Source: Nintendo
Best answer: The Battle Ring System is a unique battle system in Paper Mario: The Origami King that functions as a circular, multi-ringed puzzle, where you line up enemies to do the most damage.
- Fear the folds: Paper Mario: The Origami King ($60 at Amazon)
What is the battle system like in Paper Mario: The Origami King?
In Paper Mario: The Origami King, like most RPGs, you enter battles by encountering roaming enemies out in the world — you can avoid them if you want, and since there's not a traditional EXP or leveling system you won't lose out on a ton if you do, though there may be other rewards to battling. Once you enter the battle, you'll find yourself at the center of a circle with enemies surrounding you, each positioned on one of several "rings" circling out from you.
The battle system is turn-based, meaning you'll have a turn to choose your action and complete it, as will enemies. You can perform several different actions, such as choosing from different types of attacks or using items. You'll also have allies join you on your quest. While they don't directly fight alongside you, they can use certain abilities to make the battles easier for you or take out enemies for you.
However, your ability to win or lose is not necessarily determined by equipment or abilities in this game. Still, it is mostly contingent on how well you handle the Battle Ring System.
How does the Battle Ring System work?
Source: Nintendo
In each battle, you'll begin with a phase where you have to "line up" enemies by moving the rings around to get the enemies surrounding you into one of two patterns. You can get enemies to line up in a row so you can bounce off their heads one by one, or you can put them in a two-by-two square so you can hit them all at once with a hammer.
However, there's a catch. You have a timer ticking down while you make these selections, so you can't just take your sweet time moving them around. The timer can be increased by paying coins either to the timer itself, or to Toads in the audience, who will dole out help in the form of healing items, attacks, or helping you line the enemies up efficiently.
If you line enemies up correctly, battles are immensely simplified, with you generally able to win in just a turn or two. Effectively, this means battles in Paper Mario: Origami King are more like glorified puzzles, with combinations of enemies getting harder and harder to arrange the further you get into the game.
How does this system change during boss battles?
In boss battles where you're only facing one foe, the Battle Ring system works a bit differently. Instead of Mario standing at the center of the rings, the boss will be in the middle. Mario stands on the farthest ring. Your line up phase will be spent rotating rings with arrows placed on certain segments of the rings to create a path for Mario to run along and eventually make it to the boss at the center to land a hit. Specifically, you want to aim for the boss' weak spot, though it's not clear just yet how you'll determine what that is.
Once you've lined up the rings, Mario will run into the circle and follow the path and arrows as they lay. If he reaches the boss and stops on a segment that has an "attack" marker on it, you'll get a chance to land a blow on the boss and potentially cause further damage, depending on whether or not you hit its weak point.
Fold by fold

Paper Mario: The Origami King
Princess Peach has been...folded?!
Paper Mario: The Origami King sends Mario and Luigi to the origami festival in Toad Town, but something's wrong -- everything is folded into origami, including Princess Peach! Journey to take down King Olly, fight folded enemies, and end the king's reign of origami terror once and for all.
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