Wylie is a character who appeared in "An Appetite for Battle!" He's a local who had just won a village tournament when the episode picked him up, though he's probably better remembered for the chaotic battle that followed.
When Wylie got home, his wife Carrie challenged him to a Pokémon battle to settle an argument from earlier—apparently he'd made a snide comment during dinner, so she'd taken his bowl. Not taking her seriously as a trainer, Wylie accepted the challenge and brought out his Delphox. Carrie grabbed a Chespin that had been napping on their doorstep, figuring she'd use that instead.
The match didn't last long. Clemont showed up and claimed the Chespin was actually his—it had run away from him. Wylie declared victory since technically Carrie hadn't been battling with her own Pokémon, but the Chespin wanted to keep fighting anyway. With Clemont's permission, he took over the match. That didn't go much better; Wylie ended up injuring his back while commanding Delphox to use Mystical Fire, and the whole thing got called a draw.
Carrie brought him inside to recover. To make amends for dinner, Wylie had already bought her a cake, which she accepted. The couple invited Ash and his group to stick around and share it before saying goodbye as everyone moved on.
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