I have one of the most versatile bridge hand simulation program written in C++ which allows user to enter almost anything they want to select the bridge hands and have a complete statistical analysis of the hands selected. It screens about 1 million hands in 3 seconds and computes all the statistical data on 1 million hands in about 16 seconds. All the results in this sections are obtained by running simulations on millions of hands.
Here is where a lot of my research is done. Statistics results are most often obtain by running computer simulations. It should be used in both your bidding and playing of hands. Here are some very general type of statistics:-
Typical opening hands (one level suit opening11 HCP with 5 card suit, else 12 HCP ):-
(number in parenthesis are average tricks for the partnership. Remember the average for all hands is 8.44 tricks)
How many people know that a weak 4 opening makes on the average 0.1 more tricks than a 1NT opening.
The statistical suit distribution percentage for each opening is for reference only. This information is good only for the player who opens the bidding and can only see his own 13 cards. If his hand distribution is significantly different from the average, he should be careful in his rabid. The partner and opponent may have a wrong perception of the openerís distribution. For the other 3 players they have the advantage of seeing 13 more cards. The actual statistical suit distribution percentage for the opener should be calculated base on the opening and the 13 cards the player held.
I have seen in a few publications that quote those values like an average 1 diamond opening has 4.5 cards, an average 1 club opening has 5 or more cards over 50% of the time. Subsequent text says you should freely raise your partnerís suit. This is only partially true. If you have 5 clubs in your hand and your partner opens 1 club, his average club holding is about 4; 35% for 3, 36% for 4 and 29% 5 or more. Instead of over 50% chance to have 5 or more clubs in the openerís hand, it drops to less then 30%.