Is there any relationship between The Theorem and The
Law of total tricks?
As mentioned above, for a comprehensive study of The
Law and how it influences your bidding-decision-making
process, your best source is the set of Larry Cohen’s
books on the subject. He also has his own website which
you can visit at your convenience.
To see the correlation between The Theorem and The
Law, let us apply the same
Dirichlet'sPrinciple from mathematics (as we did
in the proof of The Theorem) to the case when the opponents
have one superfit (defined as a 10-11 cards-suit) first,
and than to the case when the opponents have a double
superfit (at least 20 cards in 2 suits).
In the first case, when the opponents have a single
superfit, this leaves you side with 24 cards in 3 suits
which means that according to Dirichlet your side has
at least three 8-cards fits instead of the guarantied minimum of 2 7-card suits
(in the worst-case scenario).
In the second case of double superfit on the opponents
side, you will be left with max 6 cards in these 2 suits
and 20 cards in the other 2 suits – again applying
the Dirichlet Principle you would be guaranteed at least
two 10-cards fits yourself in the worst-case scenario!
To summarize:
1)If the opponents have a single superfit, The Theorem guarantees
you that your side has (in the worst-case scenario)
a triple 8-cards fits.
2)If the opponents have a double
superfit, The Theorem guarantees you that your side
(in the worst-case scenario) also has a
double superfit.
Easy-to-remember
guidelines, I believe.
To
make it even simpler, the finding can be summarized
by the principle “The more they have, the more we have”
:-) And vice-versa, of course – the moment you
realize you have a double-superfit you know that the
opponents also have a double-superfit, whether they
know it or not. This may result in a tactical decision
to either:
1)hide your second fit while
still account for it, or
2)make a psychic bid in one of the
opponents’ suits, knowing that partner is “not
rich in that suit” anyway and chances that you
are going to mislead him are slimmer.
Is
the second option perfectly legal and the correct thing
to do? I don’t want to open this kind of discussions,
but the short answer is “oh, yeah …”.
As long as your partner gets the same information (or
mis-information for that matter) and acts accordingly,
you are fine and dandy. The fact that you know
that chances are 95% that you will mislead the opponents
and only 5% that you will mislead your partner only
speaks about your smarts, and if you don’t approve
of that statement you probably disapprove the bodycheck
in hokey and the fact that in boxing the guys hit each
other in the face and the referee pretends he doesn’t
notice :-)
Can
we push this simple superfits discovery a bit further,
though …
Let’s
try – it may be worth the effort.
Let’s
assume that the opponents have a double-fit in 2 of
the suits and the total amount of cards in both of these
suits is N.
Watch
what kind of simple calculations we are going to do
now.
The
total amount of cards in these 2 suits (we’ll
call them “their” suits) is 26.
This
leaves us with the amount of (26-N)
cards in their suits.
But
we have 26 cards in our combined hands between me and
my partner, so for the other 2 suits (I’ll call
them “our”
suits) we are left with
26
– (26 - N) = 26 – 26 + N =
N cards in our suits.
This
leads us to The
Superfits Theorem:
IF:Opponents have N cards in 2 suits
THEN:We have the SAME
amount ofN cards
in THE OTHER2suits.
If
they have 16 cards in the minor suits, we have 16 cards
in the major suits.
If
they have 16 cards in the major suits, we have 16 cards
in the minor suits.
I
am sure you see already where you can utilize The Superfits
Theorem. Yes – after Michaels cue-bids and after
unusual 2 NT. Such bids should not panic you, but rather
sharpen your senses and watch for the other two suit,
because most probably they are the ones you can find
a fit in.
The
easiest way to remember The Superfit Theorem is by “Whatever they have, we have”.
I
am sure you have already noticed the appearance of this magic number of 26
again …
Do
you remember it from somewhere?
Correct
– it’s the
opening amount of Zar Points that you need.
