Plenty of threads about circuit requirements. It's not the number of pins that's key, it's the power draw.
You don't say what your circuits are rated for, but you're pressing your luck. I designed my gameroom to have 5 pins on a 20 amp circuit. That's a bit conservative, but most of my games have non-LED lighting and draw more power than modern games. Whether the games are being played will make a difference too.