Re: 11 pts opposite weak NT

On Jul 11, 8:55 am, Nick France <gandal...@xxxxxxx> wrote:
On Jul 11, 8:26 am, "Keith Sheppard" <keith-shepp...@xxxxxxxxxxxxx>
wrote:



Traditionally, with 11 opposite partner's weak (12-14) NT opener, one would
invite. At IMP, when you cannot afford to miss game if it's there, that
seems to be sound policy. What about pairs though? Now the magnitude of
the expected gain/loss is unimportant. You just need to do as well, or
better, than the others with your cards.

Let's assume, for the sake of argument, that partner's 1NT could be 12, 13
or 14 with roughly equal probability. You've got a flat 11 count with
nothing really extra going for it.

There is only a 1 in 3 chance that our combined count is 25. Suppose we
assume, rather simplisticly, that 25 means we can make game and 23/24 means
we can't. In that case, inviting gives us a 1 in 3 chance of improving our
situation and a 2/3 chance of just making it harder for ourselves and
increasing the probability that partner will go off.

OK, there are some pretty rocky assumptions in there. Certainly with 23/24
you would hope to be able to make 2NT most days. On the other side of the
equation there are times when you can't make 3NT even with 25.

Assuming these considerations balance out, does that mean that, at pairs,
you would show a profit in the long term by passing 1NT with a bland 11
count? I guess the same question arises if you play, say, 15-17 NT and have
8 points as responder. Any thoughts?

Keith

It seems to me you have made a lot of assumptions that just aren't
right. First in a 12-14 point notrump, 14 points happen less than
33%. If we assume that the distribution of 12,13 and 14 point notrump
hands are similar to having 12, 13, or 14 point random hands (not
exact but fairly close) then you get the following distribution.

12 38.9%
13 33.5%
14 27.6%

Yes, but the relevant percentages would be the chance of each number
of points conditional on the given 11 point hand. I thought that would
make a big difference (the relative chance of 14 pts vs 12 pts does
change a lot if 27 points are known opposite), so I was a bit
surprised at these results for the conditional probabilities:

12 40.2%
13 33.4%
14 26.4%

My numbers, like Nick's, are based on hands with the given points
irrespective of distribution. However, I suppose the effect of
limiting the distribution would have even less effect than
conditioning on 11 points opposite. (Incidentally, as a partial
validation of my calculation, along the way I confirm the numbers Nick
cited.)

-- Charles

.

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