Studying shuffling and Shannon entropy part 2

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We did a fun project about Shannon Entropy and Shuffling yesterday:

Chard Shuffling and Shannon Entropy

That project was based largely on an old Stackexchange post (well, comment) here:

See the first comment on this Stackexchange post

Today I wanted to extend that project a little bit and thought it would be fun to look at a different kind of shuffle to see if there was a difference in entropy.

Here’s the shuffle for today as well as what the boys think will happen with this shuffle:

Next we took some time off camera to enter the card numbers in our spreadsheet. Here’s what we found for the new entropy after one of these new shuffles:

Finally, we took even more time off camera to do 4 more shuffles and write down the order of all the cards. After that we did 5 successive shuffles and wrote down the numbers after the 10th shuffle.

The kids didn’t think the cards were as mixed as they were in yesterday’s project, and here’s what the entropy calculation said:

I really enjoyed these two projects. It was especially fun to see how kids could get their arms around the idea of entropy even though the math itself is pretty advanced.

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