Taking time to reason this out would have told him that he could fall and, since he was the only person on deck at that time of night, that no one would be around to see that he had fallen and rescue him. His instinct also took over when he dropped his pipe while standing on the rail (Connell, 1924). Reaching for the pipe was pure instinct. When a person drops something, more often than not he or she reaches for the dropped object in an effort to catch it (Carlson & Heth, 2009; Gray, 2011). While that makes complete sense from an instinctual standpoint, reason would say that Rainsford was putting himself far too much at risk because he was leaning out over an open ocean with no one around. He did fall, putting him in great peril. Instinct saved him shortly afterward, however, because he remembered where the gunshots had come from and swam in that direction (Connell, 1924). At that point, he was using both reason and instinct. His reasoning told him that he could not catch the yacht, and so he instinctively swam toward the sound of the gunshots. Had he not done so, and swam after the yacht instead, he may have completely missed the island in the dark. He could have easily been completely lost at sea, and he would have drown or fallen victim to a predator such as a shark. While reason and instinct served him well there, he had more trouble with the issue when he arrived at the island. As soon as he found out that General Zaroff was hunting people as "big game" on his island, he was appalled and his instinctive reaction was to make that clear (Connell, 1924). If he had spent some time reasoning out the reaction that General Zaroff might have, Rainsford might have determined that it would be better to keep quiet and even participate in an effort to eventually get safely off the island. Instead, he became the hunted because of the courage of his convictions.

Once he was being hunted,...

He knew that he would be required to look at things in a new way in order to survive. At that point, reasoning and instinct were again mixed together to give Rainsford the best chance of escaping Zaroff's hunt (Connell, 1924). In the end, Rainsford's reasoning ability was what got him back around the island via water and into Zaroff's bedroom, where the General was not expecting to find him. However, Rainsford's earlier opinion that hunting a human being was murder had changed (or he had at least determined murder was acceptable), because he decided that a fight to the death with Zaroff was the best choice. While he won the fight, it had certainly changed him.
Conclusion

Sometimes issues of reason vs. instinct happen with everyday people who are not part of a story. They stand up for what they believe in, which is a good thing. However, they should take the time to be aware of their surroundings. By using their reasoning activity to learn about the people around them, they will be more likely to mix their reasoning and their instincts in a way that is successful. Rainsford's instinct that hunting people (i.e. murder) was wrong was the same instinct most people would have in a similar situation. Despite that, however, he failed to reason regarding how General Zaroff might feel about his opinion of the "hobby" of hunting people, which put his life in danger. A stronger ability to reason could have made things easier for Rainsford, but it would not have made for as interesting of a story.

References

Carlson, N.R. & Heth, C.D. (2009). Psychology: the Science of Behavior. Toronto: Pearson Education Canada.

Connell, R. (1924). The Most Dangerous Game. Classic Short Stories. Retrieved from http://www.classicshorts.com/stories/danger.html.

Gray, P. (2011). Psychology. NY: Worth.