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

On Aug 20, 1:09 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

In the other thread, people showed that partner's heart length DOES
NOT vary depending whether or not we have a club or a diamond
singleton. What matters is the knowledge of the number of heart cards
(the interesting suit) and the non-heart cards. Thus, by switching the
singleton between club and diamonds, one should not expect the average
number of hearts in partners hand to change. This was shown using both
logical and empirical evidence.

To confirm that, I run a simulation, setting the following conditions:

1. West hand is fixed: Axx AKxxx x xxxx first and then Axx AKxxx
xxxx x
2. North has a 1D opening bid
3. South has 5-9 HCP, no 4-card major, 4 or 5 diamonds, if 5 diamonds
then no singleton

Here are the results for the number of hearts in East hand:

D Singleton C Singleton
0 0.02% 0.00%
1 6.85% 7.44%
2 25.94% 27.33%
3 36.02% 35.94%
4 23.49% 21.49%
5 6.85% 6.64%
6+ 0.82% 1.15%

Although there are some discrepancies (each simulation was run over 1
million hands satisfying the conditions), they don't seem to be
significant. The only disturbing artifact, was that EW are more likely
to have a heart fit when West is short in diamonds, not clubs: 67.19%
vs 65.23%. I don't see any reasonable explanation, but there they are
almost two percent difference on a fairly large sample.

The next thing to look at was the trick taking potential when playing
in hearts. Over 10,000 deals for each of the two variations (short C
or short D), I counted the tricks available to EW in a heart contract.
The result was 8.67 vs 8.28 for the long D vs long C respectively.
This brings an interesting (but not surprising) conclusion - the hand
will play slightly better in hearts when we it has length in the
diamond suit. Well it's better to ruff from the short trumps ...

While working with the hands, I noticed, that under these strict
conditions, East is quite likely to have long spades when West is
short in diamonds. This lead me to think that it might be worthwhile
to bid the West hand via a take-out double (only when short in
diamonds) - giving the best chance of finding a fit. To test this
strategy, I generated about 300 hands and I am going through them one
by one (couldn't come up with an elaborate enough quantification that
can be automated). So far it seems that a take-out double is a bit
better by a small margin though.

An interesting finding - doubling with 3514 - another tool to torture
partner at the table:).

Cheers,
Ivan
.

Relevant Pages