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

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)?