Even coin flips will not tend to be exactly 50-50 until after many thousands or maybe more coin flips as often in a random walk you do encounter a run of one or the other occurring more in quick succession that lifts (or declines) the average line (requires another biased run in the other direction to realign, and typically that realignment will either fall short or over-run).
A few months back there was a Math prof. on TV conducting a simple test of two groups of people, one group repeatedly flipped a coin and recorded the results, the other had to imagine coin flips and record the results. The prof. then inspected both sets of data and could identify which was the real random group and which was the imagined random group. Simply she identified the difference as people imagine random sequences to not contain long sequences of the same outcome, whereas in the real random case long sequences of one or the other do commonly occur.
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