After analyzing almost all programs pertaining to winning complete information games, game study started to focus on the challenge of programming acceptable game players. A key factor required to create an acceptable player agent is the knowledge of the user’s internal state. People like those who want to know themselves, especially those who want to know their unconscious self-state, also called the “blind self.” This study proposes an approach to analyze an agent’s ability for estimating a user’s blind self as an improvement in human–agent interaction. The authors chose a card game called Hanabi as an evaluation of this type of recursive intelligence. Hanabi is a cooperative and an incomplete information card game in which each player’s cards are unknown to other players. A player decides whether to build a set of cards or discard them while providing hints to the other players. Previous research has demonstrated that the imitation of human behavior that corrects incomplete information increases the score in a Hanabi game between agents. The authors evaluated the agent’s function to modify incomplete information based on the behavior of the players in the game between a human and an agent. The authors experimented with humans and two types of agents. The latter differed according to the need to imitate and modify incomplete information as a cooperator among the experiment’s participants. Afterward, the game results were analyzed, and the impressions of the participants were evaluated. The results demonstrated that while the ability of estimation of the blind self is ineffective for increasing the score, the user developed a good impression of the agent when incomplete information was modified properly, resulting in a similar feeling in the case of a human collaborator.