If Sucker Punch is used against an opponent using Quick Attack, Quick Attack goes first regardless of the pokemon's speed, and Sucker Punch. Does the same thing happen with Me First i.e. a Lucario uses Me First on a Bullet Punch Scizor?
Looking at the move descriptions and move priority article hosted on this site, I assume several things:
Sucker Punch and Quick Attack are in the same priority bracket. Which attack goes first depends on the speed of the combatants: if the pokemon using Quick Attack is faster, it will successfully use it while the pokemon using Sucker Punch will fail to use its attack at all. If the pokemon using Sucker Punch is faster, it will use Sucker Punch successfully first, with the slower Quick Attack working afterwards.
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Summary:
Case 1:
(Faster pokemon) used Quick Attack! *attack animation*
(Slower pokemon) used Sucker Punch! It failed!
Case 2:
(Faster pokemon) used Sucker Punch! *attack animation*
(Slower pokemon) used Quick Attack! *attack animation*
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In a Me First vs. Bullet Punch scenario, Me First has a lower priority than Bullet Punch, so Bullet Punch will always hit first, and then the Me First will always fail, as the user has to move first in a turn for it to work.
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Summary:
Case 1:
(pokemon) used Bullet Punch! *attack animation*
(pokemon) used Me First! It failed!
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Now if we were talking about Me First versus Sucker Punch, both moves will always fail when used against each other. Sucker Punch has higher priority in this case, and only works if the opponent has selected an attacking move. Me First is not an attacking move (out of physical, special, and other (supporting) attacks it is characterized as an 'Other' type), and cannot work because it is lower in priority in this scenario, and thus also fails.
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Summary:
Case 1:
(pokemon) used Sucker Punch! It failed!
(pokemon) used Me First! It failed!
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Anyone should feel free to correct me if I've messed up my reasoning somewhere, but I do feel with the information I've garnered that I have it right. References should be self-explanitory.
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References:
http://www.smogon.com/dp/articles/move_priority
http://www.smogon.com/dp/moves/me_first
http://www.serebii.net/attackdex-dp/mefirst.shtml
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Phew! Some of these simple questions are not getting to be so simple anymore! ;3