[math-fun] Game Theory/Chess strategy question

Everyone who's ever played games like chess quickly learns an opponent's style of play, whether it be aggressively offensive, or methodically defensive. I'm curious about the _types_ of games that encourage offensive strategies v. the types of games that encourage defensive strategies. Some evolutionary biologists have claimed that Darwinian evolution optimizes by using an almost purely offensive strategy. I don't have an opinion one way or another, but was curious about what sorts of environments might favor one strategy versus another.