determined by chance

See: haphazard
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In order to achieve a successful rehabilitation, it is imperative that the patients do not lose their direction; otherwise their success will be solely determined by chance.
Gaming, according the Gaming Law, means the playing of a game or mutual betting in accordance with established regulations, where the participants, seeking to win money, voluntarily risk losing their stakes and where winnings or losses are determined by chance, the outcome of an event or a sports competition.
In other words, the winner is determined by chance or by some means in which the participant has no bearing in the outcome.
Almost too coincidental to have been determined by chance alone.
Plays which, as The Theatre Guide puts it exist in multiple versions determined by chance.
Whether a child was given placebo or risperidone was determined by chance on a random basis.
critiques the basic attitudes of some recent commentators on Qohelet: Norbert Lohfink is too quick to see repudiated ideas as quotations and as not owned by Qohelet; James Crenshaw's picture of life as determined by chance is too grim; Roland Murphy is not sufficiently aware of the crisis that contradiction and the collapse of meaning had for Qohelet.