Dice are pretty much synonymous with RPGs, but there are a few rare systems that forego them altogether, like Castle Falkenstein.
What are some other systems that don't use dice? Are there any that completely remove luck/random chance on "important player actions"?
Chuubo's Marvelous Wish Granting Engine is an amazing diceless game. It works by having a different view on success/failure. You use your own stats to set your Intention Level and then that get compared to an interpretative chart to determine how well your intention goes. The worst is essentially "you only make yourself happy" and it gets as good as "you satisfy everyone's desires." But, it's worded differently and you can always choose a lower result than what you get if it fits your real goal better.
Eidolon: Become Your Best Self uses a Tarot deck made up of specific cards. Each one has a polarity that determines "full success," "partial success" and "failure" (postive, neutral, and negative, respectively). You draw a number of cards from the deck equal to your relevant stat when making a move and pick your favorite for the scene. You pick two neutral cards to be special by picking them as like your "favorite" and "least favorite" and get a class specific effect when you choose them (and must always choose your least favorite if it comes up). Any unused cards are returned to the Tarot deck, which might sound tedious but the game is designed to not have a ton of checks.
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