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Task Group Initiative
Task Group Initiative determines turn sequence during combat. A fleet or fighter group can have its initiative set at any level up to that of its commander. Fleets/FGs move in ascending order of initiative, so set this low if other fleets need to follow you or high if you want other fleets to follow you.
This can be very useful when trying to intercept another fleet or fighter group. The advantage of moving later is that your ships can plot their courses based on the movement of other ships. This allows for closer interceptions since you're moving towards the actual position of the target, not where it was five seconds ago. Likewise, when fleeing, a higher initiative will allow you to move after the enemy has moved to intercept, possibly allowing your ships to leave weapons range, or at least lower the chance to hit.
In short: TG with initiative 100 moves->TG with initiative 110 looks where to move per its orders and moves->both of them fire if able.
I think that if TG1 can move at 10k km/s, wants to fight at 60k km, has 100 initiative; TG2 can move at 9k km/s, wants to fight at 90k km,
has initiative of 101; initial distance - 90k km, time discreteness - 5 sec:
1. TG1 moves 30k km
2. TG2 moves 30k km
3. both fire.
I suspect that there is some NPR logic to close all the way to zero in such cases but high initiative can still be beneficial.