when i added circuits to my old circuit breaker i had no more space so i put in some replacement breakers which gave me 2 1/2 width breakers in the place of 1 old one ... but they are limited to 15A.
On 15A safe load is 1440 watts.
Watts per rig varies a bunch but on minimal VC boost from stock for OC i would think budgeting 200-250 W per rig will do it, possibly including a GPU.
Assuming you have a modern breaker, and open slots for additional breakers, I would go the 20A circuit route which I think is around 1800 W safe load. Use 12 gauge wire with 20 A ( instead of 14 ga you can use on a 15 A circuit).
1 20 A circuit should be enuf for 6 rigs and maybe 8.
If you are going to be laying the circuits to just 1 point, lay 2 circuits ( or more
) at the same time since the extra work and cost will be minimal. Use 12 ga wire and you can run them as 15 or 20 A.
If you have breaker box limits like me and can only use 15A breakers then 14 guage wire is cheaper.
I think you can also run 2 cuircuits through a single 3 conductor cable like you would use for running a 240V circuit ...this may reduce the work to lay the cables. In this config I believe you need to tie the 2 breakers together since they would share a common neutral and so there is a bit of a loss of flexibility vs 2 independant circuits. Use 14 ga for 15A and 12 ga for 20 A.
I am sure the master electricians will wade in here and correct whatever i got wrong.