From: bjpt@cs.mu.OZ.AU (Ben Thompson)
Subject: Re: WC Problem - Full Hand
Organization: Computer Science, University of Melbourne, Australia
Date: Sat, 5 Sep 1992 05:40:30 GMT

A few comments and/or corrections...

desj@ccr-p.ida.org (David desJardins) writes:

]> AJ92
]> KQ7
]> 864
]> A75

]> K3
]> J43
]> A2
]> K96432

]I think that we all agree that there are two possible lines.  Line 1:
]Win the second diamond, try to run the clubs.  Line 2: Win the second
]diamond, establish two heart tricks, try to run the clubs, if clubs fail
]try for a miracle in spades.

]Everyone should also agree that, in order for Line 1 to have a higher
]probability of success than Line 2, the probability must be well over
]90% that diamonds are 4-4.  This is easy to see.  Line 1 makes 3NT, and
]Line 2 fails, when diamonds are 4-4, clubs are 3-1, and West's spades
]are QTx or QT or Qxxxxx or Txxxxx.  Line 2 makes 3NT, and Line 1 fails,
]when diamonds are 5-3 and clubs are 2-2.

You seem to have swapped the meanings of Line 1 and Line 2 for the
second paragraph.  Also, Qxxxxx spade with West is no help.


]Personally I would put the probability that diamonds are 4-4 at around
]60%.  A priori, K975 and K9753 have the same probability.  I would
]almost always falsecard with the latter.  A relevant observation is that
]East will know or strongly suspect that West is falsecarding; after all,
]if South had a third diamond then South would have ducked another round.

It is not necessarily right for South to duck a third round (if, for
example he has a weakness in spades or hearts - the last thing he wants
to see is West overtake with the K on the second round and pump and
embarrassing major through.  East cannot know this until later).

]But, the point of this article will be to show something else: even if
]diamonds were KNOWN to be 4-4, it would STILL best to play on clubs
]rather than hearts.

]So, assume that diamonds are 4-4.  The above calculation shows an IMP
]gain of 0.35 for Line 2 against Line 1, from making 3NT for +10 IMPs
]with probability 0.035.  However, we also have to consider what happens
]the other 96.5% of the time.

]On Line 2, when clubs are 3-1 and the spade queen is offside you will go
]down at least two tricks instead of one.  (Losing one spade, one heart,
]three diamonds, and one club.)  A significant fraction of the time you
]will in fact go down three tricks.  (If the opponents have the foresight
]to duck a round of hearts, win the second, and then clear the hearts
]after the diamonds.  After all, they know that diamonds are 4-4 too.)
]But, even ignoring that, the extra undertrick is an IMP loss of 0.49 for
]Line 2 against Line 1, from down two for -2 IMPs with probability 0.247.

You may choose to avoid the chance at 3 down if West doesn't produce
the S10.  If you think the other team got to 5C and it seems like you
are going 3 off if the finesse loses, then you shouldn't take it.
You may, on the other hand, attempt to save 2 imps at the
risk of 1 if you think the opponents will take line 1 in 3NT.

You also have to consider the true value of 10 imps vs 2 imps.  It is
considerably more likely that the winning margin will be 3-10 imps
rather than 1-2 imps.  Given that Line 1 is only some fraction of an imp
better than line 2, it is clear that line 2 is more likely to win the
match for you than line 1.

This is not to mention the psychological effect on your opponents of
bringing in a 'miracle' game like this (or the flip side - your own
depression and their glee at you going down in a contract you could
have made).  You think state of mind shouldn't matter?  What can I
tell you - it does.

No board is an island unto itself.

Ben
Newsgroups: rec.games.bridge