Rainsford really has no reason to believe that his life is in danger when he first appears at Zaroff's chateau on the island in "The Most Dangerous Game." Although Rainsford has heard gunshots from his yacht and as he swims ashore, and he is surprised by the appearance of Ivan pointing a pistol at him, he has no inkling of the dangers that await him. Zaroff appears to be a refined character with many beautiful objects surrounding him in his home, so Rainsford is lulled into a sense of security.
He was finding the general a most thoughtful and affable host, a true cosmopolite.
Rainsford enjoys the delicious meal and drink and finds himself bonding with Zaroff, an afficionado of the hunt in much the same way Rainsford loved the sport. It is only after Zaroff reveals his new sport and the prey that he desires to kill does Rainsford begin to worry.