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The Monty Hall problem
Things are not always as they seem.
Imagine a TV game show not unlike Deal or No Deal in which you choose one of three closed doors and win whatever is behind it. One door conceals a Cadillac - behind the other two doors are goats. The game show host, Monty Hall (of Let's Make a Deal fame), knows where the Cadillac is and opens one of the doors that you did not choose. You are duly greeted by a goat, and then offered the chance to switch your choice to the other remaining door. Most people will think that with two choices remaining and one Cadillac, the chances are 50-50. The most eloquent reasoning I could find is from Emerson Kamarose of San Jose, California (from the Chicago Reader's Straight Dope column in 1991): "As any fool can plainly see, when the game-show host opens a door you did not pick and then gives you a chance to change your pick, he is starting a new game. It makes no difference whether you stay or switch, the odds are 50-50." But the inconvenient truth here is that it's not 50-50 - in fact, switching doubles your chances of winning. Why? |
Re: The Monty Hall problem
It's easy to see why but somewhat more difficult to explain.
Essentially, if your door conceals a Goat then Monty has shown you exactly which door conceals the Cadillac. It is twice as likely that your door conceals a goat as a Cadillac - so you should change your choice. |
Re: The Monty Hall problem
Originally Posted by jimenato
(Post 10897867)
It's easy to see why but somewhat more difficult to explain.
Essentially, if your door conceals a Goat then Monty has shown you exactly which door conceals the Cadillac. It is twice as likely that your door conceals a goat as a Cadillac - so you should change your choice. Very good. Impressed! |
Re: The Monty Hall problem
I'm a bit of a nerd.:(
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Re: The Monty Hall problem
Well here it is:
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Re: The Monty Hall problem
Originally Posted by jimenato
(Post 10897867)
It's easy to see why but somewhat more difficult to explain.
Essentially, if your door conceals a Goat then Monty has shown you exactly which door conceals the Cadillac. It is twice as likely that your door conceals a goat as a Cadillac - so you should change your choice. |
Re: The Monty Hall problem
Originally Posted by jimenato
(Post 10897867)
It's easy to see why but somewhat more difficult to explain.
Essentially, if your door conceals a Goat then Monty has shown you exactly which door conceals the Cadillac. It is twice as likely that your door conceals a goat as a Cadillac - so you should change your choice. |
Re: The Monty Hall problem
Originally Posted by playamonte
(Post 10899687)
How has he shown which door conceals the caddy ?, as all he has done is show that the door he opened contained a goat.
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Re: The Monty Hall problem
Originally Posted by stuboy
(Post 10899794)
He hasn't shown you which door conceals the caddy, He is only increased the probability of the caddy being in the box you didn't chose.
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Re: The Monty Hall problem
Originally Posted by stuboy
(Post 10899794)
He hasn't shown you which door conceals the caddy, He is only increased the probability of the caddy being in the box you didn't chose.
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Re: The Monty Hall problem
Originally Posted by playamonte
(Post 10899907)
Yes that I can understand, but I still do not understand why it pays to switch ?
To think I used to be a Maths whizz kid at one time,....but now...:confused: |
Re: The Monty Hall problem
Originally Posted by Dick Dasterdly
(Post 10899931)
Still looks an even bet to me and I've yet to see anything to convince me otherwise, there again maybe I'm starting to lose the plot a little. :ohmy:
To think I used to be a Maths whizz kid at one time,....but now...:confused: This is one of the best puzzles I've seen, got me head scratching for a good while THANKS Ami for the OP. i couldnt get my head around the previous explanations sadly for me, proving I am not a whizz! Fantastic ! Here' how I figured it (finally).. Having had to split out the 2 goat option: Choice. ...... Odds. .....Change. .....Dont change Car............... 1/3 ............. Lose. .............. Win Goat. ............ 1/3. ............. Win. ............. Lose Goat. ............ 1/3. ............. Win. ............. Lose Total. ......... 100%. ........ 2 wins. .............1 win Its absolutely amazing that you can double, yes double your chances to win just by changing... Its so counter intuitive.... An amazing puzzle. I should have done the break down straight away rather than scratch a groove in my head :D Made my day thanks again Jon |
Re: The Monty Hall problem
The thing to remember is that your original choice is twice as likely to be a goat than a car and this fact does not change throughout the game.
When the other goat has been eliminated, you are left with a choice of two, your original choice and one other. Remembering that your original choice is still twice as likely to be a goat than a car then it follows that the only other possible choice is twice as likely to be a car than a goat. |
Re: The Monty Hall problem
Still not convinced myself.
I keep comparing it to the old coin puzzle where a coin is tossed ten times and comes down as heads the first nine times. That doesn't alter the fact that it's still an even money 50/50 bet on the last throw, or at least that's what I've always been given to understand. |
Re: The Monty Hall problem
I call shenanigans.. 1 in 3 chance change or not.
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