The Most Dangerous Game Curiosity

When reading "The Most Dangerous Game" I have noticed myself becoming curious about how Rainsford ended up on the island, why he stayed on the island for as long as he did, and why General Zaroff thought he could kill Rainsford. Rainsford got swept off of his yacht and somehow floated to safety. The island he floated to was General Zaroff's."The door opened then...". I wonder if it was destiny that brought him to the island knowing  that the General hunted and Rainsford was a renowned hunter. Rainsford stayed on the island for quite a while. I am curious as to why he did not want to find a way off the island fast. His daughter was still out at sea and the story never told us whether she could navigate or operate the yacht. "...Good night, Whitney" He said as his last words with her before he was thrown off the yacht. The last thing I was curious about was why the General thought he could kill Rainsford. Rainsford had made it clear to the world, that he could survive under difficult circumstances."I've read your book about hunting snow leopards in Tibet, you see" Said the General. Yet the General still attempts to kill him, but instead gets killed.