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The great debate: Spells Slots vs. Magic Points
(hexbear.net)
Tabletop, DnD, board games, and minecraft. Also Animal Crossing.
Rules
Your suggestion remind me of the "reverse mana" system from the various Ogre and Final Fantasy Tactics games - start with 0 mana and gain some each turn, so you can keep casting simpler magics, or save up for a more powerful spell.