We proceed here with the promised analyses. In the next table all hands that must be opened with 1¨, are collected. For each of these hands the probability of occurrence has been calculated.
As you can see, there is a problem to be solved. In the table we count much more types of hands then can be described in one single rebid. To enable the opener to establish a useful rebid, the number of types of hands has to be reduced drastically.
By adding all the probability percentages together, the total frequency of the 1¨ opening, 5.67%, may be obtained.
Now it is easy to calculate the table of relative chances for 1¨-opening-hands for the same hands.

All hands on which 1¨ is opened and their absolute chances of occurrence in %   length ¨ suit: 3 4 5 6 7+ 3 4 5 6 7+ 3-5 fit in major suit possible never a 3-5 fit in major suit 11-12 HCP's 4,3,3,3 0.44 0.44         4,4,3,2   0.60 5,3,3,2   0.65 5,4,2,2   0.15     5,4,3,1 0.18   6,3,2,2   0.08 0.16 6,3,3,1 0.15   6,4,2,1   0.07 6,4,3,0 0.02   7,2,2,2   0.02 7,3,2,1 0.03   0.06 7,3,3,0 0.05   7,4,1,1   0.01 7,4,2,0 0.01   length ¨ suit: 3 4 5 6 7+ 3 4 5 6 7+ 3-5 fit in major suit possible never a 3-5 fit in major suit 13-14 HCP's 4,3,3,3 0.33 0.33   4,4,3,2   0.45 5,3,3,2   0.49       5,4,2,2   0.11 5,4,3,1 0.14   6,3,2,2   0.06   0.12   6,3,3,1 0.11   6,4,2,1   0.05 6,4,3,0 0.01   7,2,2,2   0.02 7,3,2,1 0.02   0.04 7,3,3,0 0.04   7,4,1,1   0.00 7,4,2,0 0.00   length ¨ suit: 3 4 5 6 7+ 3 4 5 6 7+ 15-19 HCP's   with rebid major suit no rebid major suit 5,4,3,1   0.14         6,3,3,1   0.04 6,4,2,1 0.05   6,4,3,0 0.01 7,3,2,1   0.02 7,3,3,0 0.00 7,4,1,1 0.00   7,4,2,0 0.00

 
With the help of the next table of relative chances for 1¨-opening-hands the number of hands must be reduced to a number that is practical in bidding.

All hands on which 1¨ is opened and their relative chances of occurrence in %   length ¨ suit: 3 4 5 6 7+ 3 4 5 6 7+ 3-5 fit in major suit possible never a 3-5 fit in major suit 11-12 HCP's 4,3,3,3 7.68 7.68                 4,4,3,2   10.56 5,3,3,2   11.48   5,4,2,2   2.63 5,4,3,1 3.25   6,3,2,2   1.42 2.85 6,3,3,1 2.63   6,4,2,1   1.21 6,4,3,0 0.35   7,2,2,2     0.40 7,3,2,1 0.49 0.98 7,3,3,0 0.85   7,4,1,1   0.10 7,4,2,0   0.10   length ¨ suit: 3 4 5 6 7+ 3 4 5 6 7+ 3-5 fit in major suit possible never a 3-5 fit in major suit 13-14 HCP's 4,3,3,3 5.76 5.76     4,4,3,2   7.89     5,3,3,2   8.56       5,4,2,2   1.96 5,4,3,1 2.41   6,3,2,2   1.05   2.10   6,3,3,1 1.94   6,4,2,1   0.89 6,4,3,0 0.25   7,2,2,2     0.29 7,3,2,1 0.36   0.72 7,3,3,0 0.62   7,4,1,1   0.08 7,4,2,0 0.07   length ¨ suit: 3 4 5 6 7+ 3 4 5 6 7+     with rebid major suit no rebid major suit 15-19 HCP's 5,4,3,1   2.41         6,3,3,1   0.63 6,4,2,1 0.85   6,4,3,0 0.23 7,3,2,1   0.33 7,3,3,0 0.04 7,4,1,1 0.07   7,4,2,0 0.06

Studying the table we observe that there is not much difference in the frequency between 11-12-hands and 13-14-hands. By taking them together we reach a reduction of nearly 50%. It is not a severe omission, when the responder does not know your strength more exactly from the rebid.
Further on we note that hands with a 6+card in diamonds are very rare. It seems sufficient to distinguish only between 3-, 4-, and 5+cards. This gives a considerable reduction again. If there are more then 5 diamonds, the opener can show this to the responder in several ways. It does not need to be done in the first rebid.
There is no reason to inform the responder always about your length in the major suits. He knows already that in category A (95% of all 1¨ openings), you never have 4 or more cards in a major suit. From the probability data (the last table) he knows (or at least should know) that 85% of the 1¨-opening-hands contain at least one 3-card in a major suit; this goes for the 11-12-hands as well as for the 13-14-hands. These two facts make it worthwhile to develop a convention (MaD+, 3-5-MAs-fit-explorer after Diamond opening), which enables the responder to explore the 3-5-fit in the major suit of which he holds a 5-card. Only after the initiation of the convention, the opener will deny or confirm his 3-card major suit in his rebid.
In case of a strong 1¨ opening, the opener will show eventually (in 78% of the relevant hands) his 4-card major suit by bidding this suit on 2-level (MaD+++, 4-4-MAs-fit-explorer after Diamond opening). So it is indeed necessary here to distinguish between possessing a 4-card major suit and not having such a 4-card.
In this way the number of hand-descriptions for 1¨-openings has been very much reduced, as can be observed in the concluding table in the original 1¨-page, the one you left in order to read this separate sheet.