This article describes the process of identifying all possible outcomes when there are 8 trials of 3 coin flips each. Then, the outcomes are divided into types, and the number of outcomes for each type is determined.
The process of understanding the complexity of many 3-flip sequences for tossing a coin is about to become more difficult. This is because are going to enter the arcane world of permutations and combinations. As a result, this is counting on a scale far more complex than that learned in elementary school.
Flipping a coin three times seems like a simple process. But there are myriad complications that can arise. In Part 1 of this series, we saw that data sampling for coin flips can influence how results are interpreted. In this post, we will look closely at how probability assessments (possibilities) can lead to propositions deviating from the reality ensuing when coin flips are actually carried out. We will consider the concept of ‘alternate universes’. Who would have guessed that flipping a coin three times would go there?
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 gambling activities involve betting on events for which the outcomes obey rigid, specified odds. When there is no mechanical bias, roulette wheels have fixed odds, including some that are binary (50:50) such as red vs. black. Betting on the flip of a coin is likewise a binary 50:50 proposition: heads or tails. Why is it then that there is a propensity for some gamblers to place wagers in a pattern conflicting with the known 50:50 odds? For example, after a string of blacks on a roulette wheel, why do some gamblers keep increasing the amounts bet on red with each succeeding black?
