Chainmail Man to Man combat functions off of 2d6, consulting a matrix cross-referencing the weapon with the armor type, and checking for a target number.
What if one could do away with the matrix? This thought has occurred from some design decisions made working on my current Sci Fi game for the O.R.C.S. rules (the system that powers Spellcraft & Swordplay.
The method for doing so is pretty basic.
Each weapon in Chainmail has a class rating (daggers are class 1, swords are class 4, etc.) Instead of consulting the chart, use this class rating as a bonus, with one caveat: weapons with a class rating higher than 6 gain a bonus equal to half their class rating (Round down) + 1. So a two-handed sword gets a +7 bonus, while a flail has a +4 bonus.
Next, convert armor types into a "hit" penalty.*
No Armor = 0
Leather/Padded = 1
Shield Only = 2
Leather + Shield = 3
Chain, Banded, Studded, Splint = 4
Chain + Shield = 5
Plate = 6
Plate + shield = 7
The basics: Roll 2d6, adding weapon bonus, subtracting opponent armor penalty, and attempt to score 11 (on average, a trained warrior swinging a sword at an unarmored opponent will hit).
Optionally, if using a one-handed weapon and Dexterity is 12 or higher, add +1 to attack. If Dexterity is below 9, subtract 1 to attack.
If using a two-handed weapon (battle axe, pole arms, spear, pike, etc.) and Strength is 12 or higher, add +1 to attack. If Strength is below 9, subtract 1 to attack.
Basic magic weapons (+1, +2, etc.), then, simply increase the bonus (as we are used to) while magic armor increases the penalty to opponents' attacks.
*If using this with OD&D, convert Armor Class to penalty by subtracting AC from 9.