Percentages in Bridge
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 38% chance if vulnerable.
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.