Ł.Slawinski
1982
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PREX (1) = Play Result EXpectation |
from Pikier 9 |
What is the most important skill in
bridge ?
The answer is evident, yet shocking for many
players: PLAY
RESULT EXPECTATION
ie an ability to perform a simple task of counting
total strength.
This ability is generally neglected and simply
disregarded, both by practicians and by theoreticians !
Practician–player treats strength evaluation as
a toy beneath his dignity, made only for palookas, and – saying to
himself that „Bridge is played by the living men” – he
doesn't believe in reliability of any count or existence of any precise method.
Such an attitude shouldn't surprise us. Look at a
selt–respecting expert who is far beyond such trivialities like counting
tricks. A new, complicated and precise gadget – yes, but
counting?... a simple formula in beginner's
textbook is quite enough.
Meanwhile, both live in error, and – what's
worse – they don't realize it.
A practician who reached a clearly inferior contract
after a super–precise bidding sequence will only shrug his shoulders when
told that he had missed the target by a full trick (!). And we can even
sympathize with him, since he doesn't know any algorithm, and selects the
contract on the basis: „Perhaps I can make it” or „The room
will bid it” principle.
A theoretician who elaborated that super–precise
sequence, hardly realizes that a practician is not able to use it
intelligently, and developing an appropriate "information
transformer" (play result counting) would be much more profitable than
devising any super–gadget.
A paradox: more than a half (!!) of bidding disasters
is caused by using no count, and... no one is worried, because nobody realizes
it.
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ILLUSTRATIONs appended in 1990 |
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„The
Bridge World” October 1981 Problem G |
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Now, a very easy hand and a very clear auction. Let's show this very problem to experts: 5 votes for a slam
( 6© 6NT ) 20 votes for a slam try
( 4♠ 4NT 5© ×
) 7
votes for a
game ( 3NT 4© ). Two–trick divergence !!! and, moreover, none of experts try to count: |
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Hudecek: 4©
I'm a simple soul –
at least I've been called simple by many a partner.
Roth: 6NT
A shot
in the dark !
Rubin: 4©
It seems
automatic, though 3NT might be the winner when 4© gets set.
Begin: 6NT
My
shot for the year.
Kantar: 4NT
My rules are: (1)
after a minor suit opening and a three–level preempt, 4NT is natural; (2) after any opening and a four––level
major–suit preempt, 4NT is for takeout...
Kokish: 3NT
He won't interpret
4♠ followed by 5© correctly, and
jump to 5© is not a bid I'd
like to field from the other side. So either you bid a slam or you do your best
at a low level. Color me yellow.
Pavlicek: 6©
After giving partner
a few typical minimum hands, I find there is almost always some reasonable play
for slam.
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„The
International Popular Bridge Monthly”
June 1988 Problem 3 |
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One would expect
that experts' votes should fall into a half–trick zone, while palookas
would choose from a significantly wider spectrum of bids. However, the
reverse is true: 7
votes for 4♠ 5
votes for 3♠ 5 votes for 2♠ (= pass) 9
votes for others |
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Rowlands: 4♠
We may not make it
but I can hardly bid less.
Kilinger: 3♠
My fault if 8
tricks are the limit.
Lodge: 2♠ ( = pass )
Not so easy without
the double.
...
and so on... and so on.
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End of
ILLUSTRATIONs |
Therefore, it's high time [written in 1982] to present
an outline of a trick–count algorithm named PREX, which stands for:
|
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Play EXpectation |
Latin
PREX means: prayer The Polish
acronym is OSIKA [ aspen ] |
Don't treat PREX as an artificial product invented in
laboratory.
I have been using its most important parts for more
than 10 years, presenting them to my partners and listeners. If my trick count is
still not perfect, I am to blame because of my laziness, lack of training and
my neglect – all that shouldn't be a problem for any
practician–player.
|
Types
of tricks |
A „TRICK” is the only sensible unit of
strength. Using „POINTS” of any kind makes sense only when it helps
getting closer to a final result expressed in tricks.
PREX provides a method of calculating the total number
of tricks possessed by a partnership for a contract in any predetermined suit
or in notrump.
The total number of tricks available in offence (ie
Offensive Tricks – OT ) is calculated from the formula:
OT =
HT + LT + RT
where:
HT = Honor Tricks ( won by high
cards )
LT = Long Tricks ( won by established small cards )
RT = Ruffing Tricks
ST = Shape Tricks ( LT + RT )
and:
HT and LT in side suits are added to
the total on the assumption that opponents' trumps have been drawn.
