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What I mean by a "randomized single player problem" is roughly the following:

  • Certain information of the game is derived from a known random distribution (can assume uniform) and is hidden from the player.
  • There is a player A that knows the distribution but not the particular game instance.
  • A can make moves to reveal some hidden information that give hints about the other hidden information.
  • A fails if her revealed information becomes a certain combination. A wins if her revealed information becomes another certain combination.
  • A want to maximize her winning rate on any randomly generated game instance.

Examples of this type of game are Solitaire, SpiderSolitaire, Mahjong, Minesweeper, Purble Shop from the Windows 7 game collection.

I have been searching on this type of problems but found little related material online (maybe I searched with wrong keywords). Intuitively they should all have optimal strategies as the problem spaces are finite, but I did not find any.

Is there a general way to construct an optimal strategy for this type of game? Is there any related research? Some of those problems may be hard to classify as search problems.

Not sure if it is OK to add the tag "game theory" as game theory problems often have more than one player and perfect information.

Andrea2333
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  • Even in a variant of Solitare (Klondike) where the position of every card is known in advance, there is no definitive optimal approach known for some hands (it is just too complicated), which is why the probability of success is uncertain. The standard version is even harder to solve. See https://math.stackexchange.com/questions/121305/what-is-the-probability-that-a-solitaire-game-be-winnable and https://en.wikipedia.org/wiki/Klondike_(solitaire) – Henry Apr 26 '19 at 22:55
  • It is not a typical Game Theory problem even though it can be a special case of Game theory. Game theory can have incomplete information but is not interested in the single player problem. – S. Phil Kim Apr 27 '19 at 01:28

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