Bridge Odds
How will the cards be divided?
What are the most likely shaped hands?
How many cards will you hold in a suit?
The Odds for Card Division
Missing 2 Cards
|
LHO holds:
|
RHO holds:
|
Probability (#)
|
|
1
|
1
|
52% (2)
|
|
Any 2-0
|
|
48% (2)
|
Missing 3 Cards
|
LHO holds:
|
RHO holds:
|
Probability (#)
|
|
Any 2-1
|
|
78% (6)
|
|
Any 3-0
|
|
22% (2)
|
Missing 4 Cards
|
LHO holds:
|
RHO holds:
|
Probability (#)
|
|
2
|
2
|
40.7% (6)
|
|
Any 3-1
|
|
49.7% (8)
|
|
Any 4-0
|
|
9.6% (2)
|
Missing 5 Cards
|
LHO holds:
|
RHO holds:
|
Probability (#)
|
|
Any 3-2
|
|
67.8% (20)
|
|
Any 4-1
|
|
28.3% (10)
|
|
Any 5-0
|
|
3.9% (2)
|
Missing 6 Cards
|
LHO holds:
|
RHO holds:
|
Probability (#)
|
|
3
|
3
|
35.5% (20)
|
|
Any 4-2
|
|
48.5% (30)
|
|
Any 5-1
|
|
14.5% (12)
|
|
Any 6-0
|
|
1.5% (2)
|
Missing 7 Cards
|
LHO holds:
|
RHO holds:
|
Probability (#)
|
|
Any 4-3
|
|
62.2% (70)
|
|
Any 5-2
|
|
30.5% (42)
|
|
Any 6-1
|
|
6.8% (14)
|
|
Any 7-0
|
|
0.5% (2)
|
Missing 8 Cards
|
LHO holds:
|
RHO holds:
|
Probability (#)
|
|
4
|
4
|
32.7% (70)
|
|
Any 5-3
|
|
47.1% (112)
|
|
Any 6-2
|
|
17.1% (56)
|
|
Any 7-1
|
|
2.9% (16)
|
|
Any 8-0
|
|
0.2% (2)
|
Missing 9 Cards
|
LHO holds:
|
RHO holds:
|
Probability (#)
|
|
Any 5-4
|
|
58.9% (252)
|
|
Any 6-3
|
|
31.4% (168)
|
|
Any 7-2
|
|
8.6% (72)
|
|
Any 8-1
|
|
1.0% (18)
|
|
Any 9-0
|
|
0.1% (2)
|
Missing 10 Cards
|
LHO holds:
|
RHO holds:
|
Probability (#)
|
|
Any 6-4
|
|
46.2% (420)
|
|
5
|
5
|
31.2% (252)
|
|
Any 7-3
|
|
18.5% (240)
|
|
Any 8-2
|
|
3.8% (90)
|
|
Any 9-1
|
|
0.3% (20)
|
|
Any 10-0
|
|
0.01% (2)
|
Missing 11 Cards
|
LHO holds:
|
RHO holds:
|
Probability (#)
|
|
Any 6-5
|
|
57.2% (924)
|
|
Any 7-4
|
|
31.8% (660)
|
|
Any 8-3
|
|
9.5% (330)
|
|
Any 9-2
|
|
1.4% (110)
|
|
Any 10-1
|
|
0.1% (22)
|
|
Any 11-0
|
|
0.0% (2)
|
Missing 12 Cards
|
LHO holds:
|
RHO holds:
|
Probability (#)
|
|
Any 7-5
|
|
45.7% (1584)
|
|
6
|
6
|
30.5% (924)
|
|
Any 8-4
|
|
19.1% (990)
|
|
Any 9-3
|
|
4.2% (440)
|
|
Any 10-2
|
|
0.5% (132)
|
|
Any 11-1
|
|
0.02% (24)
|
|
Any 12-0
|
|
0.00% (2)
|
Missing 13 Cards
|
LHO holds:
|
RHO holds:
|
Probability (#)
|
|
Any 7-6
|
|
56.6% (3432)
|
|
Any 8-5
|
|
31.8% (2574)
|
|
Any 9-4
|
|
9.8% (1430)
|
|
Any 10-3
|
|
1.6% (572)
|
|
Any 11-2
|
|
0.1% (156)
|
|
Any 12-1
|
|
0.003% (26)
|
|
Any 13-0
|
|
0.00002% (2)
|
What are the 10 most likely hand shapes?
(these 10 covers about 91% of the possible shapes)
|
Rank
|
Pattern
|
%
|
|
Rank
|
Pattern
|
%
|
|
1st
|
4-4-3-2
|
21.6%
|
|
2nd
|
5-3-3-2
|
15.5%
|
|
3rd
|
5-4-3-1
|
12.9%
|
|
4th
|
5-4-2-2
|
10.6%
|
|
5th
|
4-3-3-3
|
10.5%
|
|
6th
|
6-3-2-2
|
5.6%
|
|
7th
|
6-4-2-1
|
4.7%
|
|
8th
|
6-3-3-1
|
3.4%
|
|
9th
|
5-5-2-1
|
3.2%
|
|
10th
|
4-4-4-1
|
3.0%
|
How many card will you hold in a suit?
|
Number of Cards
|
%
|
|
0
|
1.3%
|
|
1
|
8.0%
|
|
2
|
20.6%
|
|
3
|
28.6%
|
|
4
|
23.9%
|
|
5
|
12.5%
|
|
6
|
4.2%
|
|
7 or more
|
0.9%
|