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October 06, 2003
Solvable games
I'm not much into math, so maybe this problem is way too difficult, but...
Consider the set of possible perfectly played Klondike Solitaire games. By perfectly played, I mean the player knows where all the cards are (even the ones in the deck and face down on the table) and doesn't make mistakes. The number of games should be equal to the number of ways a 52 card deck can be arranged, which is huge (52! is 8.06581751709439e+67 on my calculator).
But what is the number of solvable (okay, winnable) games?
Is there a way to calculate the number of winnable games without running through every probability? Can you build an algorithm that can determine the winnability of a given game within X moves?
By the way, after 301 games I have 26 wins at Klondike (draw three, no limit on the number of cycles through the waste desk), which is almost 4 games in 52 or 1 in 13.