how old was master chief when he was enlisted? how long has the covenant been around? how much luck does chief have?
Might be kinda late on this one but Chief and all Spartan II's and III's did not enlist into the military. The II's were abducted at the age of 6 and the III's were orphans of the Human - Covenant War who volunteered for the Spartan III Program. Halo The Fall of Reach Novel explains this (specifically the Spartan IIs conscription into the military) and is a great starter book for anyone interested in Halo Lore.
The Covenant was founded in 852 BCE, First Age of Reconciliation.
Chief has as much luck as the writers allow, I mean he is a fictional character and the main character in Halo and the one most can recognize. The usage of Luck in Halo's context is actually a nice touch, most Spartan II's have something unique about them, John was never considered the strongest or fastest but simply Lucky. Which as a main character to a franchise that's a nice foundation to build off of.