From: desj@ccr-p.ida.org (David desJardins)
Newsgroups: rec.games.bridge
Subject: Re: Yet another Survey item
Date: 27 Jul 92 02:51:38 GMT
Organization: IDA Center for Communications Research, Princeton

Jeff Baron <jbaron@dirac.ssc.gov> writes:
>In article <1501@idacrd.UUCP>, desj@ccr-p.ida.org (David desJardins) writes:
>> I would estimate that your expected number of tricks is nearly 0.5
>> greater with the former hand [AKxxxx/x/xx/xxxx] than with the
>> latter [AKxxxx/xx/xx/xxx].  AKxxxx/x/xxx/xxx would be in between.

>But I don't think the number is this high.  The chance that partner
>is short is *less* than the chance that one opponent is short.  Another
>opponent may have 4 cards.  If you have 9642, what are the chances
>that you'll be able to set one up?  We can both only speculate, and
>try to do what is best for us.  *I* don't think it is 50/50.

Well, I consider this kind of probability estimation to be something
that I am especially good at.  But there *is* a way to do more than
speculate: simulation.  I generated 20 random pairs of N-S deals.  In
deal 1 of each pair, South has AKxxxx/x/xx/xxxx.  In deal 2, South has
AKxxxx/xx/xx/xxx.

The specific method for generating the hands is as follows.  Generate
hand 1 for South randomly from among all possible AKxxxx/x/xx/xxxx
hands.  (Each x could be any spot, ten or less.)  Generate hand 1 for
North randomly from among all possible hands disjoint from South hand 1.
Now generate hand 2 for South from hand 1 by deleting a randomly chosen
club spot and adding a randomly chosen heart spot.  Finally, hand 2 for
North is the same as hand 1 except that if hand 1 contained the heart
spot added to South's hand 2, then it is replaced by the club spot
deleted from South's hand 1.

The result of this sampling method is that one set of 20 deals is an
accurate sample of the possibilities when South is 6-1-2-4, and the
other set of 20 deals is an accurate sample of the possibilities when
South is 6-1-3-3, and each pair of deals is fairly similar so that they
are easy to compare.

For each pair, I then estimated how many more or less tricks N-S expect
to take in a spade contract, on average, with deal 1 than with deal 2.
Over the 20 pairs, the total is that deal 1 is 11.60 tricks better than
deal 2, or 0.58 tricks per deal.  The standard error in this estimate
from 20 samples is about 0.08.

Of course, if you disagree with my estimates, the systematic error could
potentially be much larger.  Nevertheless, it reinforces my belief in my
original estimate.  (I certainly tried not to tilt the estimates in
either direction.)

The 20 pairs follow, with my trick estimates and a brief analysis for
each.  I welcome any discussion of my analysis or my methods.

                                        David desJardins


Deal 1                          Deal 2
------------------------------------------------------------------------
642				642
KT9				KT9
J3				J3
AQJ54				AQJ54

AKT975				AKT975
5				65
54				54
T987				987

+0.50 tricks.

Deal 1 takes an extra trick when the ace of hearts is offside.
------------------------------------------------------------------------
T				T
QJT73				QJT73
AJT8				AJT8
A82				A82

AK7642				AK7642
5				95
42				42
T954				T54

+0.35 tricks.

Deal 1 takes an extra trick when clubs break 3-3.
------------------------------------------------------------------------
QJT7				QJT7
87				8
842				842
AQ73				AQ732

AK5432				AK5432
4				74
T6				T6
9842				984

-0.10 tricks.

Deal 1 has an extra risk of a fourth-round club loser, but it is not very
large because of the double finesse against the JT.
------------------------------------------------------------------------
QJ5				QJ5
JT53				JT53
AK2				AK2
KJ8				KJ8

AK9843				AK9843
8				98
84				84
T954				T54

+0.95 tricks.

Deal 1 almost always takes an extra trick, but has a slightly higher chance
of a club ruff.
------------------------------------------------------------------------
92				92
Q98				Q98
64				64
AKQ643				AKQ643

AKT864				AKT864
3				53
83				83
T875				T85

+0.95 tricks.

