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The Monty Hall fallacy

by , 09 May 2019
The Monty Hall fallacy
Imagine this…

You're on a game show, and there are three doors.

Behind one of those doors, is the car of your dreams!

Behind the others are just two plain old goats…

So, you choose door number one.

The game show host goes to door number two, opens it, and reveals it's a goat.

He gives you the opportunity to change your choice and choose door number three.

Do you stay at door number one or change and choose door number three?

Let's find out

 
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The Monty Hall Problem
 
The Monty Hall problem is a prime example of when presented with a simple challenge of choosing one favourable outcome against two unfavourable outcomes, we display an inability to correctly weigh up the chances of success.
 
In short, we have trouble calculating the chances of success.
 
The Monty Hall problem was named after the game show host of “let’s make a deal”, an American show that saw huge popularity in the 1960’s and 70’s.
 
The Monty Hall problem is a simple mathematical puzzle which effectively demonstrates how people struggle with a very straight forward choice.
 
The game show demonstrates how the average person can display counter intuitive behaviour when faced with probability and the same can be true with novice sports bettors.
 
The solution to the Monty Hall Problem
 
The solution is simple and the math will prove it.
 
Once the host has opened the second door, the car is definitely behind one of the closed doors.
 
Most of the contestants on the show saw no advantage to switching doors, assuming that each door has an equal 1/3 or 33.33% probability.
 
This is not correct.
 
While it is true that each door originally has a 1/3 or 33.33% chance of hiding the car, after the first goat is revealed, the probability that the car is behind the other door rises to 66.6%.
 
This is because once you choose your door, the other two are then paired up together to give the remaining door a 66.6%.
 
So, the obvious choice is to ALWAYS SWITCH DOORS and choose the third door.
 
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 Knowing when the odds are against you 
 
So this problem cleverly illustrates how easy it is to fall into the trap of treating non-random information as if it were random.
  
Instead of acting on false gut feelings about the chances of success, understanding when you are in a statistically strong position is crucial when sports betting.
  
Betting requires the skill to understand whether the odds offered on an event represent the statistical probability of that event occurring.
  
It does not matter if you’re playing a game show, the lottery or online sports betting, understanding when you are in a statistical strong point is key to profiting over the long-term.
 
Until next time,
Christopher Ammon,
Head Tipster, The Winning Streak Team


The Monty Hall fallacy
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