Observation 1: New players often ask if there is any way they can increase their ability scores. Old school dogma states that only magic can do the trick (often, literally through a magical trick feature.)
Observation 2: The visible frustration in old school games when a player rolls 1 on their hit point die at a new level.
d4: on a roll of 1 ,and 3-6 then rolled on d6:
d6: on a roll of 1
d8: on a roll of 1, or a roll of 2 if 5-6 then rolled on d6.
d10: on a roll of 1, or a roll of 2 if 3-6 then rolled on d6.
d12: on a roll of 1-2.
For monks' starting HP roll, if you're not using "maximum HP at first level" or similar, the stat gain ison a roll of 2 or 3 on 2d4; for rangers, 2 through 4 on 2d8.