In "The Ransom of Red Chief," the humor arises out of the conflict: instead of the kidnapped child being afraid, he terrorizes Sam and, especially Bill, who is threatened with scalping and ridden like a horse all one morning. Compromising on the ranson money so that they can assuredly be rid of the red-haired freckled terror that they have taken, the men write a ransom note which Sam surreptitiously mails in town.
The turning point/climax of the action occurs soon afterwards as the men await the depositing of the ransom money into the appointed spot. A "half-grown boy" on a bicycle deposits something into the box Sam has set up. After waiting an hour, Sam climbs down from his post and discovers, not money, but a letter in "a crabbed hand." The father of the boy, Ebenezer Dorset, contends that Sam and Bill's demands are "a little high." Instead, he offers to take the boy off their hands if they will pay him two hundred and fifty dollars. To this Sam utters an exclamation, but when he looks at Bill he sees "the most appealing look in his eyes I ever saw on the face of a dumb or talking brute."
So, in the resolution of the conflict, there is the typical O. Henry unexpected ending as Sam and Bill return "Red Chief" to his father, pay the two hundred and fifty dollars, and run when the father says he can only hold the boy for ten minutes.