```  Two hands and a windy analysis from Gryphons II. Saturday, March 24, 2001.

Jim Plank, with commentary by Kevin Wilson

Since I was not at the game, I can't give any first-hand account
of the boards, but when I was looking over the hand records,
two boards seemed intriguing.

And after some back and forth with Kevin, you get a *very* windy
analysis, but you might find it enjoyable.  I know I did.

First was board 6. My prediction was that no two scores would be
the same:

Board: 6   Dealer: E    Vul: E-W

First, look at the east hand:

S KJ8
H K4
D QJT653
C J3

What would you open?  I'm guessing that arguments can be made for
1D, 2D, and pass.  I'd open 1D, since it fits the rule of 20 (The
suits, and open if the total is 20 or more.  Here we have 11 high
card points, plus 6 for diamonds and 3 for spades, giving a total
of 20).

Some might not like the soft values and lack of quick tricks, and
so would open 2d if their system allows, or pass if their system
doesn't allow it.

Still, I'm in the 1d camp.

Kevin: Its not great but I'd open it 1d also.  My weak 2s only go up
to 10 HCP because of the rule of 20.  If I played weak 2s through
11HCP (which I'm not recommending) I'd open it 2d.

South passes and west responds 1H.  Now look at the north hand:

S 54
H AQ
D AK982
C AQT7

What is your bid?  You have 19 HCP, but no easy shape to show.  I
think cases can be made for double, pass and perhaps 1N.  All have
warts: partner might mistake you for having spades if you double; 1N
seriously understates your values, but since partner likely has 4
points or less, that may not matter, and pass might confuse partner
when you come in later.  Right or wrong, I'd choose double -- if
partner bids spades, and I correct, he/she should be able to figure
it out.

Kevin: When I used to double with these hands, partner usually jumped
in spades and we went negative.  If you think about it, it is highly
unlikely that you have game.  Partner wasn't strong enough to
overcall 1s or distributional enough to preempt, so where are our
tricks coming from???  Diamonds aren't likely to be breaking
either...  Experience has taught me to pass.  1H doesn't end the
auction.  I may get to come in later if it looks correct but it all
likelihood I will pass throughout and get a plus on a hand where
whoever defends gets the plus.

Regardless, I imagine east will bid 2d.  Now look at south's hand:

S AT97
H 9853
D 74
C 865

Do you open your mouth with a free bid of 2s, complementing partner's
presumed suit?  I don't think so -- even though I don't relish defending
2d, I think I'd pass.

Now look at west's hand:

S Q632
H JT762
D
C K942

The 1H call was easy, and I think the bid over 2d is easy too --
pass.  Partner should redouble with 3-card heart support.  It's a
misfit auction, so let's go quietly and hope that the opponents
bail us out.

Back to north.  The bidding has gone thus far:

E     S     W     N
1D    P     1H    X
2D    P     P     ?

Well, I'm lost.  Double shows a huge hand, but do I really want
partner to pull it to spades?  2N is risky, and I don't think
partner is going to have many entries to take finesses.  Like it or
not, I think I'm passing.  Perhaps this is a good reason why
passing the first time is a good idea (this is what Suzy
recommended when I asked her, and it appears that Kevin agrees).
Certainly if I passed the first time and 2d gets passed around to
me, I'm happy to double, since partner will know it's penalty.  And
I like defending 2d.

So were I in all four seats, east would be declaring 2d, undoubled.

I'll be interested in hearing Kevin's sequence.

S 54
H AQ
D AK982
C AQT7

S Q632          S KJ8
H JT762         H K4
D               D QJT653
C K942          C J3

S AT97
H 9853
D 74
C 865

2d is no picnic, mainly because of the lack of entries to the
dummy.  Looks to me like you'll be losing a spade, two clubs,
one heart if you make judicious use of the SQ as an entry,
and probably three diamonds.  Down two or three certainly seems
reasonable.

Kevin: I actually did play this hand.  Our auction:

E     S     W     N
P     P     P     1D
P     P     X     2C
2S    X     P     P
P

It was an easy double for me (south).  They were both passed hands
and they were contracting for 8 tricks when I had at least 2 and
maybe 3 trump tricks and partner bid twice even after I showed a
bust.

Here are the scores from Saturday:

- Best N/S result was +800 for George Hall and whoever he was
playing with at the time (Kevin -- see above).

- Next came Glenn Reider and Brad, bringing home 3N by some act
of god.

