Probability is a lie

[Scatty]

You know it is said that if you have two choices, from which 2 are wrong and 1 is right, and you choose 1 of then, and then 1 other of the other two is shown to you to be wrong, and you have an opportunity to change your choice, changing your choice is better by 50%-33%, for almost-obvious reasons.

 

I did the experiment, and with both tricks, reached an approximately 85% rate of failure.

 

Discuss bad luck.

[Dissonance]

.....that doesn't make probability a lie, that just makes your luck terrible.

[CrabHelmet]

This is the Monty Hall Problem; changing your choice gives you exactly a 2/3 chance of success.

 

But clearly your anecdote of this one time when it didn't work out much disproves all of combinatorial mathematics.

[Super Half Vamp Riku]

this is too smart for me

[Dark]

This is the Monty Hall Problem; changing your choice gives you exactly a 2/3 chance of success.

 

But clearly your anecdote of this one time when it didn't work out much disproves all of combinatorial mathematics.

 

For once, I thought exactly as Crab did.

[Freeman The Master]

Now it seems the Murphy's laws effect. Any bad thing that can happen, will happen.

[Kizzi]

This is the Monty Hall Problem; changing your choice gives you exactly a 2/3 chance of success.

 

But clearly your anecdote of this one time when it didn't work out much disproves all of combinatorial mathematics.

 

For once' date=' I thought exactly as Crab did.

[/quote']

 

Indeed.

[Pudpop]

In simple terms, you have three cups. One has a ball and 2 don't.

If you pick one, another one is revealed to be wrong, then in logic terms you have a 50-50 chance of guessing the right one. If you keep guessing wrong, then you have bad luck. What else needs to be discussed, this is common sense from when you're about 4 years old...

[CrabHelmet]

In simple terms' date=' you have three cups. One has a ball and 2 don't.

If you pick one, another one is revealed to be wrong, then in logic terms you have a 50-50 chance of guessing the right one. If you keep guessing wrong, then you have bad luck. What else needs to be discussed, this is common sense from when you're about 4 years old...

[/quote']

 

No, it's not 50-50. That's the whole point of the Monty Hall problem; there is a significant advantage to switching your choice, even if that seems counter-intuitive.

 

Here's a more extreme version of the problem that may make things easier to understand intuitively: there are hundred cups, under one of which is a ping-pong ball. You select a cup as your guess. Your host then knocks over ninety-eight cups, revealing that none of them hide a ping-pong ball. Thus, there remain two cups - the one you chose at the very start, and the only other cup that the host did not knock over. Do you want to switch your guess to that only other cup? Or is the chance 50-50?

[Pudpop]

Well, the thing is, why would you change? When simple (Reverse) Psychology makes him want you to change the cup? Then other Psychology makes you want to stay, which means the host wants you confused. What will you pick? 50-50 is it not?

Take a coin for example. A spazzed out coin has 100 sides. You choose heads(there are a hundred different parts). The Psychic Host cuts off the 98 parts and leaves you with heads or tails. You flip the coin. 50-50 is it not?

Oh and I don't think there was a host involved in the first place, because minus the host, means I'm probably wrong.

[Kizzi]

Well' date=' the thing is, why would you change? When simple (Reverse) Psychology makes him want you to change the cup? Then other Psychology makes you want to stay, which means the host wants you confused. What will you pick? 50-50 is it not?

Take a coin for example. A spazzed out coin has 100 sides. You choose heads(there are a hundred different parts). The Psychic Host cuts off the 98 parts and leaves you with heads or tails. You flip the coin. 50-50 is it not?

Oh and I don't think there was a host involved in the first place, because minus the host, means I'm probably wrong.

[/quote']

 

The bits of that that I understood were wrong. Everything else was nonsense.

[Pudpop]

Yeh, well, when I wrote that I was hoping to be right or be proved wrong and learn something. Of course you typing that helped me in no way...

[CrabHelmet]

Well' date=' the thing is, why would you change? When simple (Reverse) Psychology makes him want you to change the cup? Then other Psychology makes you want to stay, which means the host wants you confused. What will you pick? 50-50 is it not?

Take a coin for example. A spazzed out coin has 100 sides. You choose heads(there are a hundred different parts). The Psychic Host cuts off the 98 parts and leaves you with heads or tails. You flip the coin. 50-50 is it not?

