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Snail Trails

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Game of PIG - Sixes

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What Does Random Look Like?

Stage: 3 Challenge Level: Challenge Level:1

Ed from St Peter's College started off by experimenting and gave an initial insight into the problem:
I flipped a coin 20 times and got the following results: 13 heads and 7 tails. The best way to analyse if the coin is real or not is whether it has a significant number more of one side over the other.

Krystof from Uhelny Trh, Prague gave examples of some of his runs:
I made three runs
Number 1 is real, there are not exactly the same number of heads and tails, but nearly. There are also lots of different length runs, but mostly 2s and 3s.
Numbers 2 and 3 are made up. They have regular patterns. There is a very small probability of these occuring randomly.
There are many interesting principles of probability and statistics revealed in this simple activity. Connor from Gladesmore gave some very good points:
For a total random coin the number of "runs" of heads/ tails should be more weighted toward the smaller runs. Also a table where the result alternates e.g. h, t, h, t will be more likely the fake one as although the total number of heads and tails should be almost the same the order should be random. Finally when there are only a small number of coins flipped then you would expect that the total will not be completely identical.  
Good job everyone! Can anyone add more? What about the probability of different length runs occuring?