- Then a +300 (diamonds, undoubled), a +120 and a +110 (clubs or
diamonds making three perhaps), and that's it for the N/S plus
scores.

- Now the E/W winners: Jim and Ben chalked up 730 -- 3H doubled
making three is my guess.  I'm sure Ben will claim that it's
another top for the Big Ben system, and who am I to argue....

- Next came the defenders: Mark and Carol Harris making 150 and
there was a +100 and a +50.

As predicted, no two scores the same....

------------------------------------------------------------

Another hand that caught my eye was board 19:

Board: 19   Dealer: S    Vul: E-W

S AKJT
H A6
D K842
C J65

S 85
H KQ7
D AT963
C AT9

First -- what's the best contract and what are its chances?

If diamonds split 2-2, 6D is ice cold even after a club lead -- 5
diamonds, three hearts, two spades, a club and a club ruff (after you
pitch one of north's clubs on a heart).  If diamonds split 3-1 or if

they are 4-0 and the planets are aligned (and you started them from
the right side), then you have to bet the farm on the spade finesse.

So that is roughly 35% for the 2-2 split, and failing that, 50% for
the spade hook.  That makes it roughly (0.35 + 0.65*0.50 = 0.675)
67.5 percent -- certainly a good slam.

6N needs diamonds to split and for the club honors to be split or in

the east hand: (0.35 * 0.75 = 0.262) 26%.  Note that's a better
chance than taking the spade finesse, although I imagine the best
chances are to play the spades off the top after taking club finesse

#1 in case the queen drops doubleton.

Kevin:  I agree that 6D is a percentage slam to make but there aren't
any reasonable auctions that I can visualize to get there.

Given that, is there any way to find 6D?  On saturday, no one
appeared to -- there were three 490's, five 520's and a -200.

I'm guessing bidding went something like: 1d, 1s, 1n, 3n, making
seven after a spade lead and hook, and making 6 if south never
took the hook.

Perhaps if you play some variant of new minor forcing, you there's
a chance to find the slam.  For example, after 1d, 1s, 1n, some
partnerships play 2c as artificial and forcing for one round.  Some
(mine, for example) play 2d as artificial and forcing to game.
These let you show your shape so that you can find major suit fits,
and sometimes to find minor suit slams (and, of course, give the
opposition maximal information so that they can find the best
opening lead and defense when you eventually settle in 3N....).
After either bid, south's first obligation is to bid a three card
spade suit, and after that, a four-card heart suit.  Here south
should instead bid 2d over 2c, or 3d over 2d.  With a guaranteed
9-card diamond fit and probably between 28 and 30 high card points,
north might try to push on to a diamond slam.  At matchpoints, it's
doubtful, though, that north would like to move beyond 3n.

Here's a nice, crazy bidding sequence that me and my partners might
find if we had a few drinks before the game:

S       N
1d      1s
1n      2d
3d      4d
4n      6d

2d = 2-way new minor forcing: Artifical and forcing to game
3d = 5+ diamonds, denying 3 spades and 4 hearts
4d = Roman key card for diamonds -- this is the one that north
would not want to risk at the table, since if partner shows
one, we have no idea if clubs are stopped.  And we may not
be able to stop in 4n.
4n = Two key cards but no QD,
6d = After making the adrenaline 4d bid which pretty much commits
us to diamonds instead of notrump, and may have us in 6d
with the opponents cashing club tricks when 3n was cold,
we bid 6d, confident that at the very least that we aren't
losing two off the top.

Chalk up 920 and a top.

S AKJT
H A6
D K842
C J65

S Q973          S 642
H 98543         H JT2
D 75            D QJ
C 43            C KQ872

S 85
H KQ7
D AT963
C AT9

Kevin: Would you really bid 4d as keycard looking at a 16 count with
no 5 card suits and no singletons knowing that partner has at most a
14 count and no singletons either?  Oh yeah...  you'd been drinking,
nice auction.  I wanted to comment that this hand went against the
lesson I had just taught on restricted choice.  If you led the ace of
diamonds out of your hand then you probably would finesse on the way
back when E dropped the Quack (Q or J) and it wouldn't work this
time.  I think that's where the +490s came from.  I also played this
hand in 3nt with a spade lead.  I played diamonds starting with the
K.  Although it is only a slight inference, I played them that way
the lead and that was all I had to go on so I figured that if either
hand had longer diamonds it was likely to be E with the length.  Had
W dropped either the Q or the J on the 1st round of diamonds, I would
have finessed.

