word usage - Literal meaning and etymology of “off” in “bake off”, “dance-off” etc


Off has a lot of connotations and compound usages; my question is about the following idiomatic use:


Off: (adverb)



(also -off) used to form nouns referring to a situation in which two or more people or teams compete against each other to see who is the winner:




  • the BBC series, the Great British Bake Off




  • Audience applause determines the winner of each dance-off. (Cambridge Dictionary)





Questions:


What’s the literal meaning suggested by off here in the context of competitions? Is it a synonym of “over” in the sense of “finished”?


What’s the etymological history of the above usage?




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