Exactly what clutch said.
And i3s have more than enough power for gaming, provided you have a decent video card in your PC. That's a requirement anyway, since the FX-6300 won't even display any picture without a video card.
If you *do* decide on an i3, then this next advice is applicable:
My particular i3-4360 outperforms the FX-8320 in plenty of games, but for price/performance ratio purposes you'd be best off with an i3-4150. The i3-4330 also has a good price/performance ratio, but above that it gets thrown off a bit.