Adventures With 3 Coin Flips. Part 6: Probabilities

December 17, 2023Posted inUncategorizedNo Comments

In Part 5, we found that there are 6,435 possible outcomes for the complete characterization of a process of repeating three coin flips.  This arises because a 3-flip sequence must be repeated eight times to allow for the possibility of all eight equally probable sequence results occurring.  In this article, we calculate the probability of obtaining any individual outcome and also the probability of obtaining an outcome of each of the 22 outcome types.

Adventures With 3 Coin Flips. Part 3: Possibilities vs. Realities

November 19, 2023Posted inUncategorizedNo Comments

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?

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

May 28, 2023Posted inUncategorizedNo Comments

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)?

Adventures With 3 Coin Flips. Part 1: The Gamblers’ Paradox

May 21, 2023Posted inUncategorized1 Comment

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?