In older editions of D&D and AD&D, the monsters' hit points was typically the number of d8's rolled and a constant number added sometimes. (We'll ignore the constant number added for simplicity).

For X hit dice, the average number of hit points is:

X avg(d8) = 4.5X (*)

Recall the monster hit point formula from a previous post:

N avg(D)

where N is the number of hits it takes to kill a monster, and avg(D) is the average amount of damage a player does per attack.

In an easy example where a player's weapon does 1d8 damage per attack, the monster hit point formula is:

N avg(1d8) = 4.5N (**)

Equating the average number of hit points from (*) and (**), we get N = X. This means that without any improvements in weapons, it takes on average X hits to kill a monster with X hit dice.

For low level monsters with 1 hit die or less, they basically function like minions which die after one hit. Monsters with 2 hit dice, on average have to be hit twice to kill. (Etc ...)

Let's examine how magic bonuses to damage changes things. The formula N for the number of hits to kill a monster, in general is:

N = 4.5X/avg(D)

For different magic weapon bonuses to damage, for a weapon which normally does d8 damage, we have:

D = d8, avg (d8) = 4.5 -> N = X

D = d8 + 1, avg (d8+1) = 5.5 -> N= 0.82 X

D = d8 + 2, avg (d8+2) = 6.5 -> N= 0.69 X

D = d8 + 3, avg (d8+3) = 7.5 -> N= 0.60 X

D = d8 + 4, avg (d8+4) = 8.5 -> N = 0.53 X

D = d8 + 5, avg (d8+5) = 9.5 -> N = 0.47 X

It takes at least around a +4 or +5 magic weapon bonus to damage, to halve the average number of hits to kill a monster.