The main irony in "The Celebrated Jumping Frog of Calaveras County" is that Jim Smiley is outfoxed by the stranger. According to Simon Wheeler:
Smiley was monstrous proud of his frog, and well he might be, for fellers that had traveled and been everywheres, all said he laid over any frog that ever they see.
Well, Smiley kept the beast in a little lattice box, and he used to fetch him down town sometimes and lay for a bet.
The essential irony is that Smiley knows he had the best jumping frog in the country and perhaps in the world. He makes money by bringing the frog into town where he will "lay for a bet." That is to say, Smiley is looking for a sucker who will bet against him. Wheeler has specified that Smiley's frog is very ordinary looking. Smiley thinks he is sure to win the bet he makes with the stranger, especially since Smiley goes out and personally catches a frog for the stranger to bet on. The irony is that the stranger is not such a sucker as he appears to be. While Smiley is looking for another frog, the stranger fills Smiley's frog Daniel Webster full of quail shot, and when the contest begins, poor Daniel Webster can't even get off the ground. Smiley loses forty dollars. This is a typical story of a trickster out-tricked. Such stories were popular in Mark Twain's day. William Faulkner uses similar anecdotes in some of his novels, notably in the trilogy featuring Flem Snopes: The Hamlet, The Town, and The Mansion.