Fresh off of beating Yumemi, Yumeko challenges Manyuda to an official match in front of the same crowd, without so much as an intermission for bathroom breaks! The Vice President (she of the white mask and distorted voice) steps in as dealer of a game called “choice poker”, in which no folding or calling is allowed, but the last person to raise can decide whether the stronger or weaker hand is the winning one.
In the crowd, both Mary and Sumeragi recognize that this game overwhelmingly favors the player with more money; in this case, Manyuda with his 100 starting chips over Yumeko and her 31. But having watched three other council members fall to her, Manyuda has a good basis of data upon which to calculate the best strategy to defeat Yumeko.
Specifically, he knows she’s a compulsive gambler and a little insane, and so needlessly makes risky raises despite the fact this is a game of more measured, one-chip raises. Sugita Tomokazu’s inner monologue dominates the episode, and at times it sounds like a slightly less apathetic Kyon is playing a particularly serious game of cards against Haruhi.
But at the end of the day, it’s a simple card game, with simple rules, and when Manyuda sticks to fundamentals, he manages to easily bait Yumeko out of all her chips. It’s then when Yumeko beseeches Sumeragi, who said she wanted to be her friend, to bail her out with more cash.
It’s revealed that Manyuda recommended Sumeragi’s entry into the Student Council, after she proved to him they had similar levels of ambition, but when Yumeko beat her she was discarded, and Manyuda concluded Sumeragi never had the talent to match her lofty ambitions.
That doesn’t stop him from appealing to her desperation in trying to return to a position of power where she can again vie for the top spot, as well as inherit her family’s business, something only possible with a council seat, so he dangles that over her head to counter Yumeko’s request.
Sumeragi doesn’t fall for it, instead pledging 100 chips to Yumeko, hoping to exact revenge on Manyuda, who only ever saw her as a pawn; a stepping stone on his own road to the top. Yumeko rarely looks that reliable, but Manyuda is clearly underestimating her. There’s a method to her madness she has yet to reveal to anyone—perhaps even herself!