What part does chance and coincidence play in the short story "The Most Dangerous Game"?

There are several astounding coincidences that occur in
Richard Connell's short story, "The Most Dangerous Game." The most obvious is how two of
the world's foremost big game hunters manage to meet one another on such a remote island
in the Caribbean. The first example occurs when Rainsford manages to fall from his yacht
at the exact moment that it is navigating past Ship-Trap Island. It is by chance that
Rainsford manages to survive the fall and swim through the treacherous waters and rocks
that surround the island. Only because Rainsford announces his name to Ivan does Zaroff
recognize it, realizing he is in the presence of an equally skilled hunter; otherwise,
Rainsford would have probably joined the other imprisoned sailors awaiting to be hunted
by Zaroff. Though Rainsford shows great skill in avoiding Zaroff and his dogs, it is by
chance that Zaroff and Ivan walk into his traps. Lastly, it is only by sheer luck that
Rainsford survives his last-ditch plunge from the cliff into the rocky
waters.