Initiative

Why Bother with It?
The original Little Brown Books say nothing about initiative, but they do reference the Chainmail rules for medieval wargames by Gary Gygax and Jeff Peren as a combat resource. The Chainmail rules state that a die roll is made to determine who goes first in a turn and the winner chooses whether to go first or second (unless orders are pre-written and simultaneous movement is used). The Chainmail Man-to-Man rule section has a number of guidelines regarding who strikes first. Those rules include which miniature is moving into attack position, the weapon class/length, and relative position (higher ground) of the opponent. Longer weapons have attack priority in the first round, but shorter weapons gain initiative advantage in subsequent rounds.
The Advanced Game Dungeon Masters Guide initiative rule states that a d6 is to be rolled by each group each round with the side rolling the higher score going first that round unless surprise takes precedence. Tied scores result in simultaneous attacks. The initiative die may be adjusted by factors found in the Players Handbook's weapon "to hit" adjustment table. Later editions of the game introduce alternative methods for determining combat initiative such as individual initiative order based on a d10 or d20 score.
In the absence of explicit initiative rules, I have used various initiative systems with White Box. One of my favorites is to ignore the initiative order concept altogether and have each side roll for their attack and damage (if any) which is then applied to both sides as if the attacks are occurring simultaneously. Alternatively, I have allowed the adventurers to attack first, in effect they always get initiative unless surprised. At other times when acting as referee I have simply stated which side attacks first based on tactical considerations such as weapon length or height advantage. Yet another practice I have sometimes employed is for each player to roll a d6 and have their PC act in turn based on the die score, highest to lowest. A practice I recently adopted is to award combat initiative to all combatants (adventurers and monsters) based on their level or number of hit dice with the highest such value attacking first, lowest last.
I readily admit a preference for simultaneous combat. With 1 minute rounds and each attack roll consisting of the net result of numerous swings, parries, feints and blows which land on armor and shield, as well as those drawing occasional blood, the simultaneous approach seems more realistic (and a bit chaotic at times). It is after all the cumulative result of the entire round of actions which may produce a loss of hit points, and both sides may suffer. The mechanics of everyone rolling dice and scoring hits and damage (sometimes spoiling a spell casting attempt in the process) can give the impression of a fast and furiously fought melee. Just the effect I am looking for!