31 Finesse or drop

ª K 10 5 3

¨ 9 4

§ Q 10 8 4

ª A 4 ª J 8 7 2

¨ K J 10 8 ¨ 6 3 2

§ 9 7 6 3 2 § A K

ª Q 9 6

¨ A Q 7 5

§ J 5

South West North East

1NT Pass 2§ Pass

2© Pass 2NT End

West led ¨8, not one from any book I’ve read. Declarer won with ¨9 in dummy and should have attacked clubs immediately but chose to play a spade from dummy. He played ªQ and West ducked smoothly. Declarer then played §5 to §Q and §K. When East returned ¨6 he won ¨A (playing ¨7 would leave West on play with no good continuation). Declarer now played §J to East’s §A. Two rounds of diamonds followed, North discarding two spades and East one.

After that poor start from both sides this was the position:

ª K

¨ --

§ 10 8

ª A ª J 8

¨ -- ¨ --

§ 9 7 6 § --

ª 9 6

¨ --

§ --

If East had held the spades declarer would now be several off – three diamonds, three spades and two clubs.

But West had no good exit so played a club. Declarer spurned the finesse (surely right at this stage) and was surprised to see East discard. So West had four diamonds and five clubs. He cashed ©A Q and had another decision point. It was not his day and he played for the drop. One down.

On the diamond lead if he had played a club I would expect him to come out with eight tricks, possibly nine. East would return a diamond to ¨7 and ¨10. West would play a club to §A and another diamond would establish the fifth trick for the defence while still holding ªA. But any deviation would give him another trick.

Ignoring the start, what should declarer play from South on the third heart assuming East plays a small card? A losing finesse would mean two down, playing for the drop went one down. First, consider the likely play at other tables. Most people would lead a club with five. East would win and return a diamond to ¨10. West would probably play another club and end up with six tricks.

So one off looks like the “room” result. In that sense playing safely for the drop will give you a “normal” result or a good one. You have escaped two off as the spades were blocked. But in a low standard game some silly results are likely and defence will be the weakest point so going down one will score around 30% (actually 7/24) while making will score around 75% (actually 18/24). Going down two will be a zero.

Hearts 3-3 or 4-2	3-3	4-2
Play for the drop	75%	30%
Finesse	0%	75%

At first sight that looks a clear winner for the drop. At least a 30% board with a chance of 75%. But now let’s look at the percentages for success. With West holding nine minor suit cards and at least one spade the odds are skewed in favour of the finesse. In fact they become 70% in favour of the finesse and 30% against. So the above table needs to be reconsidered to calculate the expectations not the outcomes.

Now it’s not so clear. The finesse will give an expectation of 53% (0+0.7 x 75%) while the drop gives 43% (0.3 x 75% + 0.7 x 30%). So if it’s at the start or middle of the competition the finesse looks better. Late in the day with a winning score you might be tempted to go for at least a 30% result.