Percentages in Bridge

Percentages in Bridge


	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 

	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 
is BAD bidding.  I would add my own general rule 
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 
added after the "1").

	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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