Is it permissible to play PlayStation with my brothers, on condition that the loser washes the clothes or the dishes, or helps my mother clean the house?

It is not permissible to wager on washing clothes, dishes, or cleaning the house, because jurists have stated that financial or beneficial wagering is not permissible except in races involving horses, camels, and arrows, and what is analogously attached to them, such as competitions in Quran, Hadith, and Fiqh. This is supported by the Prophet's (peace be upon him) saying: "There is no prize except for an arrow, a hoof, or a paw." Helping one's mother with household chores should be an act of generosity, not a punishment.