What is the origin of the expression 'A Mexican standoff'?

Why is a standoff between three parties that are all enemies of each other called a 'Mexican standoff'?

What is so 'Mexican' about it?

Solution 1:

Mexican standoff: noun, (Informal: Sometimes Offensive.)

• a stalemate or impasse; a confrontation that neither side can win.

Usage note

• This expression is sometimes perceived as insulting to or by Mexicans. Its origin in the late 19th century may be connected to American perceptions of encounters with Mexican bandits of that era.

(Dictionary.com)

The origin, according to the following source the expression is just one of the many along the line of similar AmE slang expressions that use the term Mexican as a slur:

• Several sources I have found suggest that the “Mexican” modifier in the phrase refers to a supposed proclivity of 19th century Mexican “bandits” for running away from a fair fight. But the first example of “Mexican standoff” found so far in print used the phrase to describe a baseball game ending in a tie, and subsequent uses employ the term as a simple synonym of “stalemate” with nary an actual Mexican in sight.

• The “Mexican” in “Mexican standoff” is thus almost certainly just another entry in the long and shameful roster of US slang terms employing “Mexican” as a slur meaning “fraudulent, inferior, or marked by poverty, poor sanitation, lack of sophistication or ignorance.”

• Such formations as “Mexican bankroll” (one large denomination bill wrapped around a roll of smaller bills), “Mexican athlete” (a phony braggart) and “Mexican breakfast” (a cigarette and a glass of water) all reflect the same derogatory national rivalry. A “Mexican standoff,” in this light, is called “Mexican” because it is pointless, inconclusive and unproductive, not because it has any actual connection to Mexico.

(The Word Detective)

Early usage examples:

1876 March 19, F. Harvey Smith, “Mexican Stand-Off”, in Sunday Mercury, New York, page 2/col. 5:

• “Go-!” said he sternly then. “We will call it a stand-off, a Mexican stand-off, you lose your money, but you save your life!”

1891 September, N.Y. Sporting Times, volume 19, page 4/col. 3:

• ‘Monk’ Cline, who got a Mexican stand-off from Dave Rowe has signed with Louisville.

(Wiktionary)