The main conflict revolves around Yumeko wanting to retrieve library books taken by Dori, leading to a series of gambling challenges between them, including a Dance Dance Revolution game and a duel where the first to draw blood wins. Yumeko ultimately wins the duel, but the episode also features tragic news stirring gossip and off-the-books side bets at the school, with Kira trying to maintain control.

In 'First Blood', the games include a card selection challenge that results in a Dance Dance Revolution game, which Yumeko loses initially, and then a rematch duel where participants choose weapons and the first to draw blood wins. These games are part of the gambling and psychological warfare theme of the show.

Yumeko shows determination and resilience in episode 3 by first attempting to gamble for the library books, then accepting a rematch duel after losing the Dance Dance Revolution game. She wins the duel, demonstrating her willingness to take risks and face danger, which aligns with her character's gambling nature and boldness.

Kira is depicted as fighting to keep the upper hand amid the tragic news and gossip circulating the school. While Yumeko is engaged in gambling challenges, Kira is involved in maintaining control and influence within the school's social dynamics.

The 'first blood' duel is a pivotal moment in the episode, symbolizing a high-stakes gamble where the winner is determined by who draws blood first with a chosen weapon. This duel not only settles the dispute over the library books but also exemplifies the show's theme of psychological and physical risk-taking in the gambling environment.