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"?
Amber is a classic example that comes up in these discussions.
Intrepid uses playing cards instead of dice to resolve scenes and combat. For scenes, two people each narrate an outcome, and players vote on the version they prefer using red or black playing cards. A card is then selected and that outcome becomes the truth, so there is still an element of randomness.
In combat, each suit has a specific meaning for the ebb and flow of the battle, jokers change the scene, and the first person to draw the 4th ace wins the fight.
Most of Ben Robbins' don't have a random element at all and conflicts are resolved through procedure. Follow uses two coloured stones/poker chips/tokenswhich are drawn from a bag, similar to Intrepid. He also provides a "finger dice" system for getting dice-like results without using dice. On a signal, every player throws from 0 to 5 fingers, and groups of 5 fingers are eliminated. The remainder is roughly equivalent to a d6 roll.
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