For example, if the rules say you move, then attack, all on your go, this could happen if you win initiative.
That's terrible, right? Ivar the barbarian wins initiative, rushes to attack, and Koko the gorilla steals the de-facto initiative, closing and getting the first attack.
So Ivar should be smart. Ivar shouldn't advance, and if Koko wants to fight, she can come halfway and hope to get lucky on the next attack. But still, that's not the greatest reward for winning initiative.
All right, so that's terrible.What if we fix the rules so that everyone's movement happens in one phase in initiative order, then everyone's attacks in a subsequent phase? We get this:
The guy with initiative runs up to attack, and the guy without plays keep-away. Only if the gorilla paradoxically wins initiative do her slow legs not carry her beyond the reach of the barbarian's axe. This can go indefinitely even if the barbarian is faster than the gorilla, unless you have some rule about locking in combat - let's say, if the barbarian ends up with 3" or more of move left over, the gorilla can't disengage until the next round.
There's also the whole idea that you might want to wait and see what the other figure might do, stand or run, before you commit yourself. To this end, a lot of initiative-based game systems have both a forward and a backward countdown, so that an individual with initiative can go first or last, as he or she prefers. Or, the option to hold one's move until the other side has gone, which works out to much the same thing.

- High initiative is generally advantageous, especially with two combatants already in range of each other. It also allows seizing the initiative, taking over some point of vantage, grabbing the sword on the ground.
- Low initiative is a more passive and patient stance. It gives the advantage of being able to act second, seeing what the opponent has done and performing the move to outfox that. Especially where movement and melee attack are rolled into one action, having low initiative can be more of an advantage than having high initiative.
With all the initiative systems out there, is there one for you that strikes the balance between ease of use, strategic depth, and players gaming the system?