Computer Simulations from yesterday's Let's Make a Deal problem. | TigerDroppings.com

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Dooshay
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Computer Simulations from yesterday's Let's Make a Deal problem.




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quote:

Are you familiar? Monty gives you a choice of three doors. Behind one is a new car. Behind the other two are hamburgers. You pick Door #1. Before the contents are revealed to you Monty says "hold on, Jack. Let's look behind door number 3!". The door opens to reveal a hamburger. Then Monty says "OK, do you want to keep your first choice or would you like to switch to door number 2?" What should you do?











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Cap Crunch
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


I played around with simulations last night and found the same thing. They had some already made on a website and it worked so much more when you switched that it left me wondering whether or not the site programmed it that way





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Cap Crunch
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


Youtube explanation

Kind of makes sense now



This post was edited on 3/6 at 11:25 am


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Dooshay
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


I think what's important to take away from this is that while it appears better to always switch, it's purely due ability to play the game twice.

You are essentially making two choice when you switch, since the first is eliminated, so you have a 2/3 shot.

If you refuse to switch, you have a 1/3 shot since the door that is revealed is really irrelevant since it will always not contain the car.

And most importantly, if the decision to switch is purely random your overall odds are 1/2 of winning.






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threeputt
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


Correct and if the host does not know what door the car is your odds dont increase ..







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Cap Crunch
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


Watch the video.

The idea is that you have a better chance at picking the goat first than the car. So assuming you pick the goat first, when the host opens the door revealing the other goat, it means that the other door must be the car.

In that scenario, you will only get the goat 1/3 of the time when you pick the car first. But 2/3 of the time, you will pick the goat first and will automatically end up with the car if you switch



This post was edited on 3/6 at 11:30 am


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White Shadeaux
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


You still have a 50% shot at the point of final decision right?

2 doors. 1 car, 1 hamburger.






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Cap Crunch
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


Not really. See my post above and watch the video. Does a good job of explaining it. And as someone said above, it only works if the host knows what is behind each door and intentionally opens the door with a goat





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supadave3
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


Maybe I'm just a dumbfrick but I read through that entire thread yesterday and I still don't get how it increases your odds to switch. To me, it seems that either way, your chances are 50/50 once they remove the first hamburger.





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dustinm27
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


I understand you have more of a chance of initially not picking the car, but overall you know you will have a 50/50 shot of picking it being that one door basically doesn't exist





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Dooshay
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


Yep, that's the key. The object is to pick a goat, reveal a goat, then the remaining choice must be the car, so you pick it.

If the host didn't know which door the car was behind and had a chance to reveal it where you aren't guaranteed a second pick, the numbers would be more in line. If he revealed the car initially, your second pick would always be a loss just like when the first door revealed is not always the car.






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bubbz
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


You choose door number #2 and thank him for the extra odds. Have to account for variable change.





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threeputt
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


quote:

White Shadeaux


No, not if the hosts knows where the car is. You would have a 2/3 chance if you switch. If the host has no clue where the car is, then you are correct in your assumption.






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Dooshay
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


quote:

Maybe I'm just a dumbfrick but I read through that entire thread yesterday and I still don't get how it increases your odds to switch. To me, it seems that either way, your chances are 50/50 once they remove the first hamburger.


It's not swapping that increases your odds to win, but it's the process of elimination based on the mechanics of the game.






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Cap Crunch
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


quote:

It's not swapping that increases your odds to win, but it's the process of elimination based on the mechanics of the game.


Exactly. Good way of putting it






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threeputt
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


In page 4 of the thread yesterday I linked a thread from 2008 that is 27 pages long but a great thread to read if youre a stat geek like me





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Cap Crunch
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


Link? I might check that out later





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Wooly
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


They explained this in the movie 21





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threeputt
Notre Dame Fan
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


Link from 2008 for Cap Crunch





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Cap Crunch
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re: Computer Simulations from yesterday's Let's Make a Deal problem.


Thanks man

I'll read that later and nerd out after I take my statistics test this afternoon






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