Oh and I don't think there was a host involved in the first place, because minus the host, means I'm probably wrong.

[/quote']

 

There's nothing psychological about it. It's pure probability.

 

Your coin analogy fails because, with the coin, the randomization occurs at the end of the game, after the extra options have been removed. At the time of randomization, all remaining options are equally probable, but the time of randomization is crucial.

 

Consider the game with a hundred cups and a single ping-pong ball. The ball is randomly hidden in one of the hundred cups - the host knows where it is, but you do not. At this time, each of its hundred possible locations are equally probable.

 

The randomization has occurred already.

 

Now you enter the stage and need to choose a cup. Now, there are a hundred cups, the ping-pong ball is in one of them, and you only have one choice to make - and so you only have a 1% chance of finding the ball with this guess.

 

Is the cup you choose the one with the ping-pong ball?

 

Case 1: If it is not - and in 99% of cases, it won't be - then the host knocks over every cup except the cup you chose and the cup containing the ping-pong ball. If you change your choice, your new final choice will be the correct cup, and you will win. If you do not change your choice, then your final choice will be your original wrong cup, and you will lose.

 

Case 2: If it is - which will happen in only 1% of cases - then the host knocks over ninety-eight arbitrary empty cups, leaving your correct cup and a random empty cup. If you change your choice, your new final choice will be a wrong cup, and you will lose. If you do not change your choice, then your final choice will be correct and you will win.

 

The result of this is that changing your choice of cups will enable you to win 99% of the time. The key fact to realize is that, by revealing all but one of the other cups, the host is changing the game from "Which of these cups has the ball?" to "Was your original guess correct?" - and, unless you yourself have psychic powers, your original guess was probably not correct.

[Scatty]

Now it seems the Murphy's laws effect. Any bad thing that can happen' date=' will happen.

[/quote']

 

That's SO me!

 

 

You COULD survive a brain surgery and die because of a simple appendix removal.

 

Just sayin'...never be too sure that something will happen...unless it happened already.

 

I never denied the answer to the Monty something problem, I simply said that although math proves it, there is no way it can be proven experimentally. I would still change my choice in this situation, but with my inherited bad luck, I will lose nonetheless.

[CrabHelmet]

I simply said that although math proves it' date=' there is no way it can be proven experimentally.

[/quote']

 

In the sense that anything can be proven experimentally, it can.

[Zexaeon]

Bravo, Crab~

 

Anything that needs to be said on this matter can be read in any of Crab's posts. Educate yourselves, readers.

[Raylen]

For those who need to be more "Graphic"

 

[spoiler= Long Post]

 

To analyze this problem we represent this senario as a random variable on a roulette wheel. The roulette wheel on the left simulates the Let's Make a Deal game. The inner wheel represents the number of the door that the car is behind' date=' the middle wheel represents the door that is selected by the contestant, and the outer wheel represents the door Monty Hall can show. Spinning this roulette wheel once is equivalent to playing the game once. The outer wheel also tells you what your strategy should be to win. The red means that in order to win the contestant needs to switch doors, and the blue means that the contestant should not switch. Notice that there are twice as many red sections as blue. In other words, you are twice as likely to win if you switch than if you don't switch! What this wheel makes evident is that with probability 1/3 the contestant selects the correct door in which case it would be better not to switch. In the other 2/3 of the cases, Monty Hall is telling the contestant where the car is!

 

Maybe this is where the controversy lies:

[img']http://math.ucsd.edu/~crypto/Monty/images/wheel2alt.jpg[/img]

 

How does this problem change if Monty Hall does not know where the car is located? We must decide what it means if Monty should happen to open the door with the car behind by accident. The problem says only that Monty opened a door with a goat behind it so we interpret this to mean that if the car is revealed then the game is over and the next contestant plays the game.

 

 

If this is the senario then the wheel looks almost the same, the inner wheel represents the door that the car is behind, the middle wheel represents the number of the door that is selected by the contestant, and the outer wheel represents the door number Monty Hall will show the contestant. This time however, Monty Hall has the option of opening a door with a car behind it, but by chance he didn't. Playing the game under these assumptions is equivalent to spinning the roulette wheel to the right except that if the blackened area of the wheel comes up then it is spun again. Once again the red area means that in order to win the contestant will need to switch doors, and the blue means that the contestant should not switch. Notice that there is the same amount of red area as blue. In other words, it doesn't matter if the contestant switches in this case.

