If table is placed under light it may be too close to the wll for play. Hard to tell without measurements.

We previously had the pool table under the light and it was fine. It is a smaller table.

Probably 4" lights, 4 ' apart. Put them on dimmers; make sure they're bright enough for your room. Some advise 4000K LEDs, but that is up to you. Others don't care for them.

Decoenthusiaste - Thanks for your reply. Where would you suggest I put the lights? Two on each side of the room? Four in a line on one side? The existing light is not centered because the ramp.

I'd put one in each corner, minimum, and if you want more, add between those on the long sides.

to clarify: center one on the entry door (white in pics), about two feet in, and then do all the others at similar positioning in the other corners.

The ceilings are ten foot. Would that make a difference in the number or size of lights?

General rule: divide the ceiling height by 2 and that tells you yow far apart to place them (5 feet in your case.) Also to prevent shadows, mount them 3 feet from walls. As for placement, if you have any special focal point other than the pool table, start by highlighting that area (maybe a bar, or a seating area.) Lay out your furniture placement first and see what needs lighting in order to both function and look good.