Several assistive technologies for users' operations have been recently developed. A user's sense of agency (SoA) decreases with increasing system assistance, possibly resulting in a decrease in the user's sense of fulfillment. This study aims to provide a design guideline for an assistive method to maintain and improve the sense of fulfillment with SoA. We propose a mathematical model describing the mechanisms by which the assistive method affects SoA and SoA induces a sense of fulfillment. The experience in the flow state is assumed to be a sense of fulfillment. The assistance effect on the skill-challenge plane in flow theory is defined as an increase in skill and decrease in challenge. The factor that separates the two effects from attribution theory is the locus of causality, which is matched to the judgement of agency (JoA) from the two-step account of agency. We hypothesized that the assistance increases the perception of skill and sense of fulfillment is greater when the locus of causality is internal, rather than external. To verify this hypothesis, a game task experiment was conducted with assistance that varied with the ease of recognition. We hypothesized that a player's JoA is internal for hard-to-recognize assistance, resulting in a high sense of fulfillment. Experimental results supported this hypothesis.