A Math Game

I attended the seminar for PhD students on Thursday and we played one game there. It turned out to be very interesting, so I want to share this with you, my dear reader.

So the rules are as follows:

The team consists of seven people, all labeled with one label – either red or green. The manager of the game do the labeling based on random label generator, that it, the possibility to get the green (or red) label for every person is equal to 0,5. Before the labeling process people are allowed to speak to each other and to agree on some strategy of the game. After the labeling is done, no communication is allowed, except everyone can see labels of other persons. The goal of the game is to guess the color of his label for some of the participants of the team. The guessing happens when the manager of the game asks it all the persons one after another. Every person can either pass (don’t guess his color), or guess his color, but it is not allowed for every person of the team to pass. When a person is surveyed and he makes a guess, the game ends – the team wins if the person guesses correctly, and loses if the guess is wrong.

The actual process can be seen like this:

  1. all the persons of the team is allowed to talk whatever they want for some time;

  2. the time is up, and all the persons settle in a row or whatever;

  3. the manager of the game goes to each person, chooses a label (remember – the probability of both colors is the same) and sticks it to forehead of that particular person (in the way person does not see the label);

  4.  when all the persons are labeled, everyone is allowed to look around to see the labels of other persons;

  5. when the looking is done, the manager of the game starts asking the question `What’s your color?` to each of the participants in an arbitrary order;

  6. person can say either `I pass` or name one of two possible colors – red or green (except for the last person who is forced to guess the color if it comes to him);

  7. if some person says `I pass`, the manager asks the same question to the next person;

  8. if some person guesses the color, the game is over and the team wins or loses depending on the correctness of the guess.

 So, you task is now to come up with a strategy that gives the biggest probability for a team to win. And it would be nice, of course, to motivate this strategy and/or to calculate the winning probability of your strategy. Who offers the best strategy (the biggest winning probability) wins (sorry, no prices though).

Published in: on Saturday, December 8, 2007 at 3:07 am  Comments (1)  
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One CommentLeave a comment

  1. Hi,
    Nice blog there.I am in high school now and I will be going to college next year. I plan to study CS and I am trying to get a good idea of what the course will hold. Can you please point me to a few interesting resources online? my blog’s at http://shriphani.wordpress.com

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