Percentages in Bridge

# Percentages in Bridge

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Percentages

Many novices--especially those of us who
were marginal math students in school--become
intimidated by mention of percentages.  Allow
me to simplify this discussion by emphasizing
only those common "must know" percentages
and WHY YOU NEED TO KNOW THEM.

First, what odds does one require to bid
a "good" slam or game?  A game requires a 40%
chance if NOT vulnerable, a 38% chance if vulnerable.
This is calculated by factoring in the risk
(-50 or -100) of down one versus the reward of
making (+400 or +600) the game.  Apparently, the
people who calculate these odds have never been
doubled and have never been down more than one. :)

A SMALL slam requires a 50% chance.  Venturing
into a small slam which requires AT MOST a (50-50)
finesse is considered GOOD bidding.  Assaying a
small slam which will depend on AT LEAST a finesse
to this popular concensus:  bid 50% 6NT slams, but
AVOID 50% SUIT slams.  The chance of a RUFF in the
suit slam may be incalculably small, but might tilt
the balance against the suit slam bidders. :)

A GRAND slam requires a 70% chance of success.
Since this is very close to the odds of a 3-2 break
(see below), bidding a grand slam which requires AT
MOST a (68%) 3-2 break is acceptable.  Any grand
slam which requires MORE than that is to be eschewed.

The basic rule regarding suit splits is a simple
one:  "SUITS BREAK OFF-CENTER".  This means that if
there are SIX cards outstanding the odds are AGAINST
a 3-3 break.  Indeed, only 36% of the time will this
suit divide evenly.  More than 60% of the time it
will divide 4-2.  Remember this the next time you are
in a Moysian (i.e. 4-3) fit, or the next time you have
AKQ10 opposite three small.  :)

Five cards outstanding usually split 3-2.  In fact,
they will do so 68% of the time.  They will break 4-1
just less than a third of the time.  "Hawaii" (i.e. 5-0)
breaks come up about 1% of the time (unless it is Bill
and I in a slam contract, in which case two zeros can be

When there are FOUR cards outstanding the odds are
50% that they will break 3-1 (i.e. off-center), 40% that
they will divide 2-2 (down the center), and 10% that
they will split 4-0.  Remember this the next time
sometime tells you "8 ever, 9 never" !  :)

Three cards outstanding will split 2-1 about two
thirds of the time.

These percentages are combined by multiplication or
division.  For example, a contract which required a
finesse AND a 3-2 break would be a (.50 x .68 = .34) 34%
proposition.  If a game, it would be considered SLIGHTLY
"anti-percentage".  Meanwhile, a contract which requires
a finesse OR a 2-2 break will succeed
(.50 +  [the remaining .50 / .40] = .70) 70% of the time.

Often beginners will watch their side make 12
tricks and ask:   "How can we bid that slam?"  They do
not stop to calculate the odds of that "slam" making.  If,
say, it required two finesses and a 2-2 break it would be
a (.50 x .50 x .40 = .10) 10% proposition.  This is NOT
a slam you'd want to be in!  You would get NINE bad
results for every good result!

Ward's Maxim #271 applies here:  "Good bridge is
always punished in the short term."   :)

While I don't wish to disagree with the "Hardy Rule"
(which states that "99% of the time percentages are WRONG"),
I can only advise you to understand these odds and try
to bear them in mind as you play and analyze each hand.

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