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It depend on my opening.
Let's say I play a beastmaster, if I intend to start with Lair+harmonize and bring a creature on 2nd round that will act in the 3rd round, and I will want it to act first, then I will want initiative in the 3rd round so I will take it in the 1st round. If I am going with double mana flower on the first round and a mana flower and a lair on the second round, and I bring a creature only on the 3rd round that will act only on the 4th round, then I will give my opponent the initiative so I will have it on 4th round.
If I play a paladin that goes Ehren+Regrowth on the first round, then Dorseus+Leather piece on the second round and I want to bring a hand of bim-shalla on the third round to heal Ehren completely, then I will take the initiative on 1st round so I will have it on 3rd round so Ehren will be fully healed before my opponent act.
If your opening include a ballista, you will probably want to cast the ballista on a round you don't have initiative, so you will shoot on your initiative, so you would decide initiative the way it could work out.
Generally, there is a round that you think you would probably want the initiative in, so you plan accordingly.