You make a good point there. Hadn’t really put that much mathematical thought into it.
AARHE: Phase2: Game Sequence
I love copy and paste :-).
I am a big fan of Diplomacy, but can’t imagine adding simultanious movement to A&A. First, as Imperious Leader noted, there would be a large amount of moves to write. In Diplomacy a leader has to write at most 17 orders, but will generally need to issue 5-10. In Axis and Allies both the number and the complexity of the orders increases.
Second, writing down orders will likely serve as somewhat of a deterent to inivation. For example; as Germany I draft a set of orders to strike the U.S.S.R at Causcus and Karelia. If I suddenly see a stronger strategy that involves me completely changing my orders for both countries, the time I already put in that will be lost and the time I will need to write up new orders may deter me from attempting my new course of action. Having to continuously edit a page or two of orders will be tedious.
Third, in real life military leaders would re-act to enemy movements. If as Japan I ordered my units in Kwangtung, Manchuria, and French Indochina to attack China, but was attacked by units in Soviet Far East and India my attack would not proceed. Not only that, the Manchurian units would likely be diverted to re-inforce and/or counter-attack.