I recently modelled a 'Reference Fallible Player' playing a chess endgame with perfect information. Because their 'competence factor c' is not +infinity, they don't necessarily play the best moves even though they have perfect information. c = 0 corresponds to zero-skill, i.e., legal moves chosen at random. The state-space gives rise to a Markov System, from which all sorts of good things may be calculated. One can show how long a player with competence 'c' is likely to take to win a position from depth 'd', which in a way serves to characterize the difficulty of the endgame. The pdfs of the relevant papers used to be on a webpage about me on our University site, but due to an upgrade (?!) to a Content-Management System, I cannot currently point interested readers to those papers. My colleagues are still learning how to upload papers to the CMS without the 'website editor', a non-academic, vetoing their actions. However, if anyone wants to check these ideas out, they are welcome to ask for pdfs of the papers. Regards - Guy