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Flawed Thinking by Numbers
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A look at some of the ways in which people go wrong when they try to use statements of probability in arguments for supernatural beings, divine plans and dismissing evolution.
Mar 11, 2010 10:08 AM
Re: Flawed Thinking by Numbers
Here is an interactive version of the Monty Hall Dilemma for those who want to see the results of sticking versus switching:
www.shodor.org/interactivate/activities/ SimpleMontyHall/
(requires Java)
www.shodor.org/interactivate/activities/ SimpleMontyHall/
(requires Java)
By: spam_vigilante
Re: Flawed Thinking by Numbers
Here's a handy analogy for the Manty Hall problem:
Pick a card, any card, you're hoping for the ace of spades. Now see that these fifty cards you didn't choose are not the ace of spades. Would you like to keep your original choice or switch to the only other card I didn't reveal?
Sometimes bigger numbers actually make signals more obvious.
---
Mankini was funny, but the others could've been a bit harsher.
Pick a card, any card, you're hoping for the ace of spades. Now see that these fifty cards you didn't choose are not the ace of spades. Would you like to keep your original choice or switch to the only other card I didn't reveal?
Sometimes bigger numbers actually make signals more obvious.
---
Mankini was funny, but the others could've been a bit harsher.
Re: Flawed Thinking by Numbers
I know I discussed this on another page, but I've had more time to think about it.
Actually, there are 3 statistics. There is the statistic as to how many doors you can open, how many Monty Hall can open, and how many times you can play the game. No one ever considers the other 2 statistics, or at least the statistic involving Monty Hall's choice. With 3 doors, Monty Hall can only open 1 and still leave a choice. So it doesn't matter if he goes first or second. With 3 doors there is always a 50/50 chance. It doesn't work with any other number of doors.
More importantly, you have to factor in how many times you get to play the game. These brainiacs who like to show statistics about how better it is to switch NEVER factor in that people only have 1 chance. If you could play multiple times, then switch EVERY time. With only 1chance, it doesn't matter.
Actually, there are 3 statistics. There is the statistic as to how many doors you can open, how many Monty Hall can open, and how many times you can play the game. No one ever considers the other 2 statistics, or at least the statistic involving Monty Hall's choice. With 3 doors, Monty Hall can only open 1 and still leave a choice. So it doesn't matter if he goes first or second. With 3 doors there is always a 50/50 chance. It doesn't work with any other number of doors.
More importantly, you have to factor in how many times you get to play the game. These brainiacs who like to show statistics about how better it is to switch NEVER factor in that people only have 1 chance. If you could play multiple times, then switch EVERY time. With only 1chance, it doesn't matter.
By: digitalprime
Re: Flawed Thinking by Numbers
On Let's Make a Deal, there was no official rule that there must be two booby prizes and Monty must always a booby prize and give another chance. But he did it so often, it became expected. If he could decide to trick you by only doing that sometimes, or by varying the number of good prizes, then it becomes hazy.
Let's assume it's a rule of the game is, three doors, one good prize, you choose, he always reveals a bad prize, and you have an opportunity to revise your guess before the final reveal.
Unless you have some inside information, you're still running a numbers game, even if you only get one play. If you play 100 times using the "always switch" strategy, you'll end up with 67 good prizes, on average. If you play one time, you'll get 1 or 0 good prizes, buy you can double your odds of winning from 1:3 to 2:3 by switching.
Imagine there are four doors, you choose #2, monty shows you #1 and #3. Now your odds of winning are 1:4 to stay or 3:4 to switch. The reason it works is Monty has given you more to go on later in the game.
Let's assume it's a rule of the game is, three doors, one good prize, you choose, he always reveals a bad prize, and you have an opportunity to revise your guess before the final reveal.
Unless you have some inside information, you're still running a numbers game, even if you only get one play. If you play 100 times using the "always switch" strategy, you'll end up with 67 good prizes, on average. If you play one time, you'll get 1 or 0 good prizes, buy you can double your odds of winning from 1:3 to 2:3 by switching.
Imagine there are four doors, you choose #2, monty shows you #1 and #3. Now your odds of winning are 1:4 to stay or 3:4 to switch. The reason it works is Monty has given you more to go on later in the game.
Re: Flawed Thinking by Numbers
One more note. People were not idiots to stick with their original guess. In the real world, when someone does that, they're probably trying to put one over on you because they aren't required to do it every time.
Re: Flawed Thinking by Numbers
I think that an important factor in this dilemma is whether Monty Hall actually *knows* which door the real prize is behind?
By: keyser_soze
Re: Flawed Thinking by Numbers
In the pure Monty Hall problem (and not the actual game show), how does this make any difference at all?
All that the "Monty Hall agent" in this problem needs to do is open a door with a booby prize and ask if you want to switch. Beyond carrying out this function, it really doesn't matter who or what the agent is or what the agent knows, assuming that the agent is intelligent at all and not just, say, a computer program.
All that the "Monty Hall agent" in this problem needs to do is open a door with a booby prize and ask if you want to switch. Beyond carrying out this function, it really doesn't matter who or what the agent is or what the agent knows, assuming that the agent is intelligent at all and not just, say, a computer program.
By: Deh_Dude
Re: Flawed Thinking by Numbers
It is essential that the Monty *always* reveal an unselected booby prize and offer a second try.
If the Monty opens one of the unselected doors at random, revealing the good prize 1/3 of the time, you gain no new information, even if it happens to be a booby prize this time.
If the Monty sometimes decides not to give you another chance, he can manipulate the game by offering a do-over in response to your correct choice and making you stick with your incorrect choice.
It only works if the Monty reliably shows an unselected booby prize every time.
If the Monty opens one of the unselected doors at random, revealing the good prize 1/3 of the time, you gain no new information, even if it happens to be a booby prize this time.
If the Monty sometimes decides not to give you another chance, he can manipulate the game by offering a do-over in response to your correct choice and making you stick with your incorrect choice.
It only works if the Monty reliably shows an unselected booby prize every time.
Re: Flawed Thinking by Numbers
Oh, and QuliaSoup is awesome. He's a calm and clear voice of reason in a sea of shouting.
By: Deh_Dude
