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The term was initially used to describe a confrontation between three individuals, each of whom had a gun. In a duel, which occurs between two individuals, the person with the fastest draw, or who can get off the first shot, tends to have the advantage. In a Mexican standoff, however, the second person to fire a shot has the advantage, because unless the first person to draw and shoot is so fast that she can get off two shots before her opponents can draw and fire their guns, the first shooter and her intended target are occupied with each other, leaving the third individual "free" to shoot at the other two who are otherwise occupied, even if only for a split second.
The termis more commonly used to refer to a situation between any number of opponents where outside circumstances create a situation where none of the opponents can seem to gain an advantage, resulting in a stalement.
"Mexican standoff, may 30, 2011" by Tim Pierce is licensed under CC BY.
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References
Cambridge Advanced Learner's Dictionary
N.d. Mexican Standoff. Http://dictionary.cambridge.org/dictionary/british/mexican-standoff, accessed February 9. 2015.
Morris, Evan.
N.d. Mexican Standoff. The Word Detective. Http://www.word-detective.com/2011/03/mexican-standoff/, accessed February 9, 2015.
TV tropes
N.d. Mexican Standoff. Http://tvtropes.org/pmwiki/pmwiki.php/Main/MexicanStandoff, accessed February 9, 2015.