Definitions

computerized game

Simple Simon (solitaire)

Simple Simon is a Solitaire card game played with a regular 52 cards deck (4 suits of 13 cards each without Jokers). It became somewhat popular being featured in some computerized collections of Solitaire card games, but its origins possibly predate its implementation as a computerized game.

Rules

At the beginning of the play the cards are dealt all facing the player, starting from 3 columns of 8 cards each, and then 7 columns with 7, 6, and so forth cards until 1.

A card can be placed on any card on the top of a column whose rank is greater than it by one (with no cards that can be placed above an Ace). A sequence of cards, decrementing in rank and of the same suit, can be moved as one. An empty column can be filled by any card. A sequence of cards from the king to the Ace all of the same suit, can be moved to the foundations. The object of the game is to place all four suits in the foundations.

Strategy

A mixed-suit sequence of cards can be moved to a different location, given enough empty columns or parent cards to place intermediate components and sub-sequences of cards on. This is similar to FreeCell only with the individual components of the sequence being the same-suit sub-sequences rather than individual cards as in FreeCell. Note that some implementations of Simple Simon, require the player to do all the moving of the individual components by himself.

Statistics and Analysis

Freecell Solver, a solver for various Solitaire games, was adapted to solve Simple Simon, by its primary developer, Shlomi Fish. Fish initially tried implementing the solver using individual Simple Simon moves, but that ended up causing the program to check many states without a visible end. So instead, he opted for a scheme in which every sequence of moves conducted by the solver ended up in either clearing a column, moving a card on top of a card of the same suit, or (more rarely) moving a column to the foundations. Implementing this strategy turned out to be sufficient for solving many games, and so it was kept.

The statistics presented by the solver when run over a range of 4000 random games are quite interesting. About 85% of the games were shown to be solvable, with the median of the number of solver iterations for them being 59. Most of the rest were unsolvable by the solver (but not necessarily by a human player), with a median of 8 iterations. In both cases, over 95% of the boards were solved or reported unsolvable by the solver after less than 1000 iterations.

Stephan's Kulow analysis of these statistics was: "But what you found out, is what makes the game a joy: either it's impossible to solve and you see it in the first moves or it's solvable and you only have the find the best route."

A programmer called Michael Mann later on added another type of move to Freecell Solver which placed cards above a parent of a different suit. This reportedly increased the percentage of games that were solvable by the solver to well over 90%. This change was not incorporated into the mainline Freecell Solver, because it increases the necessary time and iterations to solve many games considerably.

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