When observing different variations of the Collatz Conjecture, I found that stumbling across loops instead of watching the trajectory decay to one happens a lot. When playing a game of Klondike Solitaire, "losing" looks like a loop since the only move that can be done is cycling through cards in the stock. When the player wins, it looks like the player successfully reached a "decayed to one" state.

Would further studying the Collatz Conjecture and similar iterations allow for mathematicians to calculate a game of Solitaire, and potentially solve it?

Since the Collatz Conjecture and similar rules apply to an infinite set, I made the assumption that each state of the game of Solitaire could be connected to some number and every state of the game is a finite number (52!). The operations would be far more complex than the Collatz Conjecture since there are more than two rules to the algorithm and sometimes a player has multiple choices they can perform.


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