Zaroff, Rainsford, and Ivan all have different strategies they employ during the hunt. Rainsford, forced to act as the prey for the first time, uses all of the tricks that he has learned from a lifetime of hunting to evade Zaroff. He doubles back, changes his tracks, and eventually pretends to have died in the ocean. Zaroff, meanwhile, is a hunter of equal or even greater skill than Rainsford, and while he is reactive in his strategies, he always seems able to overcome Rainsford's obstacles. Zaroff even avoids Rainsford's traps, complimenting Rainsford on the skill of their construction. The two men are very well matched in their strengths, and the only reason that Rainsford survives is because he decides the risk of a free death is better than dying as a hunted animal.
Ivan's strategy, in contrast, is simple and direct; he is a large man who has gotten by on his muscular strength, and has not needed to develop a wider skill base. Consequently, he holds the dogs during that portion of the hunt, and since he is not paying attention, he falls prey to one of Rainsford's traps:
[...Rainsford] saw in the shallow valley that General Zaroff was still on his feet. But Ivan was not. The knife, driven by the recoil of the springing tree, had not wholly failed.
(Connell, "The Most Dangerous Game," classicreader.com)
Ivan wasn't prepared for trickery the way that Zaroff was prepared; he expected nothing more than the typical men who ran in straight lines, not the trap. These three strategies are examples of action/reaction for Rainsford and Zaroff, and linear thinking for Ivan.