Friday 11 November 2022

Statistical Roulette



You have a six-shooter a pistol and three bullets.


At this time the writer would like to assert the writer does not like guns.


At all.


A diatribe about the US Constitution fifth Amendment right to bear arms and use them in self defence and to form militias in event of a rogue government, may follow.


None of that is what this blog is intended to be about.


You have a six-shooter and three bullets.


How do you load them?


Personally, despite having admitted in public my distaste for guns and an intention to never have anything to do with them if at all possible, I would load a bullet into every other cylinder. That way I can easily keep tabs on where the bullets are even after spinning the cylinder.


But as others have often pointed out, I do not think like other people.


It is from accepting that factor, I observe most other people will more probably load the three bullets into consecutive cylinders, leaving the next three cylinders empty.


Why is this important?


You could express it is important for the sake of argument. I have no intention at all in picking a half-cocked argument with somebody who is holding a half-loaded pistol. 


It is important for the sake of this blog. 


It is important for the following reason.


Today we are doing fractions. 

We are doing probabilities.


My friend, today we are doing maths.


The question is simple.


What is the statistical possibility of pulling the trigger and hitting a blank versus pulling the trigger and firing a bullet?


Most people will say, that is easy. It is a three-in-six chance, which is the same as a 50/50 chance. Those people would probably be right. What are the odds.


From here on in, it gets more interesting.


You pull the trigger a second time.


Now what are the odds?


You immediately understand the relevance of why I made a point of mentioning how we load the bullets into the barrel.


O I O I O I  = my method


O O O I I I  = majority method 


As stated previously, for the purposes of this blog we are going with what I have dubbed the ‘majority method’ for how those bullets are arranged.


I told you it would get more interesting. 


The second time you pull the trigger, is it more likely, less likely, or the same chance of firing a bullet versus firing a blank?


For the sake of argument and to keep things simple, we will go from the position that the first time you pulled the trigger, it fired a blank. No bullet. 


Are we here: 


X O O I I I 


or here: 


O X O I I I 


or here: 


O O X I I I 


Where the X signifies the first time we fired the gun (which fired a blank). 


At this time we simply do not know. 


Now you understand why I think the way I do and would personally have loaded it the way I have called ‘my method’.


So, we pull the trigger a second time. What is the statistical possibility of firing a bullet vs firing a blank? 


There are now less than 3 empty cylinders. 

It is no longer a 3 in 6 fraction. 

It is no longer 50/50. 


Or is it? 


One school of thought is that there is still a 50-50 chance. 


One school of thought is there is a 2 in 5 chance of firing another blank, which is the same as a 60% chance of firing a bullet on the second go. 


Which of these two schools of thought is correct? 


Is it possible they can both simultaneously be correct?


If they are both simultaneously correct, there are two parallel universes coexisting at the same time. 


Neither is more right or more wrong than the other. 


Has it clicked yet?


Now look at those three possibilities again. 


In two of the possibilities, the next cylinder is empty. In one of the possibilities, the cylinder had a bullet in it. That’s 2/3 probability the next cylinder will fire a blank despite we know logically there are more bullets than empty cylinders. How does that make sense? 


Theoretical philosophy is one matter. It all changes when you invest some money into it, gambling against the odds. 


It all changes significantly when a persons life is on the line, which in the case of loaded guns is deadly. 



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