The
above equation, suggesting that each type of tricks is independent from the
others, is only a simplification, because a trick–type collision occurs
relatively frequently (eg a singleton opposite
KQJ may lead to a double count: 2 RT and 2 HT).
The same formula is used to count the total number of
tricks available in defense, ie
Defensive Tricks ( DT ), but:
HT in a side suit are counted on the
assumption
that declarer has enough trumps to ruff our honors.
Such honor DT will be called
– Honor Defensive Tricks ( HDT ).
It is sometimes worthwhile (especially for a low level contract) to
calculate DT indirectly – by calculating opponents' Offensive Tricks (for
their contract) from their point of view (!) and taking into account the entire
information about the deal. Besides, remember that each hand –
irrespective of phase of the auction – has some defensive value.
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Ruffing
Tricks RT |
RT tables found in bridge literature are – in my
opinion – almost completely worthless, being too simplified (they don't
embrace all possible cases) or not using a trick as a unit.
The number of RT should be estimated statistically,
taking into account the following circumstances:
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Is there enough trumps for ruffing? |
Remember that defenders can lead trumps. |
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Is there anything to ruff? |
Sometimes, even a singleton accompanied
by four trumps is worth zero RT, because partner has a singleton, too! |
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Does collision with honors take place? |
Partner may happen to have substantial
honor values in the suit you are going to ruff (eg KQJ facing singleton may
cause doubled count: 2 HT + 2 RT). |
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Long
Tricks LT |
If you have an 8–card or
better fit with your partner, a simple formula may be used:
LT =
(your length xor partners length) – 3.
If the
bidding gives no clear information, the potential number of Long Tricks is:
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Shape |
LT |
|
Shape |
LT |
|
Shape |
LT |
|
Shape |
LT |
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4333 |
++ |
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5332 |
1++ |
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55 |
3– |
|
6 |
3– |
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|
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4432 |
1 |
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54 |
2 |
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64 |
3 |
|
7 |
4– |
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4441 |
1+ |
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5440 |
2+ |
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65 |
4 |
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74 |
4+ |
|
where:
+ = 1/4
trick extra ( eg 2+ = 21/4 ) ++ = 1/2 trick extra – = 1/4
trick less ( eg 2– = 13/4 )
Remember
that even two completely balanced hands provide nearly 1 LT (check it).
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Honor
Tricks HT |
The first three tricks in a suit are (usually) won by honors,
ie they are Honor Tricks (HT). Which side takes such a trick depends on honors'
relative ranks, distribution of honors (between all four hands), and... actual
play. It means that all four hands together have 3 HT in a suit; hence –
there are 12 HT in all if a deal is completely balanced.
Therefore, an average hand like:
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A x xx K x x |
|
Q J x |
|
K
J x 10
x x x |
is
worth 3 HT. |
The problem – what is the value of honors
– may be solved in many ways, and – what's more interesting –
independently by each partner. The simplest (and quite good) method is to valuate
honors „at a glance”, backing it by intuition supplemented by
experience and elementary estimation.
For example:
–
an Ace is surely worth 1 HT (but rather
a bit more)
–
a King is surely worth 1/2
HT (but rather a bit more)
–
a King–Queen is surely worth...1 1/2 HT (but rather a bit more)
and
so on...
Using
any point count method gives a more „scientific” background, eg:
|
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Milton Points |
MP |
: |
A |
= |
4 |
K |
= |
3 |
Q |
= |
2 |
J |
= |
1 |
|
|
Polish Points |
PP |
: |
A |
= |
7 |
K |
= |
4 |
Q |
= |
3 |
J |
= |
1 |
|
|
Limit Points |
LP |
: |
A |
= |
7 |
K |
= |
5 |
Q |
= |
3 |
J |
= |
1 |
Efficient use of any of these scales requires
recalculation to HT (this is completely neglected in bridge literature),
which can be based on an obvious equation: A
total count in a suit is equivalent to 3 HT.
Hence:
3
HT = 10 MP = 15 PP = 16 LP
and:
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|
Number of HT |
= |
MP × 3 |
= |
PP |
= |
LP × 3 |
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10 |
5 |
16 |
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But the above methods are highly
imperfect. The better and equally simple ones do exist!
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brydż, brydz, bridge, brydż sportowy, brydz sportowy, bridge
sportowy, Pikier, Sławiński, Slawinski, Łukasz Sławiński, Lukasz Slawinski, |
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All
restrictions on bidding must be destroyed