This section is just to complete the subject of my interest. Most information here are available in other sources. Mathematics and Statistics are very closely related. I am going to put materials which deals with numbers that can be calculated easily in the mathematics section. There is a very good mathematical tables section in the encyclopedia of bridge.  Things like there is a 52% chance for a suit missing only 2 cards to be split 1 -1 will fall into this category. Statistics are cases which cannot be calculated easily and most of the time obtained by computer simulation of bridge hands. I have written a very fast program to simulate computer hands and have run many simulations. A normal 1 club open has 3 clubs 16.7%, 4 clubs 25.9%, 5 clubs 37.3% 6 clubs 14.7% 7 clubs 3.8% etc. This is obtained by running 10 million hands. It is good to know some of those numbers but that is not always the best number. Other factors like the bidding or the cards already play may be just as important or even more important.  If the opponent has the K and the 7 of hearts and the play and the bidding say your RHO cannot have the K which is 3 hcp. then all the mathematic percentage of 52% is meaningless. The LHO must has K or K7. The general opening of 1c distribution is always meaningless. The reason is because you are holding a hand. if your partner or opponent open one club you must add your hand to the fact that is already known. with those 2 conditions the statistic of the 1c opening is no long equal to the "normal" or "average". Very often you  hear players say my partner open one club and I have 5 clubs. The probability of us having 9 clubs together is better then 83% ..... Actually there are 35% chance the one club opener only has 3 clubs, about twice as often as the average.