From: bharat@cs.uiuc.edu (R. Bharat Rao)
Subject: Re: Do you go on?
Reply-To: bharat@cs.uiuc.edu
Organization: University of Illinois, Dept. of Comp. Sci., Urbana, IL
Date: Sun, 11 Oct 1992 07:33:49 GMT

adam@irvine.com (Adam Beneschan) writes:
>One more note on David Grabiner's hand: 
>[ref: <GRABINER.92Oct9124107@germain.harvard.edu> grabiner@math.harvard.edu]

>> N-S vul      AKxx            N   E   S   W    
>> Matchpoints  AQTxx           P   1D  1H  1S   
>>              xxx             P   2C  P   P    
>>              K               2H  P   P   3C   
>>                              P   P   ?        

>There were a few differences of opinion about what to bid on this hand, 
>which is good.  I like seeing different opinions, lines of reasoning, etc.;
>it not only makes for more interesting reading but it really helps me learn
>(and hopefully everyone else).

>Since I was the lone voice in the wilderness who thought 3H was right because
>partner is likely to have four hearts, I got really curious about what length
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
This is a wrong assumption.
>    Partner has >= 2 and <= 5 hearts.  (With less than 2 he wouldn't have
>        bid 2H;  with more than 5 he would have said something immediately
>        over your heart bid even with no high cards.)

With 4 hearts I would raise on 95% of all hands -- if N *does* have 4
hearts and did NOT raise right away it is because he has very few (and
very badly placed) HCP (like the DQ etc) and a very square shape
(like 3-4-3-3 or 3-4-4-2).  

Therefore, you should not even consider the scenario where partner has
just 4 hearts -- it is so unlikely that you don't even think about it
(and let alone 5 hearts).


>With all that in mind, here's the results:
>        Expected heart length:  3.63867
>        Expected spade length:  2.64406
>        Probability distribution of heart length:
>           [2] 12.4%  [3] 31.4%  [4] 36.0%  [5] 20.1%


>So it makes some sense to play partner for 4 hearts, but just barely.  If 
>you bid 3H, you will find partner with only 3 hearts a substantial portion
^^^^^^^^^^^^^^^^^^^^^^^^

No way is this analysis even close to correct.  Partner would ahave
definitely raised with 4 hearts (so multiply that 36% by 0.05),
strained to raise with 3 ...

The key point that you are missing is as follows.  GIVEN THAT PARTNER
DID NOT RAISE HEARTS RIGHT AWAY, the number of hearts partner has is
in some sense IRRELEVANT...

By which I mean, if partner does have 3 or 4 hearts, he will have such
a dog of a hand that 3H will be absolutely horrendous.  In fact,
paradoxically, you may fare better when partner has ONLY two hearts,
as the rest of his hand *may* be relatively better -- but that is
again irrelevant because as you don't want to be in 3H in a 5-2.

OK, now at this point partner's first pass should be enough reason is
pass now, but if you want to analyze the hand, lets see: opponents
probably have an 8 card club fit (could be 9, but 8 is probably
right).  That gives pard 4 clubs, and to be generous lets give him 3
hearts; lets say Kxx.  This remaining 6 cards are either 2-4 or 3-3 --
lets be nice and give him an absolute max with Qx,Kxx,xxxx,xxxx.
Opposite this MAGIC hand you have 8 tricks in 5H + 3S.  The 9th trick
will come provided (a) they don't punch a 4th diamond through for a
promotion (b) you can ruff a 3rd spade in dummy and (c) hearts break
3-2.  Of course give partner the same hand with a 3-3-3-4 and now you
have no hope for 9 tricks.

>The good news for 3H bidders is that
>RHO is more likely to have only one spade, which makes it less likely that
>3C will be defeated.  So 3H going down one still wins if you don't get
>doubled.  

Which is exactly *why* you will be doubled.  Opponents *know* that 3C
rates to make and that -140 (3H making) will be a very poor score.
The double is a totally free shot and I would expect any pair that has
even a smidge of MP experience to whack 3H on this auction.

The program did not compute the probability that your 3H would get
>doubled.  

>If we don't allow partner to have 5 hearts, the probabilities look like:

>        Expected heart length:  3.29536
>        Expected spade length:  2.74075
>        Probability distribution of heart length:
>           [2] 15.5%  [3] 39.4%  [4] 45.1%

>Anyway, I don't know what all this means in terms of what the best bid is,
>but it does make 3H look less attractive than I originally thought, and it
>makes pass look better.  It's a pretty close decision.  If we were 

No its not -- as I said above, these probabilities may be right a
priori, but are TOTALLY wrong given partner's pass.

>NON-vulnerable at matchpoints, 3H would still look like the best thing to do.

If partner did not find a 2H bid when WHITE, I am *SURE* that 3H will
go down 2 or 3.  So again pass is right.

>Well, if nothing else, I had fun figuring all this out.
>                                -- Adam

bharat
--
R. Bharat Rao                          E-mail: bharat@cs.uiuc.edu 
AI Group, Beckman Institute for Advanced Science and Technology
405 N. Mathews, Urbana, IL 61801  (217)-244-1263 (O) 337-6498(H)
Electrical & Computer Engineering, University of Illinois, Urbana