Gamble Ball: 8x effective. However, if it fails to capture the target. it randomly does one of the following:
Restores 1/4th HP
Restores one move's PP
Cures any status ailment.
RS Ball: Contains an event Jirachi (kinda like the GS ball was meant to be in the anime)
Random Ball:Works as anyone of the other balls in the user's bag, chosen randomly. Of course, there will an extremely complicated formula to determine the probability, whose parameters are the ball's effectiveness and the no. of that ball currently in the bag. Works as an ordinary Pokeball if there less than 5 different types of balls in the bag.
Attract Ball: has 3x effectiveness if target's HP is the opposite as that of the leading Pokemon.
Influence Ball: Effectiveness varies with the leading Pokemon's happiness.