Simulations of Solving a Single-Player Memory Card Game with Several Implementations of a Human-Like Thinking Computer Algorithm

Abstract

The memory card game is a game that probably everyone played in childhood. The game consists of n pairs of playing cards, whereas each card of a pair is identical. At the beginning of the game, the deck of cards is shuffled and laid face down. In every move of the game, the player flips over two cards. If the cards match, the pair of cards is removed from the game; otherwise, the cards are flipped back over. The game ends when all pairs of cards have been found. The game could be played by one, two, or more players. First, this paper shows an optimal algorithm for solving a single-player memory card game. In the algorithm, we defined four steps where the user needed to remember the earlier shown pairs of cards, which cards were already shown, and the locations of the revealed cards. We marked the memories related to these steps as M1, M2, M3, and M4. Next, we made some simulations as we changed the M1, M2, M3, and M4 memories from no user memory (where the player does not remember the cards or pairs of cards at all) to a perfect user memory (where the player remembers every earlier shown card or pair of cards). With every memory setting, we simulated 1000 gameplays. We recorded how many cards or pairs of cards the player would need to remember and how many moves were required to finish the game. Finally, we evaluated the recorded data, illustrated the results on graphs, and drew some conclusions.