Will events happen the same in identical saves?

It actually depends if you have chosen to have a random seed on reload or not, which you can set when creating your game in advanced mode. It is not possible to change this afterwards.

A new random seed on every load makes the outcome of battles and other things different. Default behaviour is to store the random seed in the savegame and thus, you have the same outcome every time you load.

As leetfan points out, the random seed is stored and reloaded from the saved game unless you enable New Random Seed in the custom game options. However, this only controls the sequence of random numbers generated by the game. If you alter when and how often the game uses those numbers, you will change the outcome of random events including combat and game events.

Note: I believe that every decision the AI makes is determined solely by its programming and doesn't require any random numbers. If that's untrue, pretty much any action you perform differently that an AI can see could alter the game.

For example, in the early game you make very few decisions that can alter the flow of the game. But let's say you attack two barbarian units during a turn.

• First you attacked with your Warrior and then your Archer, and this required five die rolls followed by three.

• After reloading you reverse the order of the attacks, but this time while the die rolls themselves have not changed, attacking with the Archer first requires four rolls while the Warrior still requires five.

You've now used one more random number, and this can completely change the outcome of events. Imagine a game of craps in Vegas with fourteen people around the table making bets and rolling the dice. If you were to take the exact same sequence of die rolls and replay them, assuming everyone bet the same, the final tallies at the end would remain unchanged. Now do that again, except knock out one or two die rolls in the sequence.