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.
Occurrences of hand configuarations
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