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The Monty Hall Dilemma........goats And Caddys!
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I have come across this before and like most initially I always thought that switching or not made no difference but once the penny dropped I saw it. I have had many a difficult time trying to explain why you should switch to people and my explanations have been somewhat clumsy but this explanation is as neat as I have come across:
"In the game you will either stick or switch. If you stick with your first choice, you will end up with the Caddy if and only if you initially picked the door concealing the car. If you switch, you will win that beautiful automobile if and only if you initially picked one of the two doors with goats behind them."
So do you get it? Never got it? don't accept it? ......
I have come across this before and like most initially I always thought that switching or not made no difference but once the penny dropped I saw it. I have had many a difficult time trying to explain why you should switch to people and my explanations have been somewhat clumsy but this explanation is as neat as I have come across:
"In the game you will either stick or switch. If you stick with your first choice, you will end up with the Caddy if and only if you initially picked the door concealing the car. If you switch, you will win that beautiful automobile if and only if you initially picked one of the two doors with goats behind them."
So do you get it? Never got it? don't accept it? ......
Answers
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Right, pixie, I’ll try once more and that’s my lot!
When you make your choice whether to stick or change you are not choosing between your original selection and one other door. You are effectively choosing between your original selection and ALL the other doors.
Let’s stick to the 10,000 door game for a minute as I think it’s slightly easier to grasp but we’ll tweak the game very slightly.
You make your original choice (and remember you have one chance in 10,000 of having chosen the winner). Monty now says to you
“Right, you can now stick with that choice or you can have ALL of the other doors instead. If the winner is amongst those 9,999 you go home with the car. If you were right in the first place you take home the goat. And to be extra generous, if you choose to swap I’ll help you open the other doors.”
Only a fool would stick as you are now being offered 9,999 chances to win whereas previously you had just the one. So you swap and as promised Monty helps by opening 9,998 losing doors leaving you with just the one remaining. Is it 50:50 that either this or your original choice is the winner? Of course it is not. When you decided to swap from your original choice there were 9,999 chances in 10,000 that the winner lies amongst these doors. Those odds have not changed because Monty has helped you open the doors; they remain the same.
So moving to the three door puzzle there are two chances in three that the winner is one of the unchosen doors but only one chance in three that it is the contestant’s original choice. So you have twice as much . chance of winning by swapping than by sticking. The confusion arises in peoples minds because of the way the game is presented. They are faced with a choice of just two after Monty has opened one of the others but that is not the choice they are making. They are choosing one door, or two doors.
(New Judge retires for a lie down!)
When you make your choice whether to stick or change you are not choosing between your original selection and one other door. You are effectively choosing between your original selection and ALL the other doors.
Let’s stick to the 10,000 door game for a minute as I think it’s slightly easier to grasp but we’ll tweak the game very slightly.
You make your original choice (and remember you have one chance in 10,000 of having chosen the winner). Monty now says to you
“Right, you can now stick with that choice or you can have ALL of the other doors instead. If the winner is amongst those 9,999 you go home with the car. If you were right in the first place you take home the goat. And to be extra generous, if you choose to swap I’ll help you open the other doors.”
Only a fool would stick as you are now being offered 9,999 chances to win whereas previously you had just the one. So you swap and as promised Monty helps by opening 9,998 losing doors leaving you with just the one remaining. Is it 50:50 that either this or your original choice is the winner? Of course it is not. When you decided to swap from your original choice there were 9,999 chances in 10,000 that the winner lies amongst these doors. Those odds have not changed because Monty has helped you open the doors; they remain the same.
So moving to the three door puzzle there are two chances in three that the winner is one of the unchosen doors but only one chance in three that it is the contestant’s original choice. So you have twice as much . chance of winning by swapping than by sticking. The confusion arises in peoples minds because of the way the game is presented. They are faced with a choice of just two after Monty has opened one of the others but that is not the choice they are making. They are choosing one door, or two doors.
(New Judge retires for a lie down!)
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