Deal 1 almost always takes an extra trick, but has a slightly higher chance
of a club ruff.
------------------------------------------------------------------------
J7				J7
9643				943
AKQ2				AKQ2
K96				K963

AK6432				AK6432
5				65
43				43
8543				854

+0.20 tricks.

Deal 1 takes an extra trick when the ace of clubs is offside and clubs are
3-3.
------------------------------------------------------------------------
2				2
AK				AK
AQJ6532				AQJ6532
AJT				AJT

AK8763				AK8763
5				52
98				98
9754				975

+0.20 tricks.

Deal 1 takes an extra trick when a diamond loser is avoided with a heart
discard, and the clubs behave.
------------------------------------------------------------------------
Q4				Q4
QT5				QT5
AQ75				AQ75
A764				A764

AK7632				AK7632
9				94
64				64
T853				T53

+0.65 tricks.

Deal 1 takes an extra trick when clubs are 3-2.
------------------------------------------------------------------------
86				86
A63				A3
QJT432				QJT432
76				762

AK9432				AK9432
4				64
65				65
T842				T84

0 tricks.

No difference.
------------------------------------------------------------------------
QJ3				QJ3
AJT2				AJ2
KT6				KT6
AK8				AK85

AK8754				AK8754
5				T5
54				54
T975				T97

+0.80 tricks.

Deal 1 takes an extra trick if clubs are 3-3, or a singleton or doubleton
honor drops.
------------------------------------------------------------------------
9				9
9743				974
KQ53				KQ53
J962				J9862

AK7543				AK7543
2				32
76				76
T854				T54

+0.70 tricks.

Deal 1 takes an extra trick when clubs are 3-2, or if the opponents have
trouble maneuvering their ruff.
------------------------------------------------------------------------
Q75				Q75
T9				T9
AK76				AK76
AJT5				AJT5

AK9632				AK9632
3				73
95				95
9763				976

+0.95 tricks.

Deal 1 takes an extra trick unless there is a fourth-round club loser.
------------------------------------------------------------------------
Q				Q
A84				A84
AK954				AK954
QJ42				QJ42

AK8542				AK8542
3				73
73				73
9873				873

+0.80 tricks.

Deal 1 takes an extra trick unless there is a fourth-round club loser.
------------------------------------------------------------------------
2				2
KT974				KT974
KT3				KT3
KQT8				KQT8

AK9864				AK9864
2				32
82				82
9652				965

+0.80 tricks.

Deal 1 takes an extra trick unless there is a club ruff.
------------------------------------------------------------------------
Q842				Q842
K7				K7
KQ92				KQ92
852				852

AKT965				AKT965
6				86
53				53
T764				T74

+0.45 tricks.

Deal 1 takes an extra trick when the ace of hearts is offside, unless there
is a trump promotion in clubs.
------------------------------------------------------------------------
QT874				QT874
Q86				Q86
AKT4				AKT4
J				J

AK9652				AK9652
4				43
52				52
8765				875

+1.00 tricks.

Deal 1 always takes a trick more.
------------------------------------------------------------------------
J32				J32
QT92				QT92
QJ4				QJ4
K43				K43

AK9864				AK9864
4				84
T5				T5
T875				T87

+0.70 tricks.

Deal 1 takes an extra trick if clubs are 3-3, or spades are 2-2.
------------------------------------------------------------------------
J75				J75
85				5
AQ832				AQ832
QJ3				QJT3

AKT632				AKT632
6				86
65				65
T976				976

0 tricks.

No difference.
------------------------------------------------------------------------
QJ84				QJ84
QT96				Q96
J				J
KJ65				KJ965

AKT752				AKT752
2				T2
94				94
9743				743

+0.70 tricks.

Deal 1 takes an extra trick unless there is a fourth-round club loser.
------------------------------------------------------------------------
J92				J92
JT3				J3
Q95				Q95
AQJT				AQJT7

AKT876				AKT876
8				T8
T2				T2
8765				865

+1.00 tricks.

Deal 1 always takes an extra trick.
------------------------------------------------------------------------
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