On May 8, 8:05 pm, Douglas Newlands <
douglas.newla...@gmail.com>
wrote:
[CB] I'll mark my comments with [CB]. Yes, that's the beginning of my
comments.
> or if there is another set of comments which haven't come through..
> Which Blog were you on?
[CB] "Blog"? And who is "you"?
[DB]
> First level - Agree
>
> Second level - Disagree
> He is ignoring the fact that you have seen 3 of the opponents cards at
> the key moment in time.
[CB] More precisely, I'm ignoring what they are since, according both
to the jfn post to which I was replying as well as to your original
post, we explicitly do not know what they are.
[DB]
> Assume opponents are sound and play small cards at random (not
> necessarily true)
> If W has played the 6 and then 7, and assuming that he has a third card
> (otherwise there is no winning line) then he was dealt with 678 or 67Q
> and East 8T or TQ.
[CB] Thus DB has changed the problem by pretending that the spots are
known. This isn't necessarily a big deal, but it is a way to introduce
confusion and make the problem more difficult. I know what he will
say: "Ok, I understand we don't know the actual spots played but we
know SOME spots were played and in order to talk about them
conveniently I'll assign them names '6' and '7', whatever they
actually may be." A small problem with that is that some spots may be
treated differently than others by the defender, so to get around that
our correspondent had to stipulate random play. As I analyzed that
stipulation was unnecessary. The big problem is that DB has in effect
stipulated that from 876 defender always conceals one particular card
-- namely the one that is for convenience being called '8'. This
stipulating can be dealt with by the so-called "restricted choice"
argument, but some people find it hard to grasp and anyway if we don't
invent difficulties from the beginning we don't need to deal with
them.
[DB]
> (Note that the problem you gave me originally did not
> specify that the T had been played.)
[CB] That seems to be a private note from DB to Doug. On
rec.games.bridge we knew.
[DB]
> If E always plays the T from T8
> then it is equally likely that he has T8 or TQ.
[CB] Now DB has fallen into real error, because by assigning a
specific name "108" for the holding that is actually "10x", he
automatically overlooks the need to consider restricted choice.
Vaguely put, the point is that 108 is one holding while 10x is three
holdings and the consequence is that if you insist on labeling the
actual spot played (e.g. as "8") then you must consider the restricted
choice argument in order to back out of the confused start and come to
the right answer.
[CB] The easier approach in my opinion (opinion re the best way to
understand, not opinion about mathematics which of course isn't a
matter of opinion) is to think about "policy". By that I mean imagine
a declarer who adopts a particular policy and then calculate how
successful that declarer is.
[CB] In this case -- "second level" -- we are assuming that RHO has
played the 10, always plays 10 from 10x and also from Q10, and since
those are the only cases of interest when the 10 appears, we may as
well assume that one of them is the case.
[CB] If declarer's policy is always to finesse when faced with this
situation, declarer will succeed whenever RHO was dealt 108, 107, or
106, and fail when RHO is dealt Q10. Hence this policy succeeds 3/4 of
the (relevant) time, and of course the alternative policy of "drop"
succeeds 1/4. Note that this analysis doesn't require any assumption
of random spot play by the defender.
[CB] In summary, DB complicated the problem by changing it, then
failed to cope by taking into account LHO's restricted choice of spot
plays from Q76 versus freedom of choice from 876.