If the randomness is deterministic doesn't that mean players could peek into the future?
For NBA Inside Drive 2000, I developed all the ball physics to be deterministic and "reasonably" accurate (25 years ago, in a world without physics engines). This meant that after a player made a shot and the ball left their hands, the trajectory, scoring or bouncing off the rim, was purely controlled by deterministic physics. This in turn meant that we could foresee what was going to happen, and feed the player AI with that while the ball was in flight.
Obvious use was to move characters with high rebounds stats towards the place where the ball would bounce after not scoring, so they're more likely to pick the rebound.
[edit: for shooting the ball, the instant the ball would leave the player's hands I computed the perfect trajectory to hit a shot, and then based on the player stats, I'd nudge the trajectory off center. It was then purely up to the physics to determine if the ball went in or what]
However, you can't predict the other players' actions, and those actions can insert an arbitrary (and unpredictable) number of random() calls between now and when your next action executes, so practically there is no gameplay advantage you can get from that avenue (AFAIK).
Though maybe a cheat engine could simulate a few branches of possible inputs a few steps ahead and adjust inputs when it discovers split-second advantages?
But there are bigger exploits. IIRC, the client sends separate actions for buying a unit/tech/building and paying resources, and the other clients don't enforce that they go together. This allows malicious clients to buy without paying. It's been seen a few times even in the ranked mode of the Definitive Edition remake. https://www.reddit.com/r/aoe2/comments/fjjudp/cheaters_are_a...
This way of doing things made sense for the time, and the execution was impressive. It was pretty reliable, nobody wanted to cheat anyway, and yes lag was a big problem but there wasn't another good way to do it back then. Nowadays they should have something else IMO.
Finally found a genuine use for the blockchain, since the server is only used for the lobby!
Mine virtual AoE gold and record it in the distributed ledger. Primitive path finding is also AI, so now you just need some investors!
The only exploits that are inherently applicable in the case of a simultaneous deterministic simulation model are those of the information-revealing class (e.g, "maphack"). This is where a standard AH system comes in.
The obvious one is that the client knows where everything is on the map, even when hidden by fog-of-war - so client-side hacks can reveal that.
A hacked client can easily desync the game too, or stall it and cause it to time out if the player is losing.