On the morning of the day after Rainsford is found by Ivan, General Zaroff informs him that he is to become the prey for the Russian. The most dangerous game is to last three days: at midnight of the third day, if the general does not find Rainsford, he promises that his "sloop will place you on the mainland near a town." Zaroff gives his word that he will keep this promise, but he demands that if Rainsford wins, he must give his word to say nothing of his visit to the island."
"I'll agree to nothing of the kind," is Rainsford's response. After he says this, the general reacts, "Oh,...in that case--But why discuss that now?...." Of course, once Rainsford declares that he has no intention of keeping quiet about Ship-Trap Island, it would be highly unlikely that Zaroff would set him free.
As it turns out, Rainsford becomes reduced to "a beast at bay," and,thus having lost much of his civility after he escapes Zaroff, he climbs into Zaroff's bedroom and seeks revenge himself, proving that he, too, finds the "most dangerous game" exciting.