This paper investigates the tradeoff between reliability and effectiveness for the IPv4 Zeroconf protocol, proposed by Cheshire/Adoba/Guttman in 2002, dedicated to the selfconfiguration of IP network interfaces. We develop a simple stochastic cost model of the protocol, where reliability is measured in terms of the probability to avoid an address collision after configuration, while effectiveness is viewed as the average penalty perceived by a user. We derive an analytical expression for the user penalty which we use to derive optimal configuration parameters of the network, restricting to those parameters which are under the control of a consumer electronics manufacturer. In particular we show that minimal cost and maximal reliability are qualities that cannot be achieved at the same time.