I, too, found several things a bit unbelievable--or perhaps unrealistic--even in the context of a rather outrageous story. "The Most Dangerous Game" is an implausible tale in almost every way, but I find the fact that Ivan has been treated so cruelly yet stays with General Zaroff to be a bit much. I understand it to some degree, but even the fact that he gets to be cruel to others does not seem a compelling enough reason for him to stay.
I also find it a bit unbelievable that Rainsford does not do more to get out of the situation before the actual "hunting expedition" begins. He is certainly crafty enough and capable enough, and he is fighting for his life, after all. Why does he not do more to avoid the confrontation? All that being said, though, I still find this a satisfying story to read and enjoy.
Yes. I couldn't believe that when Zaroff had Rainsford up the tree that first day of the game that he didn't just kill him. I guess that wouldn't make for a very good ending. The author would not get to prove his point. All Zaroff did was just laugh and blow smoke rings up to Rainsford. If the game was a real game to the death, I believe Zaroff would have taken him out right then and there.
Another moment of disbelief for me was when Rainsford ended up in Zaroff's bedroom. I thought for sure when Rainsford jumped off the cliff that he was committing suicide. I thought he must have decided that it would be better to die of his own choice than to be caught by Zaroff.