What kind of flat hands should one passes and not open the bidding? There are many styles of bidding and I am not recommending whether you should open conservatively in seat 1 and 2 or not. In this section I am only going to look at some types of flat hand and see on the average whether the hand belong to their side or not. We are ignoring which seat you are in as to how many hands have pass before this hand has to bid. If a hand type is very close to the average then you must also make slight adjustment for long suit ranks and honor in long suits. In 4432 if the two 4 card suits are the majors it worth more. If honors are in the 4 card suit it worth more etc.
For 13 HCP hands to my surprise there is one hand type that is below average; namely 4333 or 4432 with exactly one K and no A. (Herbert Wilton suggested me to do this simulation and the result surprise me a little since I open all 12 HCP hands) But they are extremely rare ( a total of 0.003% of all hands or about one in 35,000) and I swear that I have never actually seen one (my excuse for being ignorance). For any practical purpose we can say one should open all 13 HCP hands.
For 12 HCP and 4333, all hands with one or less control are below average. All hands with 2 controls (even with 2 K and no A) are above average. 4333 with no A and two K is about as close to average as one can get. This hand type does better then average in NT contracts and worst then average in suit contract. Because NT is higher ranking then suit so this hand type is slightly above average overall.
For 12 HCP and 4432, all hands with one or less control are below average. All hands with 2 controls (even with 2 K and no A) are above average.
Hands with one or less control and 12 HCP are also very rare ( a total of 0.016% of all hands or about one in 6,300 compare with about 2.52% for all 12 HCP 4333 and 4432 hands or about one in 40). For practical purpose we can say one should open all 12 HCP hands.
For 11 HCP hands 4333 hands with 3 controls are below average, and 4 controls are above average and it does not make any difference what combination of A and K.
For 11 HCP hands 4432 hands with 2 controls are below average, and 3 controls are above average and it does not make any difference what combination of A and K. This is a small improvement over 4333.