Balanced Hands?
by Malcolm Channing

Over the past few months on a number of occasions, we have been cajoled by the Director to shuffle well and deal properly, because a number of members have complained that they are fed up by the fact that they receive too many balanced hands.

How many balanced hands would you expect to hold in an evening's bridge of 24 hands?

Over the last few months I have taken two sets of curtain cards home after Tuesday night's bridge tournaments and compared the actual and expected distribution frequencies. I found that out of 200 hands, 91 (45.5% compared with the expected 47.6%) were balanced in accordance with our definition above. There were 10 seven-card suits and one eight-card suit. This is 5.5% of the hands investigated compared with the expected 4.0%. The number of voids was 12 (6% actual, 5.8% expected) and the number of singletons was 71 (35.5% actual, 32.0% expected).

All the above goes to show that on the two nights investigated, the hands were slightly more unbalanced than expected. So next time you feel like complaining that you have held more than your share of balanced hands bear in mind that you should not just take one week in isolation but take a number of weeks, and back up your gut feeling with hard facts.

If it happens that you are receiving more than your fair share of boring distributions, I can only suggest you try sitting North instead of South or East instead of West.

Distribution

Frequency

 

Distribution

Frequency

 

Distribution

Frequency

4-3-3-3

10.54%

 

6-5-1-1

0.71%

 

8-4-1-0

0.045212%

4-4-3-2

21.55%

 

6-5-2-0

0.65%

 

8-5-0-0

0.003130%

4-4-4-1

2.99%

 

6-6-1-0

0.07%

 

9-2-1-1

0.017811%

5-3-3-2

15.52%

 

7-2-2-2

0.51%

 

9-2-2-0

0.008220%

5-4-2-2

10.58%

 

7-3-2-1

1.88%

 

9-3-1-0

0.010047%

5-4-3-1

12.93%

 

7-3-3-0

0.27%

 

9-4-0-0

0.000966%

5-4-4-0

1.24%

 

7-4-1-1

0.39%

 

10-1-1-1

0.000396%

5-5-2-1

3.17%

 

7-4-2-0

0.36%

 

10-2-1-0

0.001906%

5-5-3-0

0.90%

 

7-5-1-0

0.11%

 

10-3-0-0

0.000155%

6-3-2-2

5.63%

 

7-6-0-0

0.01%

 

11-1-1-0

0.000025%

6-3-3-1

3.45%

 

8-2-2-1

0.19%

 

11-2-0-0

0.000012%

6-4-2-1

4.70%

 

8-3-1-1

0.12%

 

12-1-0-0

0.000000%

6-4-3-0

1.33%

 

8-3-2-0

0.11%

 

13-0-0-0

0.000000%



Copyright Mayfield Duplicate Bridge Club 2001