Friday 14 August 2015

Intricacies In Mastermind Game

By Cheryll Tefera


Wood and Stewart (famous researchers) published a research in 1987 that shows the benefits of Mastermind. The study showed that college students who participated in the research enhanced their critical thinking abilities, making them less prone to errors in reasoning. Games capture the ideas and worldviews of their cultures and pass them on to the next generation. Games were important as cultural and social bonding events, as teaching tools and as markers of social status. As pastimes of royalty and the elite, some games became common features of court culture and were also given as gifts. There are many varieties of board games. Their representation of real-life situations can range from having no inherent theme (e.g. checkers), to having a specific theme and narrative (e.g. Cluedo). The time required to learn to play or master a game varies greatly from game to game. Learning time does not necessarily correlate with the number or complexity of rules. The rise in board game popularity has been attributed to quality improvement (more elegant mechanics and graphics) as well as increased availability thanks to sales through the Internet. Linearly arranged board games have been shown to improve children's spatial numerical understanding. This is because the game is similar to a number line in that they promote a linear understanding of numbers rather than the innate logarithmic one. The board games can be therapeutic and paying games have been suggested as a viable addition to traditional educational curriculum.

Mastermind is similar to a game that was popular hundreds of years ago which was named as Bull and Cows. It involves two players who are involved in deciphering the so-called codes of each other. It was invented in the year 1970 by an Israeli telecommunication expert named Mordecai Meirowitz. He was an acting postmaster too! His idea was at first turned down by many of the leading toy companies, but he persisted, and took it to the International Toy Fair at Nuremberg in February 1971. Released in 1971, the game sold over 50 million sets in 80 countries, making it the most successful new game of the 1970s. It has received awards like Game of the year (1973), Design Center Award and Queen's Award for Export Achievement.

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!

Now the actual game of 'cat and mouse' begins. Twelve (may be even ten or eight) turns is the thing that the Code-breaker gets the chance to disentangle the arrangement conveyed by his partner. He does as such by organizing a column of code pegs on the unraveling board. At that point, the Code-producer comes into picture by conveying 0 to 4 key pegs in the little gaps of the column. On the off chance that this key peg is colored or black, it suggests that the forecast of the other player is exact both regarding shading and position, while, a white key peg indicates the likelihood of right shade sent in the off base spot.

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.

This speculation and disentangling goes ahead until one of the thing happens, either the Code-breaker comes up short on his chances or he predicts the accurate example sent by the Code-creator. The scoring is such that the Code-creator is recompensed a point for every prediction that the Code-breaker makes. A reward point is allowed to the Code-producer if the other player doesn't disentangles the right example in the last chance available at his disposal. The victor is clearly the person who has most number of points in the wake of completing the pre-chosen number of rounds. Indeed, even the score rotating around hued key pegs set can be utilized.

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).

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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