Tuesday, 18 August 2015

Intricacies In Mastermind Game

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.

The code-breaker tries to guess the pattern, in both order and color, within twelve (or ten, or eight) turns. Each guess is made by placing a row of code pegs on the decoding board. Once placed, the code-maker provides feedback by placing from zero to four key pegs in the small holes of the row with the guess. A colored or black key peg is placed for each code peg from the guess which is correct in both color and position. A white key peg indicates the existence of a correct color code peg placed in the wrong position.

If there are duplicate colors in the guess, they cannot all be awarded a key peg unless they correspond to the same number of duplicate colors in the hidden code. For example, if the hidden code is white-white-black-black and the player guesses white-white-white-black, the code-maker will award two colored key pegs for the two correct whites, nothing for the third white as there is not a third white in the code, and a colored key peg for the black. No indication is given of the fact that the code also includes a second black.

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.

In November 2004, Michiel de Bondt proved that solving a Mastermind board is an NP-complete problem when played with n pegs per row and two colors, by showing how to represent any one-in-three 3SAT problem in it. He also showed the same for Consistent Mastermind. Varying the number of colors and the number of holes results in a spectrum of Mastermind games of different levels of difficulty. Another common variation is to support different numbers of players taking on the roles of code-maker and code-breaker. Few of its varied varieties are Word mastermind (1975), Number Mastermind (1975) and Incicta (1977).

The trouble level of any of the above can be expanded by treating "vacant" as an extra color or diminished by obliging just that the code's hues be speculated, autonomous of position. Mastermind can also be played with paper and pencil. There is a numeral variety of the Mastermind in which a 4-digit number is guessed. Digital versions have recently overshadowed the board variety as most of the youth spends their free time online!




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