[fuburules3]

Scoring: MP

1♦-P-P-X
P-1♥-P-1♠
P-2♦-p-2NT
P-4♠-P-P
P

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Lead is K♥

Playing in a robot duplicate, how do you play spades in this contract? GIB will open an occasional 11 count and many (most?) 12 counts, so E could just barely have the K. What are the odds of playing for the drop versus finesse here?

[lamford]

Let us say for a moment that West does not open 11 counts, to keep it a bit simpler. West therefore must have the ♥KQ and the ♦A. East can have the king of spades, or one or both of the queen of diamonds and jack of hearts. Or he can have none of those. East is favourite to have one high card - West is more likely to have 12 or 13 points than 15. It is a bit complicated now, as there are available spaces to consider when the great dealer from the sky allocated the remaining high cards. For East, the chances of a single high card are about the same, and of both the queen of diamonds and jack of hearts about half of that. He is around 1 - (10/23*9/22*8/21) or 93% to have at least one of the three cards! I think therefore that the chances of East having the following cards are about as follows:

King of spades only: 27%
Queen of diamonds only: 27%
Jack of hearts only: 27%
Queen of diamonds and Jack of hearts 12%
This is only approximate, as the fact that West opened a diamond will change things somewhat.

So, we have the finesse as 27%, and the drop is a lot worse. True, West is 73% to have the king of spades, but its chance of being single is only about 10%, so around 7.3% overall.

Some of my approximations may be inaccurate, but the difference is enough to convince me that the finesse is easily the best chance.

[quiddity]

The drop also offers the possibility of an endplay if LHO has Kx. You can duck the first heart, win the continuation, cash the ace of spades, and then try to strip hearts and clubs and eventually throw LHO in with the spade.

I have no idea whether this adds enough chances to make the drop a viable option.

[lamford]

quiddity, on Sep 15 2010, 07:47 PM, said:

The drop also offers the possibility of an endplay if LHO has Kx. You can duck the first heart, win the continuation, cash the ace of spades, and then try to strip hearts and clubs and eventually throw LHO in with the spade.

I have no idea whether this adds enough chances to make the drop a viable option.

Yes, ducking the heart, winning the next, crossing with a club and ruffing a heart, crossing with a club, and guessing whether to cash another club or ruff another heart before playing ace and another spade may be the best line. Too tough, and too late to work out all the odds.