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Both systems, the third and fifth installments, are well-known subjects of criticism and are not considered successful. In the third game, there's a total imbalance with acceleration and deceleration, plus units that move across half the battlefield. In the fifth game, there's monstrous randomness, plus even more bullying of creatures with low initiative. The system with initiative, speed, and rounds simultaneously appeared in Heroes 6 and has been in all Homm-like games since then. It works simply: the one with the highest initiative goes first, but if the stat is equal, then either speed or the slot number in the army decides. This is so much simpler than the fifth game's system that I don't understand the complaints. It actually contributes to balance to a greater extent.
And also... no one calculates initiative in PvP. In the third game, the first speed is important, and it's achieved with specific units. And in the fifth game, there are several artifacts that affect initiative, and expecting the opponent to have strictly default values is a very dubious idea, plus there's a range. And both games have an initiative scale, so there's no point in thinking about initiative. Yes, the third game too. Because competitive third-game play is HotA.
Why is solo speed at the top of the list of shortcomings of the third game, and why is it not needed by anyone except discerning connoisseurs? It becomes obvious when you watch a couple of matches. The same is true for the fifth game. The OE system is already a standard, and it's not new. If the third game's system were implemented, that would be a disaster.