Luck is a measure of your general good fortune, and affects the recharge rate of Critical Hits. Now you instantly gain 1 point!”— In-game description
As each S.P.E.C.I.A.L. skill can only be set to 1, at minimum, taking Luck Training 10 times is a waste, as no S.P.E.C.I.A.L. stat can be raised above 10.