Felix Felicis is introduced as a potion capable of turning any ordinary day into an extraodinary day.
"However if brewed correctly, as this has been, you will find that all your endeavours tend to succeed"
In Half Blood Prince, where Harry uses the potion to attempt to retrieve the Horcrux memory from Professor Slughorn, there is a scene where it indicates the potion is providing a mental nudge.
"The Felix Felicis gave Harry a little nudge at this point."
So my question is, does this potion provide inevitable luck or does it only invoke lucky instincts which no one has yet ignored?