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Thank you for clarifying, so you meant Picks/Bans choosing system in general, and not refer to the step order.
It's advantageous to go last because it lets you react to opponent moves and you have less chance of wasting your own moves.
Example: both players love MME. Player A picks MME. Player B can now pick his 2nd favourite template. It's a clear advantage if you know what I mean.
Interesting, but you are right. I mean interesting, because I remember that I read that the first step is better and belong to the higher seeded team in CS:GO. Maybe I read this when not simple 2bans 2picks 2bans was implemented but other step order where really better the first step, I dunno. Because the combination of the steps are endless, only depends on us which one will be used.
The advantage gets bigger as template pool is smaller. In extreme scenario, when 2 players pick 1 template each from a pool of 3, the first player to make a choice has (statistically) a 1-in-3 chance to waste his move by picking the same template his opponent would pick. The second player who makes the final pick out of 2 templates remaining has no chance to waste his move anymore.
Although this is not true imo. I mean here no wasted picks, because the remained template will be used for the decider game (in case of 1-1). Or if you have best of one (bo1) format, then after two bans the remained template will be played. But your previous paragraph is still true (in case of 2bans 2picks 2bans, etc. combination). And your last paragraph is true as well, the situation is very different when you stealing and not forcing things.
Ok, the simplest solution is that the higher seeded player will decide if he wants to be first or second ;)