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[Nivim]

 We might not have deciphered their language (which might change every couple of years anyway), but that does not me we do not understand each other. Here's the Bottlenose Dolphin Research Institute Wikipedia page, although I'm not sure if this is the one that made a deal with a pod of dolphins (they come back every year for weirdness in return for entertainment and free fish).

[Kagus]

How many more learned African Greys are there? I never heard of Griffon. What did he/she learn?

If you look in the introduction to the first article you linked to, you'll see Griffin (sorry, spelled it incorrectly) mentioned.

Another sign of intelligence is the [MEMORY_LOST] test, where you are offered a choice of 3 doors (or cups) and told (truthfully) that behind one of them is a prize, behind the others, nothing. When you make a decision, the teller opens one of the other doors (picks up one of the cups) and asks you if you want to stick with your decision or switch to the other remaining door (cup). Humans tend to fail this test about 70% time, while pigeons tend to succeed about 60%. (I found this puzzle on the xkcd forums, found the research on it afterwards.)
In the above, what answer would you pick?

I *hate* this thing.  I've heard it spread so many different places, and it's just not right.  If this is the question I think it is, then the "right" thing to do is to change your decision for the other cup.

This is completely bogus.  When picking one out of the three cups, your choice is 1/3 or 33% likely to be the right one.  This is generally explained, and is correct.

However, the problem then goes on to explain that, somehow, after the second cup is picked up you are left with the other cup (50% right) and your original choice (33% right).  There is a fundamental logic gap that so many people seem to have completely missed, as I've seen this thing spread across numerous magazines, websites, and so on. 

The chances of being right are exactly the same regardless of whether you stick with your original choice or switch to the new one.  You don't magically lose a number of percentage points to the ether, and you're not 'stuck' with the first 1/3 choice you made, because the problem has changed.


Sorry, but I just had to vent.  This thing is faulty and needs to be stopped in its tracks.

[Leafsnail]

Uh, Kagus, you misunderstood.

If you switch, you have a 66% chance of winning.  If you stay, 33%.  I have an easy way to demonstrate.

Let's say we have fundamentally the same game, only there's 100 doors.  There are 99 goats, and one car.

You choose a door.  The host opens 98 doors, and there are goats behind all of them (he knows where the car is, and avoids picking it if you haven't got it already).  Do you stick, or do you switch?

Remember: you had a 1/100 chance of getting it first time.  That stays the same when the doors are open.  As you say, "You don't magically lose a number of percentage points to the ether".

[Eugenitor]

Here's another way of thinking about it:

It's either 1, 2, or 3. You pick 1 on the outset.

If it's 1, your initial choice was correct.

If it's 2, the host opened the other door and you can switch to it.

If it's 3, the host opened the other door and you can switch to it.

[lordnincompoop]

Ah, game theory. Gotta love it.

The point that you all missed however is this: How did they get the pigeons to do this?

[Criptfeind]

That makes no sense.

[Renault]

Its one of those things that seems baldly illogical, but when you get to the math of it, actually works out. I can see how you'd find it hard to accept, though. Thats the deal with statistics. In fact, I think the most important lesson my first statistics class gave was "Never trust your gut on statistics. It will be wrong."
This game in particular demonstrates that, heh.

[lordnincompoop]

On the topic of conversation, it's good to know that such confused opinions are still around, since I'll presumably have to deal with them antagonistically at some point.

 Intelligence (of any variety) exists in steps; you need a floating point integer (0.24, 24.98, 7.021, 90.1), not a boolean (1, 0), to begin quantifying these steps. We already have identified many signs that may suggest what relative numbers we could assign to each individual of each species.
 One of those signs mentioned here was the individuals reaction to a mirror (...), and whether or not they understand they perceive themselves and not another of their species. Humans tend to ~score high in this test; parakeets fail it almost every time.
 Another sign of intelligence is the [MEMORY_LOST] test, where you are offered a choice of 3 doors (or cups) and told (truthfully) that behind one of them is a prize, behind the others, nothing. When you make a decision, the teller opens one of the other doors (picks up one of the cups) and asks you if you want to stick with your decision or switch to the other remaining door (cup). Humans tend to fail this test about 70% time, while pigeons tend to succeed about 60%. (I found this puzzle on the xkcd forums, found the research on it afterwards.)
 In the above, what answer would you pick?

