"To know a peasant is to dread knowing a peasant. It seems the only hero eager to fight a peasant or have a peasant in their army ranks is the Necromancer." AB manual
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The peasant has the lowest health and defense in the game, with a value of 1. Merely one hitpoint means that any damage dealt to Peasants will kill at least one unit, unless you have artifacts which improve your units' health.
With a fixed damage of 1 and an attack stat of 1, peasants aren't affected by either Curse or Bless, unless Bless is cast by Adela, specialist in this spell, increasing their damage output based on the levels of peasant and Adela's. Usually, when they attack, in spite of their fixed damage and due to their low attack, they deal less damage than there are units in the stack.
Efficiency and cost
If recruited on the adventure map, the peasant joins the army for free. However, if recruited from a Refugee Camp or a Portal of Summoning built in a Dungeon town, they cost 10 gold per unit, the lowest price in the game.
A good tactic is to not recruit them. An even better one, if you're playing with a Necropolis army and hero, is to bring them to town and transform them into skeletons in the Skeleton Transformer (in Horn of the Abyss, they can also be brought to a Skeleton Transformer found on the adventure map if it's present), which has multiplied stats compared to the peasant.
Against peasants, you can usually just kill them with the shooters, because they're that slow. Or even with melee attackers, if you're sure one or some of your troops won't die, which can happen if there are hundreds of peasants in a stack. Such numbers are a common thing for them and a pleasure for the Necropolis heroes.
In the Heroes of Might and Magic 3 community, the peasant has become the symbol of the weakest unit in the game, and also a good source of skeletons and memes, based on transforming the peasants into skeletons and also on their weakness.
Ghost Dragons' aging ability, which halves the unit's hit points, formally affects Peasants, but in fact it does nothing against them as Peasants have themselves only 1 hit point, and aging takes out "zero health points" (unless a health-boosting artifact is equipped).
Amusingly, the peasant is one of the "strongest" units in the game in terms of cost effectiveness. An Azure Dragon (whose gold cost is 30000) will lose to a stack of 3000 peasants (also with a cost 30000 gold ). Ranged units fare better against their peasant-equivalent stacks but none of the melee units, except Vampire Lords, have any chance of surviving the peasant horde. Unfortunately, this is of little use in an actual game since 3000 peasants would require 120 weeks to accumulate from one dwelling, time in which other units will be accumulated in such numbers that the peasant legion won't be a threat at all.
In the former Heroes of Might and Magic games, the peasant was the first tier unit for the Castle equivalent faction, Farm in the first game and Knight in the second. They were both just as weak as the peasant found in Heroes of Might and Magic III, though, all stats having a value of 1.