The American-English phrase Mexican standoff denotes a situation in which neither side in an argument or contest can win.

However, in early use, this phrase denoted a situation in which a person loses their money, but saves their life.

The phrase Mexican standoff originated in a story, set in Mexico, in which a Mexican bandit robs a traveller from the USA, but lets him escape with his life. This story was first published as follows in the Sunday Mercury (New York City, New York) of Sunday 19^th March 1876:

[For the N. Y. Sunday Mercury.]
A MEXICAN STAND-OFF.
BY J. HARVEY SMITH.

Has the reader ever played faro? If not—like Punch’s advice to young people about to marry—don’t! A little acquaintance with one of the “tiger’s” characteristics is necessary, however, in order to see the point of this tale. When you play the ace and the ten for an X each and both “open,” you are horrified when the dealer exhibits the ace as a “capper;” but as the ace glides off and the ten shows its smiling face, you breathe a sigh of relief; you are saved! What you lose on the ace you win on the ten—in other words it is a “stand-off.” But a Mexican stand-off is something not quite so soothing, as I discovered to my sorrow. “In thus [sic] wise,” as the romancers say. It was in May, ’75, I was on the wrong side of the Rio Grande where the sunny Mexican freebooter lugs away the swag from under Uncle Sam’s vigilant nose, and then throws the mantel of neutral ground over himself to escape punishment. I was at that time agent for the Eudoria Silver Mining Company, of New York. The Eudoria’s stockholders having put their money in the concern blindly, had waked up after it was too late and sagely resolved to appont [sic] some one to find the mine, and I happened to be that some one; not that the job was to my liking, but the pay was excellent, and the desire to see “strange lands and countries new” was still strong within me. And so, on this sultry day, mounted on a pestiferous mule, who would rather lie down than walk, I “might have been seen” making my way over the cactus-covered plain towards the village of Saint something-or-other, my first stopping place; the mine—or the place where the mine ought to be—being about a hundred miles in the interior. I say, I might have been seen; I may add that I was, in nearing the village, by a dashing cavalier on a sorry plug, who “dashed” up to me and saluted courteously. I returned the salute, as in duty bound, and inquired as to Saint S. or O. and then we rode on together. My Mexican acquaintance was a fantastic looking rapscallion, in his velvet coat, peaked hat and tattered gold braided breeches, and rather handsome; although he evidently hated soap and water—but they don’t mind such trifles in Mexico, our sister republic, as we fondly call her. His face was dark to be sure, with sun and dirt, but fully sixty per-cent more honest than the average Mexican, and I rather opened my heart to the man; something I ought to know better than to do—but, live and learn, they say.
On arriving at the village, my new acquaintance conducted me to a first-class poseda, or inn (second-class barn it would be anywhere else), and I there had the pleasure of eating a greasy supper, and then retiring to rest in a dubious-looking bed. I slept but very little, the surroundings being too horrid, and to this day, if measels [sic], small-pox, or dishonesty should break out on me, I should certainly place it to the credit of that night. Near morning I fell into a troubled sleep, from which I was awakened by mine host at daybreak, and then arose, feeling worse than if I had not slept at all.
The landlord had a most diabolical breakfast prepared for me, or rather us, as my friend Don Pablo y Vegas y, etc., joined in with me, eating his share of the meal with a hearty relish which I envied, but failed to comprehend.
After breakfast I paid the bill for self and Don Pablo, and the pestiferous mule and Mexican plug having been brought out and saddled by this time, we set out together, Don P. and I.
During the ride the Don let himself out for my delectation, apparently.
He pointed out the most prominent bits of scenery, such as a rock, a stump, a ravine, and so on, and it appeared that each particular spot had received its baptism of blood. Thus:
“This, senor, is the ravine where Don Martin Gonzales and his two daughters were killed last summer; the Don was rash; he would not give up quietly. The brigands only wanted his daughters and his money, not his life. This stone marks the spot where the notorious Sancho Martinez killed seven soldiers with his own hand, and then escaped.”
“Yes,” said I, “I have heard of that accomplished ruffian before; is he still alive?”
“O, yes, senor; and yonder ravine—the farthest one—that also is famous.”
“Ah, indeed! Did Sancho—”
“Yes—killed a man and a boy; was caught by the troops. They camped for the night on the rising grounds just north of the ravine. They tied Sancho to a tree, the soldiers did, with ever so many cords; but he escaped; he left his knife behind him, and you cannot guess where he left it?”
“No. Where?”
“In the captain’s heart, Senor.”
I shuddered; I couldn’t help it. The fellow narrated such fiendish deeds with such an exasperating air of indifference. It evidently did not worry him.
“You are a very entertaining man, Don Pablo,” I said at last; “your powers of description are marvelous; but, if you please, we’ll change the subject.”
I was riding slightly in advance of Don Pablo as I spoke, and was just about to turn to emphasize my words by a reproving look when I felt something cold touch my cheek. I turned slowly and looked into the wicked muzzle of a six-shooter!
“Good God, Don Pablo, take that thing away! What does this mean, anyhow?”
“Senor,” returned Don Pablo, showing his white teeth—the only clean thing about him—with a deprecating smile, “I am very sorry for you; but this is a poor country, and what is a poor man to do?”
“You mean,” said I, “that a poor man must rob to live in Mexico? Then you intend to rob me?”
“Ah, no! Good God!” cried Don Pablo—holding up one hand to heaven—not forgetting his pistol-hand, however. “But—but—I must live. Your watch, purse and jewels, Senor!”
My heart sank within me like a twenty-pounder. To be robbed in a strange land—left to starve, maybe. Horrible thought! And what would the stockholders of the “Eudoria” say? I was in despair. I would appeal to the Don’s heart.
“Don Pablo,” said I, in as melting a tone as I could assume on such short notice, “Let me appeal to your generosity—to your sense of honor—to your manliness—to anything you may have about you; don’t rob me thus. Have pity on me. In memory of the last two days that we have spent in such pleasant companionship, take that horrid thing away and let me depart in peace.” To my inexpressible relief Don Pablo showed signs of relenting.
“Senor,” said he, gently, at the same time lowering the revolver to the third button of my coat, “You speak the truth. We have been good friends. Indeed, I will—yes, Senor, it is against my principles—but—you are such a fine gentleman, we will call it a stand-off!”
I broke out into a perfect rash of smiles.
“You will give me,” he continued, blandly, “your money, watch and jewels and then you may go.”
“But, good Heavens,” I cried, angrily, “I thought—” He took a sight between my eyes and said sharply—
“I am Sancho Martinez.”
I nearly fell off my horse in fright. He was an expeditious rascal and had me despoiled inside of two minutes.
“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!”
I went; and, O! how gratefully I felt! I got out of Mexico, nearly starved, and inside of three months arrived in New York to be posted by the Eudoria’s stockholders as a swindler. A Mexican stand-off has its advantages, but—excuse me!

