MSPeconomist

If someone needs the bed due to age, disability, medical problems, pregnancy, etc., that person should be sincerely offered the bed.

Otherwise, it depends on the relationship and how the trip was set up:

A last minute invitation for someone to share the room because, for example, they're drunk, means that they get the sofa bed (or floor), as the room's owner is doing them a favor or preventing something worse from happening.

If the invitation was along the suggested lines of "you can take the sofa bed for free", then the "guest" gets the sofa bed because that's what was offered and accepted (as in a contract), with no further discussion except possibly for a last minute broken leg or some similar emergency. The guest should still offer to pay for something else, even as a gesture that doesn't come close to half the value of the room, or otherwise eventually offer a thank you gift.

If the invitation was "be my guest" for a birthday or special occasion, the birthday boy/girl gets the bed out of courtesy, just as I would offer a guest the most comfortable chair in my living room.

If it's some version of friends traveling together, then I'd look at how expenses are being split more generally, possibly versus what each party can afford to contribute if they philosophically take this stance. So the OP might be using his/her points for the room, but if the other person has used their miles for both tickets or if the other one is paying for dinners, etc., they have equal claims on the bed, so tossing a coin is reasonable.