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To-hit is the colloquial shorthand for "chance to hit in combat" and refers to the statistic individual creatures use in checks to hit with melee or missile attacks or kicks against the DV of other creatures. On weaponry, bonuses or penalties to-hit precede the damage formula and is depicted with a " " or "-" in front (as in: " 1, 1d8 2"); on equipment, they are displayed in parentheses. Armor and most other pieces of equipment, like cloaks, may modify both melee and missile to-hit and will display two values in parentheses accordingly, if to-hit is modified at all; shields may only modify melee to-hit and will only ever display one value in parentheses.
To-hit for melee attacks or weapons except whips is governed chiefly by the Strength attribute, for missile attacks (and whips) the governing attribute is Dexterity. In both cases, a value of below 10 gives a penalty, a value of above 10 gives a bonus; with the size of either proportional to the deviation. Apart from the weapon used itself (every item in the game has melee and missile to-hit and damage stats, including shields, which are the only ones which cannot actually be used as weapons) and modifiers granted by all other equipment, class powers, weapon skills, status conditions and tactics may further affect to-hit. When fighting with two weapons, the presence and level of the Two weapon combat skill and the weight of the weapons involved become major factors.
Circumstantial penalties to to-hit are common: various status afflictions can be presumed to affect to-hit directly, and being adjacent to more than one monster (two for martially-trained characters such as fighters, barbarians or rangers) causes to-hit as well as DV penalties. To-hit is also highly affected by tactics settings.
The changelog for ADOM 0.9.9 Gamma 13 includes an official commentarty on how to-hit calculation works:
"The internal mechanics for the melee and missile combat system have been rewritten to use different mechanics: attacks no longer need to surpass the DV of the opponent on a roll of 1d20 bonusses but rather 1d(20 bonusses) is rolled to surpass the DV value. This adds some randomness to combat (no longer will there be automatic hits in all cases). Also monster hit bonusses (at high levels) have been increased to counter the 'a DV of X is enough -- you'll never need more' effect observed in recent versions. Everyone still has a 5% chance to score an automatic hit (actually the chance is slightly higher, especially for extremely powerful monsters, but that's the baseline)."
It is not known whether this exact formula is still in effect or has been modified for newer versions of the game.
In summary, your to-hit value is of crucial importance in combat with melee or ranged weapons, at least as much as damage. No amount of damage is sufficient if you can't hit your opponent in the first place. The higher the DV of the creatures you encounter, the higher your to-hit needs to be to stay competitive, though there are diminishing returns once your to-hit surpasses the DV of even the most elusive monster by a large margin.
Note that spells are not affected by to-hit in any way since they do not check against DV. The chance of bolt spells being shrugged off appears to be governed by other stats. This means spellcasters can, and should, cast spells in Coward mode with impunity.