In Delver, dice are relevant in combat - and combat is very dangerous. When attacking your foe, you roll a number of d6s based on your weapon and any of those that equal or exceed the enemy's Might are successes. If none of your dice are successes, you can choose between overextending your Stamina (a precious resource necessary to attack and defend in combat), reducing your weapon's Grade (when it hits 0, your weapon is broken), taking some damage (your health pool is very limited), or choosing to miss.
Most of the game will not necessarily be spent in combat, though, and during those times you will have to rely on your wits to keep your character out of danger, rather than dice.