Mastermind
About the Game:
Mastermind is a simple game of strategy and logic. It was developed in 1970 by Mordecai Meirowitz. The game was manufactured by Invicta Plastics in 1971, but since then, it has been manufactured by Hasbro and various other companies, though Invicta Plastics still own the rights.
It has been made into various applets by many individuals on the internet, and can be played online at no cost. It can also be played on paper, with letters representing the various colours.
A Mastermind board typically has ten rows with four slots each (this is greater in Super Mastermind and some internet versions) for game pegs, and four slots each for indicator pegs. There are up to eight colours of game pegs in the manufactured version of the game, although there are probably more than that on some of the internet versions of the game.
Mastermind involves the "codemaker" making a code of coloured pegs in different slots, and having another person, the "codebreaker" try to decipher the code. The object of the game is to decipher the code in as few moves as possible for the codebreaker, or, for the codemaker, to make it so that the codebreaker uses all or most of his or her tries in guessing the code.
How to Play:
First, the two players decide on a set number of games (with the same number of times as codemaker and codebreaker.) Then, they decide who will be the codemaker and who will be the codebreaker first. They take alternating turns as codemaker and codebreaker.
The codemaker secretly makes a hidden code of coloured game pegs in (usually four) slots. This is then shielded by the code shield (in the manufactured version, that is.) The codemaker should try to make a code that is very difficult for the codebreaker to decipher.
The codebreaker must crack the code in 10 moves or less. He or she makes a guess using coloured pegs in the given number of slots, and is given information about this guess by the codemaker.
Information is given in the form of indicator pegs. The number of indicator pegs is the same as the number of slots in the code. There are two kinds of indicator pegs: pegs indicating a correct colour in the wrong position, which are most often white (although this may differ, so read the rules of the game before you play), and pegs indicating a correct colour in the correct position, which are most often black or red. The indicator pegs are in no particular order when placed, so don't think that they are giving you information on the corresponding game pegs They could be giving you information on any of the game pegs.
Scoring:
This is where the game differs a little depending upon the makers and or players.
Sometimes, the score is tallied like so: the codemaker gets one point for every guess the codebreaker makes, to a maximum of eleven (that's only if the codebreaker uses all of his or her tries). Three points are given to the codebreaker if he or she can prove that the codemaker gave him/her the wrong information (there is a replay, also.) The person with the most points after a set number of rounds wins.
The way I play, however, is like so: the codebreaker gets one point for every guess she or he takes. Three points are taken away from the codebreaker's score if he or she can prove that the codemaker gave him or her the wrong information, OR three points are added to the codemaker's score. The person with the smallest score after a set number of rounds wins.
Either way, the game play is the same, and the scoring reflects the number of guesses, so it is up to the player to decide how to score the game.
Strategy:
Mastermind is a very simple game to learn, but quite a bit more difficult to master (in my case, anyway.) Some people have played the game many times over the years, and their main strategy involves guesses using all of one colour. Others only play a few games once in a while, but can guess almost any code in five tries or less! How is this possible, you say?
There is one simple rule for any strategy in Mastermind: try to narrow down the possibilities of the code in the smallest number of tries. Men such as Knuth, Koyama, and Lai have tried to find the optimal strategy to Mastermind on computers. Knuth found a strategy that cracked the code in an average of around 4.64 moves (correct me if I'm wrong). The closest have been Koyama and Lai, in 1993. Their findings were published in the Journal of Recreational Mathematics, in that year. They found an optimal strategy which has the codebreaker cracking the code in an average of 4.340 guesses, with a maximum of six guesses for certain codes.
I, myself, when playing a standard game of Mastermind, usually crack the code in 4 to 5 moves. I have no specific strategy, but I have a general one that works fairly well:
1. Use one of every colour in the slots in the first move. This will
narrow down your initial possibilities very
quickly.
2. Use more than one colour in each move, until you know the code.
3. Look at the positioning of the game and indicator pegs carefully, and think
out possibilities fully. (Ex. If red is in the correct position here, then blue
is in the wrong position here, and green isn't a colour in the code.) This may
narrow down your choices drastically.
4. Don't make random guesses after the first try! You should make informed
guesses after the first try that will narrow your choices down by a large
number!
5. Practice! Practicing helps you develop the strategy (ies) that work best for
you!
6. Remember that every game is different, so you may have to use slightly
different strategies for different games!
Ok, so maybe I'm no expert on Mastermind, but I gave it a try, and I got better at it. Maybe, if you give it a try, you'll like it, and get pretty good at it, too!
Links:
Mastermind Applets:
Downloadable Puzzles:
Contact Me:
