How common is it or rare to have a stroke during surgery?

It is rare: Unless it is cardiac surgery on cardiopulmonary bypass. If you have peripheral vascular disease or audible bruit of your carotid artery, you should get a duplex ultrasound to assess possibility of a plaque. If you don't have this, chances of a stroke during surgery and general anesthesia is low.

Stroke : It is extremely unlikely to have a stroke during surgery with modern anesthesia. The rate is less that 1 in 2000 general anesthesia patients. That number includes people who are at higher risks for strokes.