Many devices allow you to check your connection speed within the Netflix app. (I would presume HBONow offers a similar utility.) The Netflix Page explaining how to do this is here:
https://help.netflix.com/en/no....
On the same Netflix page are their internet download speed recommendations for playing TV shows and movies:
0.5 Megabits per second - Required broadband connection speed
1.5 Megabits per second - Recommended broadband connection speed
3.0 Megabits per second - Recommended for SD quality
5.0 Megabits per second - Recommended for HD quality
25 Megabits per second - Recommended for Ultra HD quality
Remember that these figures are
per stream, so concurrent streaming to multiple devices is
bandwidth additive.