Micropayment schemes are recently considered to have a variety of practical applications. Such kind of schemes handle a sequence of very small payments which therefore should be quite efficient to be payed and verified. An electronic lottery ticket scheme was proposed by Rivest as a means of probabilistic micropayment scheme in order to reduce the administrative cost of the bank. In this paper, the above probabilistic micropayment scheme is extensively studied and get improved. Analysis shows that the scheme by Rivest may reduce the administrative cost of the bank, however it brings extensive computational overhead to the merchant. A proposed simple modification improves the performance of Rivest scheme extensively. Furthermore, a novel development of self-randomized winning number generation is proposed in order to improve the fairness of the first proposed probabilistic micropayment scheme.