Re: Is length or shortness in the opponents' suit a plus when overcalling?

On Aug 20, 4:09 pm, Andrew <agump...@xxxxxxxxx> wrote:
There is much interesting analysis in Bill Cambell's thread on whether
length or shortness in RHO's suit is an advantage for overcalling at
the one level. It got me thinking about this related situation. You
hold one of these two hands:

Hand 1.
Axx
AKxxx
x
xxxx

Hand 2.
Axx
AKxxx
xxxx
x

Auction
(1D)-P-(2D*)-?

* = standard single raise

You'd overcall 2H with either hand, but which one is a better
overcall?

Larry Cohen says Hand 1.
He argues that with diamond shortness, the opponents are more likely
to have extra diamond length and that this has two positive
implications for bidding:
*  Partner is more likely to have extra hearts when the opponents have
extra diamonds.
*  When the opponents have an extra diamond, the total trumps are
increased by at least one and possibly two if partner also has extra
heart length, hence we can expect significantly more total tricks.

Mike Lawrence says Hand 2.
He argues that facing known diamond shortness in partner's hand:
*  the average number of hearts partner holds is increased
*  the hand will play well opposite diamond shortness since we can
ruff diamond losers in dummy and any values partner has rate to be
working.

So who is right? To answer we must break the problem into three
questions:
1. Does diamond length or shortness increase average heart length in
partner's hand?
2. Does diamond length or shortness change the variance in heart
length?
3. Does diamond length or shortness increase or decrease the number of
tricks we can take in a heart contract?

I suspect that Larry is right about question 1 (although the effect is
probably quite small) since a 9 or ten card diamond fit for the
opponents will increase the chance of catching extra heart length with
partner. However, the simulation will be interesting because on hand
2, the fact that partner passed while short in diamonds constrains his
possible shapes significantly. For example, he is less likely to hold
any:
*  6+ card suit (He might have preempted)
*  5-card major (He might have overcalled)

These constraints should strongly bias his shapes towards hands
containing 3-4 hearts. Opposite hand 1, Even though the opponents are
more likely to have a 9+ card diamond fit, partner could easily hold
shapes like: 4-1-3-5 and 4-2-3-4. Also if he holds a 5-card major or6+
card suit, he is more likely to hold bad outside shape that might have
discouraged him from taking a call.

On question 2, My guess is the variance in partner's heart length will
be smaller when holding hand 2. Even if partner holds more hearts on
average on hand 1, Partner probably holds hearts shortness less often
on hand 2. The average number of hearts partner holds is not as
important as the frequency distribution. For example suppose the
frequency distributions looked like this:

Heart length     Hand 1     Hand 2
1                      10%         2%
2                      20%        10%
3                      20%         50%
4                      30%         36%
5                      20%         2%
Avg length:       3.3            3.26

On hand 1 there is a 30% chance of catching a misfit. On hand 1 where
there is only a 12% chance of catching a misfit, we might do better to
overcall on hand 2 even though our average fit is shorter. Please note
that all percentages and averages were pulled directly out of my ass
and that until we have accurate numbers, any argument is pure
speculation...but interesting speculation I hope!

On question 3. I am virtually certain Mike is right. When we hold 4
small diamonds, we gain two enormous positive effects for scoring
tricks in a heart contract:
1. partner is known to be short in diamonds
2. partner's high cards are much less likely to be wasted in diamonds.

Which hand would you rather catch from partner:

Kxx
xxxx
Qxx
xxx

or

Kxxx
Qxx
x
xxxxx

Although we have an extra trump in the first hand, we have lost a
useful singleton and a working queen. The loss of these positive
features overwhelms the power of the 4th trump. So even though with
hand 1 opposite dummy 1 there are 2 more total trumps, hand 2 opposite
dummy 2 will take more tricks.

Any comments will be welcome and of course I'd be delighted if someone
wanted to run simulations.

Andrew

When the opponents have bid and raised a suit, hand 2 is much better.
This is based on the fact that partner will have no wasted values in
their suit. On Hand 1, partner could easily have QJxx in their suit
which is useless on offense but great for defense.

A better question would be which hand is better after a 1D opening on
your right. Lawrence (if I read the book right) would suggest not to
worry about having 4 cards in RHO suit. Not sure he says it is better
than a singleton.

Nick France
.

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