# Probabilities

## INTRO

Bridge is also a game of statistics . Numbers are important. As a bridger you have to be aware about certain probabilities in order to define the correct playing line. We also used the statistics to make certain choices when building MUTOS.

## Coverage of the MUTOS openings

- to be constructed

• A few numbers are important during the play, for instance, the probability of remaining cards :
 x=2 x=3 x=4 x=5 x=6 x=7 x=8 1-1: 52% 2-0: 48% 2-1: 78% 3-0: 22% 2-2: 40% 3-1: 50% 4-0: 10% 3-2: 68% 4-1: 28% 5-0: 4% 3-3: 36% 4-2: 48% 5-1: 15% 6-0: 1% 4-3: 62% 5-2: 30% 6-1: 7% 7-0: 1% 4-4: 33% 5-3: 47% 6-2: 17% 7-1: 3% 8-0: <1%
• Next, honneur count point (hcp) -related,  it is interesting to know that, with randomly dealt cards, no matter what hand you hold, it follows a statistical law. Don't be surprised if you can not open and feel you always have to pass : nearly 50% of randomly given cards are pass-hands.
•  N 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 cumulative % of hands with min. N hcp 28.6 37.5 46.8 56.2 65.2 73.2 80.1 85.9 90.2 93.5 95.86 97.46 98.49 99.09 99.39 99.59 % of hands with N hcp 8.02 8.9 9.3 9.4 8.9 8 6.9 5.7 4.4 3.3 2.36 1.6 1.03 0.6 0.3 0.2
With the normal openings (12-15 hcp) we reach (only)  25% of the possible hands, and we use all the bids on 1-level , except 1 , for this purpose. 1 is mainly meant for the strong hands >=16hcp, being 10% of all possible hands.
As the statistics show, it is worthwhile to invest some bids to cover the weak hands between 7-11hcp as they cover 45% of all hands. For this we have the 2-level and 3-level openings.
• Distribution probabilities :
• 65% of the hands contain a suit with a FIVE+ card
• 21.5% has a (4432) and
• 10.5% has a (4333) distribution.
• 3 % has a (4441) distribution.
We will present also statistical data on the coverage of our bridge system(s) : in how many % of the cases can we use a certain opening. We need the relationship between the distribution-probability and the hcp's of a random hand. As we are great fans of re-use in general, we are happy to re-use the data on this relationship provided by Chiel Verwoest, author of the M.A.F.system.

At the bottom of this page, you find 4 buttons to this data which I used to assemble the coverage picture of RISC and MUTOS. Find also an interesting link to one of Richard Pavlicek's pages on bridge calculators.

Coverage MUTOS  Coverage RISC   hcp0-9  hcp10-19   hcp20-29  hcp30-37   R.Pavlicek's Bridge Calculators