The thing is that BB's attitude towards the HMs improvising their own entertainment changed quite a bit in the later series. In the first few years, improvisation was positively encouraged. I remember being impressed by the sight of Elizabeth (BB2) constructing a "Kerplunk" game out of a plastic bottle and joss-sticks. It wasn't just games: who could forget the Ticklemeister's solar-powered water heater?
There was also the time (can't remember which year) where the HM's complained that the bedrooms were too stuffy, and asked for a fan. BB refused to provide an electric one, but suggested that the HMs submit plans to
build some sort of device, and BB would supply the materials! (The HM's didn't take BB up on that one...)
However all that changed in recent years, and games were
discouraged unless BB supplied the equipment themselves. I think it was BB8 when any attempt to improvise even a ball out of socks resulted in it being confiscated...