What makes it a pleasure to interact with a computer system? In this paper,we discuss some possible factors contributing to a pleasant interaction. We study the pleasure of interaction under the domain of a two-player game called word tennis, Shiritori in Japanese, conducted through a computer network. Two sets of experiments were carried out. The first set consisted of game sessions between a subject and a computer player. Half of the subjects were informed (correctly) that their opponents were computer players, while the other half were informed (incorrectly) that their opponents were human players. All subjects could quit the game session whenever they chose to do so. The second set was the same as the first one except that the computer player was replaced by a human player. From the results of both sets of experiments, we reveal that, regardless of whether the actual identity of the opponent is a computer or a human player, subjects who were told to be facing with a human player gave significantly higher pleasure-ratings than those who were told to be facing with a computer player. Furthermore, subjects who found the game pleasant kept playing the game until the end of the pre-determined time limit (one hour). As the word tennis game is dry and monotonous in essence, the exceptionally long game session suggests that the subjects must have had an intrinsic motivation for the game. However, previously recognized intrinsic motivation for games in general fails to explain our observed phenomenon satisfactorily. Hence, we make an attempt to characterize a novel intrinsic motivation, and postulate that the cognition of being involved communication with a human mind is indeed a valid intrinsic motivation in interacting with a computer system.