Randomness in systems introduces interest
while luck is not often greeted with welcoming reactions, introducing randomness in system can generate interest
on Note-taking systems such as Zettelkasten, this could introduce more surprise thoughts that a user could make
on video games
critical and missing hits on most turn-based RPGs (e.g., Pokemon, Battle for Wesnoth, Fire Emblem)
Mortal Kombat 9 has the Toasty boost mechanic that requires fast reaction and button inputs rewarding you with a full meter on success
most gambling games are also this (e.g., blackjack, poker)
with the randomness in effect, several strategies are forming with the factor in mind
on competitive settings, this can keep the players on their toes
on creative environment, this could be a source of inspiration