Facebook Inc. is making a $2 billion bet that a virtual-reality headset will one day become the center of its users’ social lives.

The world’s largest social network yesterday said it is buying Oculus VR Inc., pushing into wearable hardware for the first time and stepping into a race with Google Inc. (Nasdaq: GOOG). Oculus, based in Irvine, Calif., makes a ski-goggles-like device called Rift that people can wear to play games and that may eventually let them feel like they are watching sports courtside.

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