1. A server device that provides a predetermined network game to a user through a communication line, the server device comprising: an event lottery unit that selects by lot one event from among a plurality of events including an encounter event with an enemy character present in a predetermined area in the network game; a command accepting unit that accepts from the user a command indicating action taken on the enemy character, when the encounter event is selected by lot by the event lottery unit; a game processing unit that performs a process on the enemy character, based on the command accepted by the command accepting unit; a memory that stores a status of the enemy character obtained after processed by the game processing unit; and a capture determining unit that determines, according to a predetermined capture success rate, whether capture of the enemy character has been succeeded, when the command accepting unit accepts a capture command from the user, wherein the event lottery unit selects by lot an encounter event for re-encountering an enemy character encountered in past, with a predetermined probability, the game processing unit reads from the memory a latest status of the re-encountered enemy character and sets the latest status as an initial status of the re-encountered enemy character, and the capture determining unit sets a higher capture success rate for a re-encounter than a capture success rate for a first encounter.