I can see two sides to this....

On one side if the problem only affected the OP then IMO it is the OP that should recieve compensation. If the hotel had wrote the OP a check should he share it with his roommate?

On the otherside from the friends perspective the bill for the room was less than originally planned. IMO the OP might come out looking cheap and greedy if he ends up collecting more than half of the total room bill from his friend. I'll also add the OP will then be earning a cash profit from his friend, not the hotel.

When I have had a problem at a hotel when someone else is paying I ask for any other compensation beside a free night/deduction from the room bill because that would not benefot me. Maybe the OP could have asked for a free night voucher or points to be used later.