I head that luck level is one of the aspects of the programming that you have no control over. It can affect your tamagotchis health and growth and is determined at birth and is random. Apparently, all of the tamagotchis brought by the match-maker have low luck level and if you mate your tamagotchi with them their luck level will be lower. If you mate with someone elses tamagotchi with high luck level you can get yours higher... I dunno. I thought I read it somewhere valid. But i'd rather it be untrue, I suppose.