Ok, back to the 6d issue, because although it is crystal clear to
Kevin, it's not to me.  The question is -- after 1d-1s-1n-2d-3d,
should north chance the diamond slam in preference to 3n?  Let's
make the following assumptions: 4d over 3d is key card in
diamonds, and if south bids 4h or 4s, 4n is to play.  And suppose
that north decides to to bid 6d if south shows 2, but 4n
otherwise.  How are we faring?

Kevin:  Follow this thought carefully everybody... it is very good.

Before getting to that, what kind of hand opens 1d, rebids 1n
over 1s, and then 3d over 2d?  I think the only one would be
a 2353 hand with 12-14 points.  With 4 clubs, you'd probably
bid 3c over 2d, and with 4 hearts, you'd bid 2h over 2d.

So, I simulated 10000 hands opposite AKJT,A6,K842,J65 and of
those, 164 were 2353 hands with 12-14 points.   I divided
these into two classes -- those showing two key cards, where
we're in 6d, and those showing fewer, where we're in 4n.
They were split roughly 46/54.  I went over 40 of the
6d hands, and assigned percentages to their chances of success,
and got that the expected percentage of success was 59.7%.
If south has the queen of diamonds, that went up to 68.9%
(if south has the QD plus two aces and no other cards, it's
always 50%.  Give south the QS and it's 100%.  Etc.).

So here's the breakdown:

2 aces plus the queen:

20.5% of the hands.
Slam makes 68.9% of the time.  No idea about 3n, but
it certainly can go down some of the time. (actually,
this is wrong -- 3n is cold, but it's now later, and
I don't have time to change the numbers).

2 aces, no queen:

25.2% of the hands.
Slam makes 52.2% of the time.  Again, no idea about 3n.

0 or 1 ace.

54.3% of the time.

Now I'm going to make stuff up since I don't have the time or
the inclination to go over how hands fare in notrump:

Suppose that if south has 2 aces, that 3n makes 90% of the time.
And suppose that if south does not have two aces, 3n makes 85%
of the time, and 4n makes 75% of the time.

Then you get the following for three bidding strategies.

- Bidding 3n -- you get an average score (plus or minus depending
on your brilliant declarer play and the defense)

- Bidding 6d on two aces, and 4n otherwise:

On 20.5% of the hands, you will get a top 69% of the time,
and a bottom probably 21% of the time.  I'm guessing
that on 10% of the boards, both 6d and 3n go down because
they both rely on bringing home diamonds/spades before the
opposition cashes their hearts.

On 25.2% of the  hands, you will get a top 52.2% of the time.
Let's say 10% of the boards will have 6d/3n match, so you
get a bottom on 37.8% of the boards.

On the remaining 54.3% of the boards, you will get an average
75% of the time, and a bottom on 25% of the boards (if both
3n and 4n go down, 4n goes down more).

Let's assign 10 to a top.  This gives:

.205 * (.69*10 + .1*5) +
.252 * (.522*10 + .1*5) +
.543 * (.75*5)

= 4.99  -- No difference from the first strategy.

If you change assumptions --

4n makes 80% of the time:             5.13
4n makes 70% of the time:             4.86
3n makes 85% of the time with 2 aces: 5.10

- Bidding 6d on two aces and the queen, and 4n otherwise:

(Let's suppose that 4n makes 85% of the time with
two aces and no queen): 4.62

So, I'd say it's not crystal clear that you should ignore 6d in
favor of 3n.  I don't think I'd have time to do this analysis at
the table though....

(Another consideration is that south might be 2254 or 1354 -- if
so, the slam chances go way down, but as I said above, south
probably won't bid 3d over 2d with those hands).

Kevin: Wow!  thats quite an analysis...  I'll take your word for it
being so correct.  I hope everyone sees how much time you have put
into this and finds it as interesting as I do.  I just have one small
thought to add here.  If the slam is less then 65% then I think 3nt
will score best for me because I can usually take the maximum number
of tricks; so I don't want to risk a 0 when my likely gain is not
much more then I am about to get for taking an extra trick.  (As
evidence, for getting diamonds correct and scoring +520, I got 6 out
of 8 Matchpoints, which is 75% already).  I like to be in the same
contract as everyone else in the field and then play the cards better
to gain my scores.  It's hard to figure this into the discussion.
However, this can never beat someone who always gets to the best
contract.  The higher the level of the tournament the more important
it is to bid and make 6d.
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