アメリカ数学協会（MAA)のページでPeter Winklerのゲームが紹介されてる
https://www.maa.org/meetings/calendar-events/games-people-dont-play

Winkler ended his talk, however, with a claim more astounding yet,
one related to the axiom of choice fundamental to Zermelo-Fraenkel set theory.
He described a two-player game in which Alice seems to have the clear advantage
and then argued that in fact Bob can win with 99 percent probability.

“That’s clearly ridiculous,” Winkler admitted.
“But this is not a trick. This is a consequence of the ridiculous axiom that we use to do almost all of mathematics.”