[Trumpace]

Ralph will probably like this question

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In the above end position, you need 2 of the last 4 tricks. hearts are trumps and opps are out of spades and hearts. 7 clubs are still out and you have no clue as to the distribution.

You are currently in the South hand.
[edited]
Suppose the chances that LHO holds the Club Q is x. (not this was about club A first, but i changed the problem based on awm and echognome's comments)
[/edited]

Is there some value(s) of x which will cause you to switch your line of play? (i.e if x > y then you take line 1, else you take line 2 etc (or something similar))

What will be your line(s) of play?

(Sorry if the question does not make sense , I can later try to clarify what I am getting at)

This post has been edited by Trumpace: 2007-August-20, 18:12

[awm]

Hmm I guess this should've been in hidden text... edited:

Spoiler

The normal line seems to be to play a club towards the seven. If LHO plays low then putting in the seven endplays RHO and the contract is cold. If LHO plays the ace or queen you're obviously making also. So assume LHO plays the nine or ten, you cover with the king. If LHO has the ace you've just made the contract. So say RHO wins the ace and returns a club. Now you can play the jack (hope RHO has queen) or the eight (hope RHO has the other of 9/T that LHO didn't play first round). Because of restricted choice, the eight is the better play. This makes any time:

(1) LHO has the ace of clubs.

(2) LHO has at most one of the ♣T9.

Overall odds are around 7/8 or 87.5%.

if LHO "probably has the ace" it doesn't change my line since I am always making if LHO has the ace anyways. If somehow RHO is "more than 75% likely to have the queen" then I could see putting up the jack after RHO wins the ace (like say RHO opened the bidding and is almost marked with ♣AQ).

[Echognome]

Hidden text added (in addition to Adam's comments):

Spoiler

But suppose, for example, that you *know* LHO does not hold the A. This is easily imaginable if LHO has shown enough points in the play thus far that he cannot hold the Ace and have passed throughout. Adam's line of putting in the 7 if covering a small card or catching two tricks if lefty puts down the A or Q is still true. But the question is what to do if lefty puts in the 9 or T? Do we want to still cover and guess on the Q or T (9)? Or do we want to duck? Here we need to know more than the chance that lefty has the A, but rather the chance that lefty has the Q. For example, if lefty holds QT9(x), we can make by ducking. Overall, I agree with Adam, that you would have to think the odds are very, very likely that righty hold the A to consider any other play than ducking.

[Trumpace]

Ok. Say x were the chances lefty holds Club Q (not club A as originally stated).

(I have also modified the original problem statement)

[Echognome]

Trumpace, on Aug 20 2007, 04:13 PM, said:

Ok. Say x were the chances lefty holds Club Q (not club A as originally stated).

(I have also modified the original problem statement)

Actually, you care about both probabilities. For me to deviate from Adam's line, I'd have to feel very strongly that righty had the A and lefty the Q.

[awm]

Spoiler

Well suppose there's a probability X that LHO has the club queen. If X is really high, it seems like you can play a club, and when LHO plays the nine or ten you can duck. Now you'll make by ducking LHO's return to the jack. This works if LHO has no club nine/ten (25%) or if LHO has the club queen, for overall about 1/4 + (3/4)X chance of success. For this to be better than my original line we need X > 5/6.

On the other hand, say X is really low. Now you can start with my original line, but when RHO returns a club put in the jack. This works if LHO has the club ace, or if LHO has neither T nor 9, or if LHO has no queen. Overall odds are 5/8 + (3/8)(1-X). This is better than my original line when we have X < 1/3.

[Trumpace]

Thanks for the analysis awm and echognome..

There are three lines, each of which might be right depending on the chances LHO holds Q... and that too in just a 4 card ending!

Add in the chances of A, and things get too complicated