If Rainsford wins the hunt, what does Zaroff promise him?
If Rainsford manages to win the hunt, Zaroff promises Rainsford freedom.
I would like to clarify the above statement a bit. Rainsford doesn't actually have to beat Zaroff by killing him. Rainsford wins if he is able to avoid being killed by Zaroff for three days. Rainsford is the prey, and Zaroff is the predator. Zaroff's agreement to every prey of his is that if the prey survives for 72 hours, then the prey wins the game.
"If my quarry eludes me for three whole days, he wins the game."
When it is Rainsford's turn to be hunted, Rainsford asks for some further clarification about what surviving and winning will actually get him. Zaroff gives his word as "a gentleman and a sportsman" that Rainsford will get to leave the island alive on Zaroff's boat.
"And if I win--" began Rainsford huskily.
"I'll cheerfully acknowledge myself defeat if I do not find you by midnight of the third day," said General Zaroff. "My sloop will place you on the mainland near a town."
Readers never get to see if Zaroff would actually keep his word, because Rainsford kills Zaroff. Rainsford doesn't give Zaroff the chance to keep the promise.
The "promise" made by Zaroff is that Rainsford will be allowed to leave the island if he manages to evade Zaroff in the hunt for three days; however, the reader is left to make a judgment call as to whether he is to be trusted or not. Please do keep in mind that this is the same man who hunts people for fun; in the end, we are left, once again, to make a decision. What does Rainsford do with Zaroff in the end, once he has him at his mercy in Zaroff's bedroom? Do you release a master hunter back into the jungle and give him the opportunity to hunt you down again, or do you become a killer yourself and sleep at peace?
If Rainsford wins, Zaroff promises him to let him go free from the island to continue his pursuits as a hunter. He makes Rainsford promise not to tell anyone about their hunt- should he survive. In the end, Rainsford wins and he sends Zaroff out into his own deathly island- not originally part of the deal, but a just ending.