From: adam@irvine.com (Adam Beneschan)
Newsgroups: rec.games.bridge
Subject: Re: Do you go on?
Date: 11 Oct 92 01:11:05 GMT
Organization: Irvine Compiler Corp., Irvine, California, USA


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
I could actually expect from partner.  I threw together a C program that
computed all the possible distributions of the other three hands, satisfying
certain criteria, and computed the expected length of partner's heart suit.
The criteria were as follows:
    
    LHO has 5 or 6 spades for his bid.  (With >= 7 he probably would have
        rebid spades.)
    LHO has at least 4 clubs (since he competed in partner's second suit).
    LHO has more clubs than diamonds (since he didn't take a preference to
        diamonds).
    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.)
    RHO has fewer than 3 spades (since he didn't support spades).
    RHO has at least 4 clubs and 4 diamonds, but he is not 4-4 in the minors
        unless his distribution is exactly 1-4-4-4.  (Many people systemically
        open 1C with a flat hand and 4-4 in the minors.)

My program considered only distribution, not high-card strength.  Certainly,
since RHO has to have enough to open, and LHO has to have enough to respond,
the program counted a lot of hands that shouldn't be counted.  I don't know
how much effect this would have had on the probabilities it computed.  Also,
there are many hands on which partner would not have bid as he did.  With 
many hands with only two hearts, he would not have balanced with 2H.  (E.g.
with xxx xx Axxx QJxx, he probably would have preferred to defend 2C.)  Also,
with many hands with three or more hearts, he would have supported your heart
overcall at his first opportunity.

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
of the time.  Also, the spade length tends toward 3, which makes it more
probable that you have a spade loser.  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.  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 
NON-vulnerable at matchpoints, 3H would still look like the best thing to do.

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