pocket billiards

EPBF- is the European Pocket Billiard Federation http://www.epbf.com/

pocket billiards would include all cuesport disciplines making use of tables equipped with pockets (bags) to get billiards balls sunk (potted) into. This applies to Snooker, English Billiards, British Pool, American Pool eg Nineball or even the Russian Pyramid game in contrast to Carom games such as Three Cushion Billiards making use of a pocketless table.

But I can not assure you that the expression also transports the subtle sexual content in the widespread german meaning of "Taschenbillard spielen" with regard to "playing with one's own balls in one's own pocket" (masturbate).

If you mean the sexual connotation, in the US we would say: He's playing pocket pool.

If you just mean that someone is playing billiards, we'd say: Do you want to play go some pool?

I don't know anyone (US) that would say: Do you want to play billards.