[amichail]

For the ESP Game, it might be the case that they replay one person's session.

But for Phetch:

"Emulating Seekers in a convincing manner is more difficult. If a real player enters useless descriptions of the image, we do not want the emulated Seekers to find it. Although this is not a significant problem since most Describers enter accurate descriptions of images, we nevertheless address it to protect the illusion that a real game is being played. The solution to the problem relies on the fact that we are using images from the ESP Game database, so the keywords associated with the images in the search engine are already known. Therefore, we emulate Seekers by not guessing the right image until a certain number of the ESP keywords have been entered by the Describer."

http://reports-archive.adm.cs.cmu.edu/anon/2005/CMU-CS-05-193.pdf#page=56