J. Harvey Smith’s story was reprinted in several U.S. newspapers, which probably popularised the phrase Mexican standoff.

The subsequent occurrences of the phrase Mexican standoff that I have found are as follows, in chronological order:

1-: From The Sporting World. Daily Bulletin of Outdoor Games and Pastimes, published in the Buffalo Commercial Advertiser (Buffalo, New York) of Tuesday 9^th November 1886:

Dan de Long, a well known character in the West, is reported by Yank Adams as having said that he once had $20 on a billiard match in Syracuse, and got “a Mexican stand off.” In answer to the question what that meant, he replied: “I lost my money but saved my life.”

2-: From The Lounger’s Observations, published in the Cleveland Plain Dealer (Cleveland, Ohio) of Sunday 14^th November 1886:

On some of the eastern railway lines a peculiarly ingenious device for the ventilation of cars is in use. Fans, revolving underneath the cars through gearing attached to the axles, forces [sic] air into the cars through water chambers and pipes with bell-shaped mouths above each seat. The device is said to work most satisfactorily. How badly it is needed on the western sleeping cars! The air in one that a man enters in the middle of the night is horrible, and more colds are caught upon them than by wet feet. If they were well ventilated and equipped with safes for valuables a traveler could even pay the extortionate prices charged for a berth and not grumble. But as it is one pays the price, takes all the chances and is satisfied if he gets a “Mexican stand off”—loses his money, but saves his life.

3-: From one of the unconnected paragraphs making up the column Everybody Knows, published in The Clifton Clarion (Clifton, Arizona) of Wednesday 23^rd March 1887:

That the religious editor of the Clarion, as usual, fell among the Phillistines [sic], in Lordsburg, and made a Mexican standoff there—lost his money and saved his life.

4-: From The Anaconda Standard (Anaconda, Montana) of Saturday 9^th August 1890:

LIKE OLD TIMES.
Henry Brooks Held Up and Robbed In the Mountains Near Homestake.

Special Correspondence of the Standard.
Butte, Aug. 8.—Henry Brooks, a rancher, residing on the other side Homestake pass, arrived in the city late last night and told a story savoring of old times. He said that when he had reached one of the loneliest parts of the pass he found farther progress stopped by a couple of men and the same number of Winchester rifles and he was told to throw up his hands. He obeyed promptly and while one of the men kept him covered with his gun the other searched him and took $55 which he had in one of his pockets.
After relieving him of his money the road agents ordered him to step off lively and not look back on pain of being shot. Mr. Brooks had no particular curiosity to satisfy and therefore did as he was told to do and continued to walk until he had reached the city. He is happy that he succeeded in making a “Mexican stand-off”—lost his money, but saved his life.
The men were disguised by masks made of something that looked like blue jeans, and consequently Mr. Brooks was unable to distinguish the toll collectors.