Of American-English origin, the phrase the only game in town means: the only option worth considering.
This phrase occurs, for example, in the following from Left is marginalised as Starmer allies dominate at Labour conference, by Jessica Elgot, deputy political editor, published in The Observer (London, England) of Sunday 25th September 2022:
Hilary Schan, Momentum’s co-chair, […] said that was one reason the campaign group remained committed to the Labour party. “At the moment, under first past the post, the Labour party is the only game in town. That’s the message that we send to people: you’ve got to be in it to change it.”
The phrase the only game in town originated in the oft-repeated story of a man who is so addicted to faro * that he takes part in a game despite knowing it to be rigged, because it is the only game available in town.
[* The noun faro denotes a gambling card game, in which the players bet on the order in which certain cards will appear when taken singly from the top of the pack.]
The earliest occurrences of this story, and of the phrase the only game in town, that I have found are as follows, in chronological order:
1-: From The Kansas City Star (Kansas City, Missouri) of Sunday 15th July 1894—brace game denotes a game in which there is concerted cheating:
Better Than None.
From the New York Advertiser.
“Where have you been?” asked one sporty looking lounger in front of the Imperial of another.
“Down to Brighton Beach races,” was the reply.
“Don’t you know better than that?”
“Yes, but I am like the steamboat captain out West.”
“How was that?”
“The captain went up town while the boat was taking on some freight. When the first mate went after him he found the captain sitting in front of a faro layout and losing steadily.
“‘Come away,’ whispered the mate. ‘This is a brace game.’
“‘I know that,’ replied the captain, ‘but it is the only game in town,’ and he continued to play until he was broke.
2-: From Sign of the “Loaded Die.” The Kind of Gambling the Ghost of the Old-Timer Saw, an unsigned story published in The Kansas City Star (Kansas City, Missouri) of Sunday 4th October 1896:
The ghost […] wandered over to a crowded faro table. There he noticed an honest looking chap playing recklessly and desperately. He evidently knew little of the game. Going to his side the ghost whispered:
“Come away from here, I have something to tell you.” The man paid no attention to the voice and went on playing. The ghost noticed the hands of the gamblers. Long-fingered, they were, and nervous, constantly at work playing with the red and blue checks or the coins that laid before them on the green cloth. A hand would divide a stack of checks into two equal parts, place one half beside the other and with a deft movement of the fingers slip one pile into the other. This trick was done quickly, and repeated over and over again unconsciously. When a gambler desired to place a bet on a card he had a habit of picking up a stack of checks in a peculiarly handy manner, setting them down and then sliding them across the table with the tips of his fingers.
The ghost had watched the man at the table lose stack after stack of checks and again he whispered to him: “Come out of here.” This time the man heard, looked around and, seeing nothing, became alarmed. He left the table hurriedly and went down stairs to the bar room, the ghost following. In the bar room the ghost approached him and said:
“Don’t be afraid of a voice, my friend. I am the ghost of an old time square gambler. I saw that you were playing against a brace game and I wanted to warn you. No offense, suh, I assure you.”
“That’s all right,” said the man wearily. “But what’s a fellow going to do? That’s the only game in town.”
3-: From The Road Agents. Old Cattleman’s Story of the Robbery of the Red Dog Stage, by the U.S. novelist and short-story writer Alfred Henry Lewis (1855-1914), written for, and published in, The St. Louis Republic (St. Louis, Missouri) of Sunday 22nd December 1901:
“‘Thar’s no use tryin’ to head off old Peg-laig. He’s the most invet’rate sport that a-way, an’ faro bank is his leadin’ weakness. They even tells once how this Peg-laig is in a small camp in Iowa, an’ is buckin’ a crooked game. A pard sees him an’ takes Peg-laid [sic] one side.
“‘“Can’t you-all see them sharps is skinnin’ you?” says this friend, an’ his tones is loaded with disgust. “Ain’t you wise enough to know this game ain’t on the squar’, an’ them outlaws is dealin’ two kyards at a clatter an’ puttin’ back right onder your ignorant nose? Which you conducts youse’f like you was born last week!”
“‘“Of course, I knows the game is crooked,” says Peg-laig, plenty doleful, “an’ I regrets it as much as you. But whatever can I do?”
“‘“Do?” says his friend; “do? You-all can quit goin’ ag’inst it, can’t you?”
“‘“But you don’t onderstand,” says Peg-laig, eager an’ warm. “It’s all plumb easy for you to stand thar an’ say I don’t have to go ag’inst it. It may change your notion a whole lot when I inform you that this yere is the only game in town,” an’ this reedic’lous Peg-laig hurries back to his seat.’”
4-: From The Spenders: A Tale of the Third Generation (Boston: Lothrop Publishing Company, 1902), by the U.S. novelist and playwright Harry Leon Wilson (1867-1939)—as advertised in The Sun (New York City, New York) of Saturday 27th September 1902:
UNCLE PETER TALKS OF BILLY BRUE
“THAT’S like Billy Brue,” said Uncle Peter. “Billy loves faro bank jest as this gentleman loves New York. When he gets a roll he has to play. One time he landed in Pocatello when there wa’n’t but one game in town. Billy found it and started in. A friend says: ‘Billy,’ says he, ‘cash in and come out; that’s a brace game.’ ‘Sure?’ says Billy. ‘All right, much obliged fur puttin’ me on.’ And he started out lookin’ fur another game. About two hours later the feller saw Billy comin’ out of the same place. ‘Why, you geezer,’ says his friend, ‘didn’t I put you on that they was dealin’ brace there?’ ‘Sure,’ says Billy, ‘sure you did. But what could I do? It was the only game in town!’”
5-: From a special dispatch to The Cincinnati Enquirer, dated Columbus, Ohio, Thursday 31st December 1903, published in The Cincinnati Enquirer (Cincinnati, Ohio) of Friday 1st January 1904:
Once there was a man who, in a wild Western town, sat down with his bag of treasure to play faro. He lost steadily, and at last a Good Samaritan, kicking him on the foot under the table, said softly: “Hie [sic] thee away, friend; thou art playing against a brace game.”
“I know it, pardner,” said the victim; “but it’s the only game in town.”
The earliest occurrence that I have found of the phrase the only game in town used in the sense of the only option worth considering is from the following paragraph, published in the Albuquerque Morning Journal (Albuquerque, New Mexico) of Wednesday 20th April 1904:
A CASE OF NECESSITY.
Our democratic brethren must excuse us for giving so much attention to the row going on in their family between Willie and the Judge, but we haven’t any row on our side except the little one with the Bernalillo county gang, and that has such a bad smell you couldn’t expect us to stay shut up in the room with it all the time. As a democratic governor of New Mexico one remarked: “What’s a man to do—it’s the only game in town?”