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”?
I imagine you could make Fate diceless without too much trouble. Maybe increase the starting pool of Fate points so people have more say in what checks matter. You could also do simultaneous commits if you want more tension (ie: everyone put some number of fate points, even 0, in their closed hand. Reveal at the same time)