![]() Without looking at human gameplay data though, this is probably the best heuristic of difficulty for unsolvable layouts. Humans aren't computers, and our brains probably aren't using depth-first search in the way a solver might. This isn't a perfect measure by any means. Another good solver is Klondike-Solver, although I'm not aware of what metrics it reports. Using a tool like Solvitaire (full disclosure: I am one of the authors of Solvitaire) can identify unsolvable layouts and record the number of unique states that needed to be searched to prove that there's no solution (often a very large number of states!). Alternatively, a layout may have a huge number of promising moves, only to turn out to be unsolvable in the end. ![]() In the extreme case, if to begin with there are no legal moves available in the tableau (main cards) or the stock, then although the layout isn't solvable, in a sense it is easy because you can immediately give up. However, even for unsolvable layouts, the depth of the search tree can reflect a kind of difficulty. If a layout is not solvable then in one sense it's infinitely difficult. Let's consider this case first: Unsolvable Layouts ![]() does a sequence of legal moves exist that results in a win) is obviously key. If, for our purposes, we use a rough definition along the lines of, "how much time the average player spends on a layout", then there are a few interesting things we can say about the relationship between a layout's difficulty and its general features.Īs your first point suggests, the solvability of the layout (i.e. From a human perspective I suppose one's interpretation of difficulty is quite subjective: what one person might find difficult another may find easy. ![]()
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