Typical result:
494644 results in rooms less than 10: 449838 had 10 rooms (90.9%), 44806 had 100 rooms 9.1%
Note that anyone who finds themselves in a high-numbered room can draw the obvious conclusion. The question is, what can you infer about the situation if you find yourself in a low-numbered room?
To hammer the point, let say the coin toss decides between 1 room and ten million. If you find yourself in room One, do you still think the chance the coin has come up heads is 50%? If you do, don't tell me, write a letter to Monty Hall.
My vague ponderings about the actual doomsday problem is that it holds up, i.e. it's a reasonable argument that it makes eventual populations of say 10^400 simulated souls using the whole universe as a computer highly unlikely. But the sheer bigness of the possible-but-unlikely population leaves plenty of room for astronomical-sized future populations and doom isn't necessarily imminent in human terms.
http://jsfiddle.net/3f49ry5u/
So... unless I did the simulation wrong, it supports my conclusion.
If I did do it wrong, please show me a corrected simulation which supports your position.