It is interesting that while Turing is considered a creative genius at a level I am not sure how to characterize but he was certainly very important and successful in the code-breaking efforts during WW2, he worked with some of the best British chess players among them Golombek and Alexander. He would play with Golombek who I think could allow Turing to change color at a point of his choosing during the game (I am not sure of the constraints -- maybe it was up to a certain move) and Golombek could then beat Turing from Turing's presumably losing position. I have never played at those odds but I can't imagine, assuming that Golombek was playing to win that Turing had much of a position -- on the other hand, perhaps Golombek would try to keep a more or less even game so that he had chances. Anyway, I really wonder how weak of a player Turing was and if perhaps some of his games survive.
A similar question was asked on another forum a few years ago, and the answer that was given was "Alan Turing wasn’t a very strong chess player at all. He was probably at the level of a beginner. He certainly knew the rules of the game, but not much more."
Wikipedia notes, regarding the chess program that Turing and a colleague designed, "... the algorithm is primarily designed around the decision to take a piece or not; according to Turing, the resulting gameplay produces a low level game of chess, which he considered commensurate with his self-described average skill level at the game." According to the article, Turing's algorithm (it's really difficult to call it a "program", as it never ran on any actual computer - Turning only ever "ran" it on pencil and paper) only looked two half-moves ahead, applied a static evaluation function to each resulting position, and selected as the next move whichever one led to the highest average evaluation after the following half-move.