Hit dice (or HD) is roughly equivalent to a monster's level and gives the approximate hit points the monster has. Normal calculation for monster's HP is total of hit dice amount of 8-sided dice. Exceptions[1] are golems, riders, special "fixed" HP monsters (which are usually uniques), adult dragons, elementals on their home planes, and HD:0 monsters.
When a monster is generated, the number of hit dice it gets can vary. Each monster type has a base HD allotment. If this is higher than the current dungeon level, its HD are decreased by one; otherwise, HD are increased by one-fifth the difference. Then, if its base HD are less than your current experience level, they are increased by one-quarter the difference. This will never take the monster above 1.5 times its base HD (rounded down) or above 49. [2]
When the player is polymorphed into a monster, the status line shows HD instead of experience level. Player's hit points are also usually HD times d8. Exceptions[3] to this are golems, adult dragons, elementals on their home planes, and HD:0 monsters.
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