I heard that a one horse race means a competition which one particular person or team is very likely to win because they seem much better than the other people competing. Anyone know about the origin of this expression? why one horse?

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    If there's only one horse in a race, who do you think is going to win? – TimLymington Feb 19 '14 at 16:56
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    Also notice that this is often written as one-horse race to remove the ambiguity of whether this is a single horse in the race or a single instance of a horse race. – virmaior Feb 19 '14 at 17:53

In a true one-horse race, the one horse comes in first (and last, too, if you choose to look at it that way) because it is the only horse entered in the race. However, the term "one-horse race" is also used figuratively to refer to a contest in which one of the entrants outran the others by a huge margin or (viewed before the race) is a prohibitive favorite to win.

One early example of the post-race usage that Google Books finds occurs in California State Board of Agriculture, Transactions (1889), reporting on a race that took place in the San Joaquin Valley of California on September 19, 1888:

The second race, a district trot for three-year olds, was a “one-horse" race, Moses S winning in a go-as-you-please fashion. Two started: Grace Vernon might have been started in an opposite direction, if it was intended that she should pass Moses.

The pre-race use of the term appears in, for example, Bailey's Magazine of Sports and Pastimes, volume 56 (1891):

Perhaps the unexpected excitement of the race, the entire alteration in the preconceived ideas of most of the spectators, the surprises, of which there were many, all tended to make the great race a memorable one. When one reflects what we all thought the [St.] Leger would turn out to be after the race for the Derby, our readers will understand our meaning. Did we not repeatedly hear the expression “a one-horse race,” and old racing men question if it was worth while to go to Doncaster to see Common romp in? And when Mimi made that inglorious exhibition at Leicester, then more than ever did the path of Common seem clear.

Writers were applying the phrase to sporting events other than horse races as early as 1892, as this account of an intramural cricket match in The Oxford Magazine (May 11, 1892) demonstrates:

The Freshmen's match was what the reporters would style a “one-horse race,” as Fry, the facile, easily carried off the honours both in the batting and bowling department. As a matter of fact, he was very lucky to secure his century on the first day, as two certainly of the catches he gave ought to have been safely held : on the third day his fifty-three was an excellent performance, as he timed the ball well, hit it hard, and ran some good runs.

One of the earliest occurrences that Google Books finds of "one-horse race" used in a non-sporting context occurs in an advertisement in The Moving Picture World, volume 18 number 7 (November 15, 1913) in which Universal Pictures quotes a congratulatory telegram it received from Washington Film Exchange:

"Can't find words to properly voice praise due to Universal program and Universal progress. This is a one-horse race. You can't lose."

One frequent situation where people refer to a "one-horse race" is in elections where a candidate on the ballot is running uncontested. This situation comes very close to the sense of being the only horse participating in a horse race. Sayyid Mir Qasim, My Life and Times (1992) offers this example:

The 1951 elections to the Constituent Assembly, held not long after the Pakistani invasion, were in fact a one-horse race: all the National Conference candidates, including me, got elected unopposed.

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