Monday, August 24, 2015

Strategic Brain Utilization: Mastermind

By Cheryll Tefera


Board games involve a number of participants, studies conducted by social scientists show that they help in the development of interpersonal intelligence skills as well. The reason for such is the fact that the games involve competition - and collaboration at certain times. As a result, they help the person understand and interact with others more effectively. Common features of games include uncertainty of outcome, agreed upon rules, competition, separate place and time, elements of fiction, elements of chance, prescribed goals and personal enjoyment. Early board games represented a battle between two armies, and most modern board games are still based on defeating opposing players in terms of counters, winning position, or accrual of points (often expressed as in-game currency). A 2012 article in The Guardian described board games as "making a come back". Another from 2014 gave an estimate that put the growth of board game market at "between 25% and 40% annually" since 2010, and described the current time as the "golden era for board games". Much research has been carried out on chess, in part because many tournament players are publicly ranked in national and international lists, which makes it possible to compare their levels of expertise. Playing board games has also been tied to improving children's executive skills. It helps one and all in improving their respective Decision making skills. The adults tend to relate the board games to tedious Project management decisions as well!

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.

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.

It is picked toward the beginning between these two players that what number of rounds of the game they will play. One of the two players turns into a Code-creator and the other is Code-breaker. It is to be noticed that the quantity of rounds to be played must be an even number. The odd number of games is not possible as it would ensure that one of the players does not have equal chances compared to the other personnel. An array of four code pegs is then picked by the Code-creator, since the imitations are allowed, the player has an alternative to convey these pegs of the same color. The array is organized in the four openings by the Code-creator and is concealed from the Code-breaker. This guarantees that the Code-breaker thinks that it's extremely hard to decode the conundrum!

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.

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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