I would like to end this question with a couple of lines from the paper (emphasis by me): There seems to be some programming going around, but what is the big idea behind their approach to the question? I tried reading the paper, but I'm too far away from those lines of thinking to understand what they're talking about. ![]() It came as a surprise to me that the answer is not really known, and that there are only estimates. The reference for the thresholds is this paper by Ronald Bjarnason, Prasad Tadepalli and Alan Fern. The number of unplayable games is 0.25% and the number of games that cannot be won is between 8.5-18%. In the same wikipedia link, it is stated thatįor a "standard" game of Klondike (of the form: Draw 3, Re-Deal Infinite, Win 52) the number of solvable games (assuming all cards are known) is between 82-91.5%. How does one even begin to find the number of solvable games? I couldn't even begin to figure out how would one go solving this problem! Immediately my interest shifted from the answer to the above question, to the methods involved in answering it. I have no probability formation (save for an introductory undergraduate-level course), but anyway I started thinking on how could the problem be tackled. When I came up with the question, it seemed a pretty reasonable thing to ask, and I thought "surely it must have been answered". What is the probability that a solitaire game be winnable? Or equivalently, what is the number of solvable games? ![]() ![]() By "solitaire", let us mean Klondike solitaire of the form "Draw 3 cards, Re-Deal infinite".
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