From: desj@ccr-p.ida.org (David desJardins)
Newsgroups: rec.games.bridge
Subject: Re: Play this slam
Date: 29 Sep 92 15:55:47 GMT
Organization: IDA Center for Communications Research, Princeton

Ben Wing <bpwing@phoenix.princeton.edu> writes:
>[suggests trying to set up spades or finesse diamonds]
>
>Another possibility would be to play for a 3-2 heart break and for either
>player to have Kx or Kxx of diamonds.  My odds calculations don't come as
>fluidly as David's -- let's see ...
>
>20/32 for 3-2 heart break, (70/128)*(3/7) for 3-4 diamond break,
>(42/128)*(2/7) for 2-5 diamond break.  That's ... 20.5%.  Not so good.

I think that approximating the chance of a 3-2 heart break as 20/32 is
not good enough to get accurate results.  The true probability is
2*(5C3)*(21C10)/(26C13) = 67.8%, which is quite a bit larger than
2*(5C3)/2^5 = 20/32 = 62.5%.

By my results weren't right either.  I have been making mistakes on
virtually every solution I post.  That's what comes of doing these
postings late at night.

Let me show all of the computational details for a change.  Playing a
diamond to the ace works if either player has one of the following
hands:

    xx hearts &   Kx diamonds = 5C2 * 6C1 * 14C9 / 26C13 = 1.15%
   xxx hearts &   Kx diamonds = 5C3 * 6C1 * 14C8 / 26C13 = 1.73%
    xx hearts &  Kxx diamonds = 5C2 * 6C2 * 14C8 / 26C13 = 4.33%
   xxx hearts &  Kxx diamonds = 5C3 * 6C2 * 14C7 / 26C13 = 4.95%
                                                          ------
                                                          12.16%
                                                             * 2
                                                          ------
                                                           24.3%

Taking the diamond finesse, cashing the ace, and ruffing a diamond,
works if East has one of the following hands:

     x hearts &  Kxx diamonds = 5C1 * 6C2 * 14C9 / 26C13 = 1.44%
    xx hearts &  Kxx diamonds = 5C2 * 6C2 * 14C8 / 26C13 = 4.33%
   xxx hearts &  Kxx diamonds = 5C3 * 6C2 * 14C7 / 26C13 = 4.95%
  xxxx hearts &  Kxx diamonds = 5C4 * 6C2 * 14C6 / 26C13 = 2.17%
    xx hearts & Kxxx diamonds = 5C2 * 6C3 * 14C7 / 26C13 = 6.60%
   xxx hearts & Kxxx diamonds = 5C3 * 6C3 * 14C6 / 26C13 = 5.77%
                                                          ------
                                                           25.3%

Playing on spades works if West has one of the following hands:

    xx hearts &   Ax spades   = 5C2 * 4C1 * 16C9 / 26C13 = 4.40%
   xxx hearts &   Ax spades   = 5C3 * 4C1 * 16C8 / 26C13 = 4.95%
    xx hearts &  Axx spades   = 5C2 * 4C2 * 16C8 / 26C13 = 7.42%
   xxx hearts &  Axx spades   = 5C3 * 4C2 * 16C7 / 26C13 = 6.60%
                                                          ------
                                                          23.37%
                                                        / 88.69%
                                                          ------
                                                           26.3%

(The last division is to take the fraction of those hands where West
does not hold a small singleton spade; we assume that West would have
led the singleton.)

So now I think that the spade play is the best after all.  It really
rates to make more often than this, as the opportunity for misdefense is
high.

                                        David desJardins