A few years ago, two Russian friends made a pledge to play more sports and stay in shape. Mikhail Prokhorov, a billionaire oligarch, and Boris Nemtsov, an aggressive opposition leader, shared more or less the same liberal views, and their decision to stay fit and healthy was driven by a political hunger: they wanted to live to see a time when Prime Minister Vladimir Putin’s authority began, finally, to decline. But for all the two men’s shared tastes—for democracy, for sports, for beautiful women—they could never agree on one crucial thing: whether they should compromise with their archenemy Putin.