In this paper we introduce a novel technique, the scheduler luck game
(in short sl-game) for analyzing the perform ance of randomized distri
buted protocols. We apply it in studying uniform self-stabilizing prot
ocols for leader election under read/write atomicity. We present two p
rotocols for the case where each processor in the system can communica
te with all other processors and analyze their performance using the s
l-game technique.