(Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger and arxiv.org)

Written: July 18, 2019.

In a delightful article that recently appeared in Mathematics Magazine, David and Lori Mccune analyze the board game "Count Your Chickens!", recommended to children three and up. Alas, they use the advanced theory of Markov chains, that presupposes a knowledge of linear algebra, that few three-years-olds are likely to understand. Here we present a much simpler, more intuitive, approach, that while unlikely to be understood by three-year-olds, will probably be understood by a smart 14-year-old. Moreover, our approach accomplishes much more, and is more efficient. It uses symbolic, rather than numeric computation.

Maple packages

• CountChickens.txt

• UmbralMarkov.txt

Sample Input and Output Files for CountChickens.txt

• If you want to see an example of the game played, so that you would understand it
  The input gives you the output.

• If you want to see a computer-generated article analyzing the board game "Count Your Chickens!"
  The input gives you the output.

• If you want to see a computer-generated article analyzing the simplified board game described in David and Lori Mccune's article "Counting Your Chickens with Markov Chains"
  The input gives you the output.

• If you want to see what happens if you replace the set of blue squares (where you get a bonus of one chick) by all the possible subsets, in the original Count Your Chickens! game,
  The input gives you the output.

• If you want to see the original Count Your Chickens! simulated 1000000 times, with a comparison of empirical statistics to the theorerical one (in particular confirming that the McCune claim that the expected number of chicks is 39.22 is erroneous (probably a typo), the correct value being 39.32223.
  The input gives you the output.

• If you want to see a similar analysis on four randomly-chosen games (with the same parameters) [a spinner with 6 equally likely outcome, a board with 40 squares and 6 blue squares]
  The input gives the output gives the

• If you want to see a similar analysis on four randomly-chosen with a spinner with 4 equally likely outcome, a board with 60 squares and 8 blue squares,
  The input gives output.

Sample Input and Output Files for UmbralMarkov.txt

• If you want to see the expected number of chicks, and expected number of rounds, for the original Count Your Chickens! game using this more general Maple package (that includes the previous one)
  The input gives output.

• If you want to see 20 randomly-generated weighted Markov chains, together with their statistical data
  The input gives output.

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