What would be the elo of a computer program that plays at random? What would be the Elo of a computer program that plays random moves?

For the sake of simplicity, assume that he never asks for a draw or resigns and never accepts a draw offer.
Right at the bottom of the Computer Chess Rating List for the 40/4 time control is Brutus RND, an engine that simply selects random legal moves.

http://www.computerchess.org.uk/ccrl/404/cgi/engine_details.cgi?print=Details&amp;each_game=1&amp;eng=Brutus%20RND#Brutus_RND

It has a rating of 205 (as of 6/6/2018). This is not a FIDE rating of course, but it is using the Elo system.

It has 0 wins, 242 losses and 64 draws. The draws are due to faulty programs that accidentally cause draws by repetition or occasionally stalemate, though they generally have a substantial material advantage when this occurs.

FIDE has a rating floor of 1000. Brutus RND would simply fail to establish a rating that high and would be unrated.

If we ignore the FIDE rating floor, it is possible to have a negative rating under the Elo system.

One point to mention is that FIDE uses a table to calculate rating changes and if the rating difference is greater than 735, no change occurs when the stronger player wins. This means Brutus could never have a rating of -5000 or anything like that because it would need to lose points to spectacularly incompetent players that would not be capable of delivering checkmate.

https://www.fide.com/component/handbook/?view=article&amp;id=197

We are left guessing here. 1000 Elo rated players would be able to get Brutus's rating down to 265, but since there are no players with worse ratings, we cannot say exactly how much further they could push Brutus's rating down if they did exist.

I would guess that players that are 500 Elo or worse would have trouble delivering mate consistently, much like the faulty programs. Draws by 3-fold repetition or the 50 move rule are not automatic under FIDE rules and would only occur if Brutus claimed them. But a human could lose by running out of time, as well as drawing by accidental stalemate.

So I'm guessing somewhere in the -200 to 200 range if FIDE allowed ratings below 1000 and allowed Brutus to compete.