Strategic Brain Utilization: Mastermind



By Cheryll Tefera


For the longest time, playing board games has been linked with the development of the mind, especially in young people. According to Dr. Gwen Dewar of Parenting Science, games such as chess and Mastermind help hone a person's logical-mathematical intelligence - brilliance that is often found in scientists, mathematicians and investigators. The history of games dates to the ancient human past. Games are an integral part of all cultures and are one of the oldest form of human social interaction. Games are formalized expressions of play which allow people to go beyond immediate imagination and direct physical activity. A board game is a game that involves counters or pieces moved or placed on a pre-marked surface or "board", according to a set of rules. Games can be based on pure strategy, chance (e.g. rolling dice), or a mixture of the two, and usually have a goal that a player aims to achieve. While the board gaming market is estimated to be smaller than that for video games, it has also experienced significant growth from the late 1990s. A dedicated field of research into gaming exists, known as game studies or ludology. While there has been a fair amount of scientific research on the psychology of older board games (e.g., chess, Go, mancala), less has been done on contemporary board games such as Monopoly, Scrabble, and Risk. Research studies show that board games such as Chutes and Ladders result in children showing significant improvements in aspects of basic number skills such as counting, recognizing numbers, numerical estimation and number comprehension.

Mastermind resembles a game that was mainstream prior many years. It was named as Bulls and Cows. It includes two players who are included in interpreting the purported codes of one another. Mordecai Meirowitz developed this game in the year 1970. Mordecai was a famous Israeli telecom master and an acting postmaster! Mordecai Meirowitz is considered as a Board Game geek by many. Game of the year (1973), Design Center Award and Queen's Award for Export Achievement are three of the major recognition awards won by this wonderful board game!

Something about this game caught the imagination of the public, and it became the most successful new game of the 1970's. The game is played using: a decoding board, with a shield at one end covering a row of four large holes, and twelve (or ten, or eight, or six) additional rows containing four large holes next to a set of four small holes; code pegs of six (or more; see Variations below) different colors, with round heads, which will be placed in the large holes on the board; and key pegs, some colored black, some white, which are flat-headed and smaller than the code pegs; they will be placed in the small holes on the board. In 1993, Kenji Koyama and Tony W. Lai calculated that the best strategy uses an average of 5625/1296 = 4.340 moves.

One of the two players becomes a Code-maker and the other is Code-breaker. It is chosen at the start between these two players that how many rounds of game they will play. It is to be noted that the number of rounds to be played must be an even number. A pattern of four code pegs is then chosen by the Code-maker, since the replicas are permitted, the player has an option to deploy these pegs of the same color. The pattern is arranged in the four holes by the Code-maker and is hidden from the Code-breaker. This ensures that the Code-breaker finds it very difficult to decipher the enigma!

Twelve (may be even ten or eight) turns is what the Code-breaker gets to unravel the pattern deployed by his counter-part. He does so by arranging a row of code pegs on the disentangling board. Then, the Code-maker comes into picture by deploying 0 to 4 key pegs in the small holes of the row. If this key peg is colored or black, it implies that the prediction of the other player is precise both in terms of color and position, whereas, a white key peg specifies the possibility of right color deployed in the incorrect spot.

There may be an occasion when there are comparative hues in the predication set out the Code-breaker and it is not doable to concede a key peg to every one of them unless they coordinate the definite number of comparative shading in the shrouded code. It should be noted that, if the concealed code is B-B-A-A and the Code-breaker demonstrates A-A-A-B, the other player should award two hued key pegs for the right B, nothing for the third B lastly, a shaded key peg for the last A. This guarantees, that the anticipation of the players is kept alive, concealing the way that the code has a second B in it! Here A and B are hues that may be utilized as a part of the table board.

This pattern of guessing, unraveling goes on until one of the thing happens, either the Code-breaker runs out of his chances or he predicts the exact pattern deployed by the Code-maker. The scoring is such that the Code-maker is awarded a point for each prediction that the Code-breaker makes. A bonus point is granted to the Code-maker if the other player doesn't unravels the correct pattern in the last prediction. The winner is obviously the one who has most number of points after finishing the pre-decided number of rounds. Even the score revolving around coloured key pegs placed can be used.

There have been many mathematicians involved in researching concrete solutions to this game. Many number of algorithm have been presented on the world stage. Michiel de Bondt has used one in three 3SAT basics to prove that it can be solved by NP-complete logic. By examining different probabilities to deploy different number of players on the table, more number of holes on the game-board and another set of substantiated colors, different versions of this game have come into existence. Mastermind Secret Search (1997), New Mastermind (2004) and Mini Mastermind (2004) are its latest types.

Online versions have recently overtaken the popularity of board versions. Many companies have used different combinations of pieces and colors to avoid infringements pertaining to Intellectual Property Rights. If the unoccupied parts (holes) of the board are treated as another color, it would definitely lead to a more intense battle between the player.




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