In 1974 when Gary Gygax and Dave Arneson published White Box the designers assumed many players would already be using Chainmail's Fantasy Supplement for combat rules. The three Little Brown Books were campaign rules to use the Fantasy Supplement and Man-to-Man rules in Chainmail and expand them beyond anything that had been done before. Chainmail is listed as part of the recommended equipment for play along with dice, paper and pencils.
Chainmail fills in a lot of the blanks in the LBBs, like initiative/turn sequence...role a die and high score chooses to move or counter-move. The Fighting Ability column on the Statistics Regarding Classes Table in Men & Magic is for use with Chainmail's Man-To-Man or Fantasy Combat Table. Using the Chainmail tables allows the PC, especially the Fighting Men, to really pulverize opponents with multiple hits - a third level Swordsman attacks as 3 men (or a Hero-1) and can potentially hit three opponents, killing each with good damage rolls, all in one turn. A score of 6 or better is needed to hit an opponent wearing leather armor and a shield with a two-handed sword.
The same third level Swordsman using the alternative system presented in Vol. I Men & Magic will need to score a 13 or higher on a d20 roll to hit an opponent with leather armor and shield. The type of weapon used in the alternative system doesn't change the to-hit number or affect the amount of damage done (d6 for all weapons). Against single hit-die opponents, the alternative system may allow the third level Fighting Man three attacks depending on interpretation (Strategic Review Vol. 1, No. 2). There remains a difference in chances of success, however. A d20 score of 13 or higher is a 40% chance to-hit with each roll. A score of 6 or better on two d6 is likely to occur about 72% of the time making the PC using Chainmail more likely to hit the opponent - multiple times!
The odds of scoring a successful hit using the Chainmail tables varies according to weapon used. For example, the same Swordsman using a hand axe will need to score a 9 or better on two d6 (about a 28% chance of success) to achieve a hit. Weapon selection is Chainmail can also influence who attacks first (longer reach) and whether opponents can step under one's weapon for an advantage (after the first round of melee).
Combining Chainmail and White Box is not a simple task. There remain many unexplained questions regarding how the two work together. White box introduces hit-points and hit dice which are not covered in Chainmail. In Chainmail a hit is usually a kill unless dealing with higher level creatures (including Heroes) which take multiple hits to kill. The Hero takes four simultaneous hits (kills) to eliminate them using the Chainmail non-Fantasy Combat Tables. Otherwise there is no effect. It is left to the referee to determine if a second level character takes two simultaneous hits to kill them or just one, or maybe even a second hit, simultaneous or not?I suppose it helps to remember Chainmail came first and stood alone as a rules set. White Box is the "add-on".
The group I learned White Box with did not have access to Chainmail and the system we first used for combat was the "alternative" d20. As this system became the standard for all later editions, it was many years before I even gave the Chainmail "alternative" a look. I find it is an interesting change to the game. There are some simulacrum and OSR re-interpretations that use the 2d6 Chainmail combat system and I find them interesting (esp. Five Ancient Kingdoms and Spellcraft & Swordplay).
As for the subtitle to this post, it is indeed a shameless reference to an entertaining video series of the same title by Zak Smith and friends.The knight & dragon image is taken from Chainmail.
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