilateral for my taste, the second is rather feeble on a 4-loser hand, and the third may give partner a choice of losing options (as here).

At our table Ann chose the first option and ended in 5♦ doubled. The opponents started with a heart and then South mysteriously playing three rounds of spades, so that Ann escaped for -300. A heart continuation would be a much stronger defence; declarer can escape for 3 down by playing just one round of trumps and switching to clubs, but is likely to lose control and go for 800.

In the other room West bid 2NT and left South to declare 4♥.  West cashed two clubs and then switched to a diamond.  The play is not easy as at least one of the major suits is going to break badly. At the table declarer started with two top hearts. This would have worked if West held a singleton spade and a doubleton heart, as declarer can now cash ♠A, ruff a club and lead a spade towards the K 9. When the trumps were unkind, he could still have succeeded by playing West for ♠10 x, but he tried to drop a doubleton queen and went one down.

The winning line is to run the ♥10 at trick 4, leading to an easy make (and an overtrick if you guess spades).

Is it being wise after the event to suggest that it is right to run the ♥10? We know that West has at least 10 cards in the minors and can assume that East has at least 5. (If he has fewer, West has at least 12 cards in the minors and would surely bid again.) In that case the odds on the major suit distributions are
          3-2      6%
          2-3      36%
          1-4      46%
          0-5      12%
A big difference from the a priori numbers! So cashing two top hearts has a 36% chance for the 2-3 break, plus about 9% for a singleton J, a total of 45%. 

What about the finesse for  ♥J? West has 3 'vacant spaces' and East has 8, so the chance of the finesse is 8/11 or about 73%. You probably wont be making if the trumps are 5-0, but that still leaves over 60%.

Is it possible to work this out in the heat of battle? Maybe. The vacant spaces calculation is easy enough so I think that you could estimate that the finesse is about 70%. The calculation of suit distributions is much more complicated (I used an Excel spreadsheet) but I think you should realise that bad breaks are much more likely after a 2-suited overcall, so that the finesse is a better play.