Players Handbook (page 34)
Each character has a varying number of hit points, just as monsters do. These hit points represent how much damage (actual or potential) the character can withstand before being killed. A certain amount of these hit points represent the actual physical punishment which can be sustained. The remainder, a significant portion of hit points at higher levels, stands for skill, luck, and/or magical factors. A typical man-at-arms can take about 5 hit points of damage before being Killed. Let us suppose that a 10th level fighter has 55 hit points, plus a bonus of 30 hit points for his constitution, for a total of 85 hit points.This is the equivalent of about 18 hit dice for creatures, about what it would take to kill four huge warhorses. It is ridiculous to assume that even a fantastic flghter can take that much punishment. (Well, Reacher could!) The some holds true to a lesser extent for clerics, thieves, and the other classes. Thus, the majority of hit points are symbolic of combat skill, luck (bestowed by supernatural powers), and magical forces.
House Rule
As stated on Character Classes.
All characters start with d4+6 hit points (ie 7-10). There after they increase in line with the Hit Die Type as per PH p19. Well, ignore any roll under 50% of the possible hit points per level. So for magic users, every level they gain either 3-4hp, and for fighters 6-10hp. It doesn't make sense for a 10th level magic user to potentially have 10hp if they'd rolled 1 every time.
There are no class level limits and therefore no maximum hit die. If we get to level 15 and beyond then they get to be super heroes like 5e starts with!
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