[Math] Pencil-and-paper random number generator

random

I was picking football teams for my office's weekly "pick'em pool", and decided to pick randomly.

Since I only had a pencil and a legal pad handy, and I only needed outputs of 0 or 1 (0 being the home team wins, 1 being the away team wins) I invented my own "random number generator".

For each 2-team matchup, I generated an output by:

  1. drawing a zig-zag squiggle (sine-like random waveform, with near-zero bias) using a designated ruled line on my notepad as the x-axis.
  2. Then I counted the number of times the waveform intersected the ruled line.
  3. Then took that number mod 2 as my output.

Assuming each waveform was long enough (i.e. had at least 10 local minima and maxima) is my expected output somewhere near 0.5?

Just curious.

Best Answer

I know the OP is 7 years old, but you could have treated your pencil as a d6. Because a pencil has 6 edges, only one of which is usually printed on, assign 3 edges "team 1" (printed and adjacent edges), and 3 edges as "team 2" non-adjacent edges to printed edge), then roll the pencil across the desk, and see which edge comes up on top. Provided the pencil has no obvious blemishes or other problems that could influence a bias, this is a good HWRNG.

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