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Are all difficult Rogue-likes considered Foddian games? Does there need to be climbing? In a Foddian RPG, are characters allowed to level up?

I think what generally separates a roguelike from a Foddian game is that roguelikes are generally made up of different levels instead of a single large level like most Foddian games. There doesn't need to be climbing, although climbing is a really easy way to make a game feel Foddian.

As far as I know, there aren't any Foddian RPGs out there to work from, it's up to you to figure out what feels Foddian in that context.