Is a one-sided bet valid, and how does it work?

A competition without a prize is permissible by consensus. However, with a prize, it is permissible in certain cases: if the prize is from the ruler or an external party, or if one of the competitors contributes money on the condition that he takes it if he wins and loses nothing if he is defeated, or if the money is from the competitors and they include a "muhallil" (an impartial participant) who equals them in strength, wins if he outruns them, and loses nothing if he is outrun. It is a condition that the muhallil's victory is not guaranteed, otherwise it becomes gambling. The competition is only permissible in what is suitable for war, such as camels, horses, and arrows, and it is not permissible for cows, rams, dogs, chess, or other games. Some scholars have permitted the expenditure of money in beneficial academic competitions for the establishment of religion, such as competitions for memorizing the Quran and Sunnah. There is no harm in wagering on beneficial academic issues.