Yumeko's desire for revenge is driven by her discovery related to 'Ray,' the killer she is after, and her connection to the Kakegurui Club and its members, including Michael's father who was involved in dark past events. This fuels her determination to confront and stop Ray at the school board retreat.

Ryan and Michael chase after Yumeko during the school board retreat to stop her from killing Ray, trying to intervene before she acts on her revenge plan, indicating their concern about the consequences of her actions.

The school board retreat is the critical location where Yumeko's revenge plot comes to a head, serving as the backdrop for the confrontation involving Yumeko, Ryan, Michael, and Ray, making it a pivotal scene for the episode's climax.

Michael confesses that his father, Gabriel R. Adams, was not a business tycoon but a gangster known as 'Ray,' who was involved in the dark history Yumeko is investigating, which adds complexity to Michael's character and his relationship with Yumeko.

Yumeko's expertise in reading people and gambling strategy allows her to see through Michael's lies and navigate the dangerous situation at the school board retreat, driving the tension and progression of the plot in this episode.