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Word Origin & History
jig
"lively dance," c.1560, perhaps related to M.Fr. giguer "to dance," or to the source of Ger. Geige "violin." Meaning "piece of sport, trick" is 1592, now mainly in phrase the jig is up (first attested 1777 as the jig is over ).

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2: trick, game —used chiefly in the phrase the jig is up.

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5. A piece of sport, a joke; a jesting matter, a trifle; a sportive trick or cheat. the jig is up (or over) = ‘the game is up’, it is all over. Now dial. or slang.

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Alternative: Webster's gives the origin of the word "jig" as a transliteration of an Old French word defined as "frolic" (c. 17th-18th century). Hence, "jig" is referred to as a dance, not a game. In the 18th century British Navy, the captain of the ship held the power of life or death over the crew of his ship. For certain offenses he could impose the death penalty. That penalty was carried out as follows: a line was thrown over the lowest yardarm, tied 'round the offender's neck. No blindfold, no feet or hands tied. At the command "take him up" two or three crewmen hoisted the man up and he writhed, jerked and twitched as he strangled to death. His feet and legs especially jumped about. He literally danced at the end of the rope. The crew of the ship were interested but not all were assembled as witnesses. Some of the crew had to remain on station to sail the ship. The word was passed: “the jig is up”. All hands were thus informed that the sentence had been carried out.