The classical Mexican standoff occurs when three people level guns at one another in such a way that if one gunman shoots a member of the trio the person not being shot at will in all likelihood kill the first shooter.
In other words, a stalemate ensues.
It’s a no-win situation.
The expression’s roots are in the American West where conflicts with the original Mexican settlers were often resolved with guns and even war, which is how Texas, New Mexico, and California became part of the United States.
The term Mexican standoff came out of these struggles as an ethnic slur, just as the word “gringo” arose as an epithet for the other side.
The expression is now considered a movie cliché through its frequent use in B-movies and Spaghetti Westerns.