My brief research couldn't find a version of this game so its possible its a made up term Mion made since she jokingly refers to herself as an old man to go along with Keiichis jokes that she's more like a boy. Old Maid is similar in concept to Black Peter and may have derived from it. Therefore, like the clubs rules of old geezer, no one loses. Black Peter is the English name of the European game of Schwarzer Peter which originated in Germany where, along with Quartett, it is one of the most common childrens card games. However, Hanyuu and everyone else is able to overcome the tragedy and as a result, with Tomitakes survival he is even able to save Takano in the only way possible through getting her treatment for HS. This is seen through how Takano could become the one loser through her shooting herself in the head or killing one of the kids and therefore taking the blame. I'm not sure if its a game in real life but thematically Hanyuu was the card that was missing however with her prescence in Matsuribayashi no one has to become a loser. Mion calls it the Old Geezer essentially its a version of the game where no one wins or loses as long as the missing card is added back at some point so all cards match.
