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%