 It is true I'm totally skipping the "morals" part of this discussion because those things are usually insane and a pain to quantify.

[Criptfeind]

Okay, can you link to a place that has the math of it then? Because I am curious.

[Nivim]

 The reason pigeons get this is because they look at nothing but the numbers for the treat; no calculation, no percentage, just experience. And thus while a person may continue to be stubborn for 30 tries or more, the pigeon takes half that to learn it should always switch. Of course, the smart human has a chance of getting it right from the start.

 I have failed to find the articles on this because I can't remember what this test is called! What's the name?

Edit: You know, you really can test this yourself with a friend, three cups, and a pebble. I recommend you bet small amounts of money on it and see the numbers add up.

[Leafsnail]

You can also do a probability tree.

Ok, you pick your door.  Let's call the picked door Door A.  We'll call the other doors are Door B and Door C (surprisingly).

Now, there are 3 possibilities:
- The car is behind door A
- The car is behind door B
- The car is behind door C

You should agree that all three of these are equally likely, and have a chance of 1/3 each.

Now, let's play out each scenario:

- In world A, either one of door A or door B is opened (doesn't matter).  If you stick, you win.  If you switch, you lose.  In this world, switching will make you lose.
- In world B, door C will be opened.  If you stick, you lose.  If you switch, you win.  In this world, switching will make you win.
- In world C, door B will be opened.  If you stick, you lose.  If you switch, you win.  In this world, switching will make you win.

Tally up the odds: there's one case of switching making you lose, and 2 of switching making you win.  So switching has a 2/3 chance of winning, while sticking is 1/3.

If you have a problem with the explanation, please say where.

Incidentally: "The Monty Hall Problem" (although apparently Monty Hall didn't actually give people the option to switch on the show).

[Criptfeind]

I have a issue with arbitrariness in which you chose how you win.

Please explain how you got to:

If you stick, you win.  If you switch, you lose.  In this world, switching will make you lose.

If you stick, you lose.  If you switch, you win.  In this world, switching will make you win.

If you stick, you lose.  If you switch, you win.  In this world, switching will make you win.

[Leafsnail]

If you pick the car, you win.  That's a fairly basic premise of the problem.

Oh, wait... I think I know what you mean.  Gimme a moment.

[Kagus]

Remember: you had a 1/100 chance of getting it first time.  That stays the same when the doors are open.  As you say, "You don't magically lose a number of percentage points to the ether".

No.

You are given a choice between one out of 100 doors.  Each door has a 1/100 chance of being the right one, as there are 100 doors and only one of them can be right.

The host opens 98 doors, revealing all those doors to be wrong.  There are now only two doors left.  The one you originally chose, and one other.

There are two doors, one of them can be right, and you have to choose between the two.  What are the chances for each door to be correct?

Your door does not have a 1/100 chance of being correct, because it is one of two choices.  The other door does not have a 99/100 chance of being correct, because it is one of two choices.


Your door is not a 1/100 chance!  At the start, you picked one door out of 100 equal doors.  Then you had a 1% chance of being right.  But then the host eliminated 98 choices by opening them and showing them to be false.  Now you are presented with an entirely new problem where you must pick between one of two doors.

Your statistical chances do not carry over from the first problem.  There's no magic in this.  You are given a choice between two doors.  It's faulty logic that follows from being tricked by word play.

*post*

Yeah, this makes no sense to me.  If you wouldn't mind elaborating on the 'worlds' section, as it gets a little confusing as to how you're making your statements.

[Renault]

You know, this problem has a Wikipedia page. Its not a trick of words, Kagus, it's just an example of the way statistics messes with your head.

http://en.wikipedia.org/wiki/Monty_Hall_problem

This should end this discussion, hopefully.