Hmm... I get the feeling that you're talking about limit breaks in general. Lots of the things you've said seem to hint at various different characters' limit-type attacks, from several different games:
[qq]Hit a moving target,[/qq]
Renzokuken
[qq]Or maybe get lucky.[/qq]
Reels/slots or some other random attack
[qq]Put two and two together,[/qq]
Dice
[qq]Go round and round,[/qq]
Reels, again
[qq]Or summon all your strength.[/qq]
Omnishlash or Grand Summon, to name two possibilities, depending on how you interpret "summon".
[qq]Use well what you've learned,[/qq]
Some Limit Breaks, such as Duel, use moves that are learned.
[qq]Or just do the right moves.[/qq]
Fairly general limit-breakey kind of phrase
[qq]Just pack a punch![/qq]
Zell, Tifa

Wonder if I'm getting closer, or losing the plot completely?