1. A game-providing device comprising: a game management control module that sequentially provides a player with a game that includes a plurality of independent battle scenes, each respectively featuring an enemy character that appears therein as an opponent of a player character such that when the player clears one of the battle scenes, the next battle scene is provided to the player; a carryover condition determination module that determines whether or not a carryover condition has been satisfied such that the attacks against the enemy character, which are carried out by the player character in a first battle scene against the enemy character that appears in said first battle scene, can be extended to other such enemy characters that are configured to appear in battle scenes other than the aforementioned first battle scene; and a carryover processing module that, once the carryover condition has been satisfied, sequentially executes a process that uses a first attack value generated as a result of the player character's attacks against the enemy character in the aforementioned first battle scene to offset defeat parameter values required to defeat enemy characters that are configured in each of the enemy characters appearing in each of the battle scenes provided subsequent to said first battle scene, skips the appearance of the enemy characters whose defeat parameter values have been reduced to zero and, additionally, causes the subsequently appearing enemy character to appear in a state in which the defeat parameter value of said enemy character has been offset.