Thursday, 20 August 2015

Mastermind: Game For The Brain

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 is a board game with an interesting history. Some game books report that it was invented in 1971 by Mordecai Meirowitz, an Israeli postmaster and telecommunications expert. After many rejections by leading toy companies, the rights were obtained by a small British firm, Invicta Plastics Ltd. The firm originally manufactured the game itself, though it has since licensed its manufacture to Hasbro in most of the world. However, Mastermind is just a clever re-adaptation of an old similar game called 'Bulls and cows' in English, and 'Numerello' in Italian. Actually, the old British game 'Bulls and cows' was somewhat different from the commercial version. It was played on paper, not on a board. Over 50 million copies later, Mastermind is still marketed today! It went on to win the first ever Game of the Year Award in 1973. It also received a Design Center Award, and the Queen's Award for Export Achievement.

Mastermind is an extremely game in its own distinctive way, which is played using an unraveling board. This board has a shield toward one side covering a line of four inconceivable openings, and twelve (or ten, or eight, or six) additional lines containing four broad crevices alongside a course of action of four little holes. It also comprises of code pegs of six (or more) unmistakable shades, with round heads, which will be set in the far reaching holes on the board are required. It also encompasses, key pegs, some shaded dim, some white, which are practical and smaller than the code pegs are obliged to be placed in the little holes on the board.

The two players decide in advance how many games they will play, which must be an even number. One player becomes the code-maker, the other the code-breaker. The code-maker chooses a pattern of four code pegs. Duplicates are allowed, so the player could even choose four code pegs of the same color. The chosen pattern is placed in the four holes covered by the shield, visible to the code-maker but not to the code-breaker. The code-breaker may have a very hard time finding out the code.

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 instance when there are similar colors in the predication laid down the Code-breaker and it is not feasible to grant a key peg to all of them unless they match the exact number of similar color in the hidden code. Now, if the hidden code is A-A-B-B and the Code-breaker indicates B-B-B-A, the other player ought to grant two colored key pegs for the correct A, nothing for the third A and finally, a colored key peg for the last B. This ensure, that the suspense is kept alive, hiding the fact that the code has a second B in it! Here A and B represent colors that might be used in the table board.

Once feedback is provided, another guess is made; guesses and feedback continue to alternate until either the code-breaker guesses correctly, or twelve (or ten, or eight) incorrect guesses are made. The code-maker gets one point for each guess a code-breaker makes. An extra point is earned by the code-maker if the code-breaker doesn't guess the pattern exactly in the last guess. (An alternative is to score based on the number of colored key pegs placed.) The winner is the one who has the most points after the agreed-upon number of games are played.

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.

The difficulty level of any of the above can be increased by treating "empty" as an additional color or decreased by requiring only that the code's colors be guessed, independent of position. Computer and online versions of the game have also been made, sometimes with variations in the number and type of pieces involved and often under different names to avoid trademark infringement.




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