Suppose you want to mate with K and Q against K, but you must throw a fair coin labeled with K and Q and move the piece it shows. This seems not a big deal to me since you can't hang your Q :-) Example: Kb6 Qd7/Ka8, White to move, has an expectation value of "mate in 2".
Who gives the fastest # from the standard worst setup Ka1 Qb2 - Ke4 (give your algorithm as Markov chain) and does it take 2*10=20 moves on the average?
And what about KR/K, can White win at all?
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