[kenrexford]

I had trouble assessing what to do last night with a specific problem type. I'd appreciate any input some may have.

Matchpoints. I was in a 3NT contract that seemed extremely normal. No major fits; no 7-card major semi-fits of real interest, and 26 HCP. Should be the field contract.

The lead seemed extremely normal. The line that any declarer would take would be identical throughout the room as to the first couple of tricks, and the defense will likely do the exact same thing my opponents did. (This is not exactly true, as there is a slight possibility that some will take a line on defense that suggests some extra reason for me to do what I wanted to do. I leave this out initially to establish a pure theory question.)

So, at a certain point, I end up in a position where I have two roads to possibly take.

Option #1: Concede a specific trick, which guarantees -1.

Option #2: Try a new line that no one else will try. That new line has odds to it, and the odds might be off a bit. But, assume for the sake of argument that the line has a 50-50 chance of resulting in the exact same -1, a 25% chance of having the game make, but a 50% chance that you will be down two tricks.

It initially seems that this new line will fail more than it gains, right?

So, how much additional information or inference would you need to overcome this odds problem?

The actual problem (not exactly within the parameters given):

Dummy: ♠Qxx ♥Jx ♦AQ1098 ♣Axx
Declarer: ♠AKx ♥Kxxxx ♦xx ♣Kxx

1♥-2♦-2NT-3NT.

A club lead is ducked and then won with the King. A diamond to the 10 loses to the Jack, and a third club hits. A spade back is followed by a diamond to the Queen, winning. The diamond Ace fails to drop LHO's King.

It seems that a fourth diamond will result in LHO winning the King and cashing the fourth club. Now, the heart King is protected, but the opponents must take a fifth trick.

However, LHO is now known to have started with 4-4 in the minors. With such an ugly club suit, LHO surely does not have four spades. He probably has 2-3-4-4 or 3-2-4-4 shape. On spades, however, LHO gave count of even, so 2-3-4-4 is extremely likely (LHO never falsecards). Thus, hearts split 3-3. If RHO started with A-Q-x, then I can make the contract by playing the heart Jack off of dummy. If RHO rises with the Ace, I win the spade return on dummy, cross to the heart King, give up the last heart, and claim. (If RHO jettisons the heart Queen, I still have one heart, two diamonds, three spades, and two clubs, for the -1 I started with.) If RHO covers the Jack with the Queen, I can duck and do the same essential thing. If RHO ducks the Jack entirely, I could float this and then repeat the heart hook. But, I could also panic in that situation, assuming that RHO only has the Ace, and rise with the heart King to THEN claim down one.

If LHO started with A-Q in hearts, he probably would have given a Smith Echo indication suggesting a heart switch when RHO wins the diamond, to be able to win that heart Queen before clearing the club suit. So, the chances of LHO having the A-Q in hearts seems lower than normal odds suggest.

[han]

kenrexford, on 2011-March-11, 10:56, said:

But, assume for the sake of argument that the line has a 50-50 chance of resulting in the exact same -1, a 25% chance of having the game make, but a 50% chance that you will be down two tricks.

I stopped reading after this sentence. I assume that you know that 50 plus 25 plus 50 does not equal 100, but I am too lazy to try to figure out what you meant. I think it should be the writer who makes an effort to ensure that the readers can easily understand what is meant, not the readers who have to figure out the idiosincratic language of the author.

[kenrexford]

True. Weird wording. What I meant was complicated by the actual problem.'

So, assume, I suppose, 50-25-25. 50% down more. 25% make. 25% same.