We would not want to classify such a layout as difficult just because it has a large search tree. For instance, the search tree for a layout could be huge, but have one solution that's very obvious to a human. Here are some heuristics one could use instead: Size of Search Treeįor a computer this is important, but in the solvable case it may not tell us much about human play. Just looking at the static cards in the starting layout is unlikely to tell us much, but by running the solver we can deduce more about a deal's difficulty (for a human). Let's assume though, that we don't have this data available, but we do have a computerised solver. Solvable LayoutsĪs was the case for unsolvable layouts, if one has access to human gameplay data then that's almost certainly going to be the best source of understanding how difficult humans will find a layout. 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.

Microsoft solitaire collection levels