Connecting the Micro to the Macro. Adventures With 3 Coin Flips, Part 2

In Part 1, we saw that increasing the observation window changes the results for the occurrence of tails following heads.  That raises the question: How does the micro (small observation window) relate to the macro (large observation window)?  More specifically, what is the relationship between results from a small observation window (three flips) and those from a large observation window (100 flips)?

Many Collected Micro Events Are NOT The Same As A Macro Event

Blair Fix (Is Human Probability Intuition Actually ‘Biased’?) shows that the apparent bias in favor of tails following heads decreases as the observation window increases.  Fix goes from an observation window of 3 flips to 5 flips, 10 flips, and ultimately 100 flips.  When Fix repeats 3-flip sequences many times and accumulates the results, these accumulations are unconnected to the results for any other n-flip sequence(s).  The accumulated micro-events of one type (type = number of flips) are unrelated directly to any macro-event constituted by many successive coin flips of other types.

Let’s recall two graphics from Part 1 that show the results of simulated iterated coin flips using random number generation.

Read the original article.

Tags: coin flipping, John Lounsbury