 

 

[Zexaeon]

I just played the cup game with my siblings.

 

Thorugh psychological warfare, I almost won. But the bet got spoiled during the alst game by outside interference and I only broke even.

[Pudpop]

Well' date=' the thing is, why would you change? When simple (Reverse) Psychology makes him want you to change the cup? Then other Psychology makes you want to stay, which means the host wants you confused. What will you pick? 50-50 is it not?

Take a coin for example. A spazzed out coin has 100 sides. You choose heads(there are a hundred different parts). The Psychic Host cuts off the 98 parts and leaves you with heads or tails. You flip the coin. 50-50 is it not?

Oh and I don't think there was a host involved in the first place, because minus the host, means I'm probably wrong.

[/quote']

 

There's nothing psychological about it. It's pure probability.

 

Your coin analogy fails because, with the coin, the randomization occurs at the end of the game, after the extra options have been removed. At the time of randomization, all remaining options are equally probable, but the time of randomization is crucial.

 

Consider the game with a hundred cups and a single ping-pong ball. The ball is randomly hidden in one of the hundred cups - the host knows where it is, but you do not. At this time, each of its hundred possible locations are equally probable.

 

The randomization has occurred already.

 

Now you enter the stage and need to choose a cup. Now, there are a hundred cups, the ping-pong ball is in one of them, and you only have one choice to make - and so you only have a 1% chance of finding the ball with this guess.

 

Is the cup you choose the one with the ping-pong ball?

 

Case 1: If it is not - and in 99% of cases, it won't be - then the host knocks over every cup except the cup you chose and the cup containing the ping-pong ball. If you change your choice, your new final choice will be the correct cup, and you will win. If you do not change your choice, then your final choice will be your original wrong cup, and you will lose.

 

Case 2: If it is - which will happen in only 1% of cases - then the host knocks over ninety-eight arbitrary empty cups, leaving your correct cup and a random empty cup. If you change your choice, your new final choice will be a wrong cup, and you will lose. If you do not change your choice, then your final choice will be correct and you will win.

 

The result of this is that changing your choice of cups will enable you to win 99% of the time. The key fact to realize is that, by revealing all but one of the other cups, the host is changing the game from "Which of these cups has the ball?" to "Was your original guess correct?" - and, unless you yourself have psychic powers, your original guess was probably not correct.

 

Ohhhh.....

Makes a lot of sense.

[Scatty]

I simply said that although math proves it' date=' there is no way it can be proven experimentally.

[/quote']

 

In the sense that anything can be proven experimentally, it can.

 

Prove the Big Bang theory EXPERIMENTALLY. Prove the existence of a neutron star EXPERIMENTALLY.

[Pudpop]

The Big Bang Theory, funny show, annoyingly stupid theory.

How can particles explode randomly?

[Scatty]

The Big Bang Theory' date=' funny show, annoyingly stupid theory.

How can particles explode randomly?

[/quote']

 

*handshake*

[Guest Chaos Pudding]

I simply said that although math proves it' date=' there is no way it can be proven experimentally.

[/quote']

 

In the sense that anything can be proven experimentally, it can.

 

Prove the Big Bang theory EXPERIMENTALLY. Prove the existence of a neutron star EXPERIMENTALLY.

 

Theories don't or can't be proven. They can only be disproved with evidence. Otherwise, they would be facts. That being said, the Big Bang model has a metric ton of evidence to support it. Not saying that it answers every question that can be posed yet, but it's got enough evidence to be the accepted model for the birth of the universe.

 

Step 1: Look up examples of neutron stars.

Step 2: Observe them.

Step 3: Stop being stupid.

[Scatty]

I simply said that although math proves it' date=' there is no way it can be proven experimentally.

[/quote']

 

In the sense that anything can be proven experimentally, it can.

 

Prove the Big Bang theory EXPERIMENTALLY. Prove the existence of a neutron star EXPERIMENTALLY.

 

Theories don't or can't be proven. They can only be disproved with evidence. Otherwise, they would be facts. That being said, the Big Bang model has a metric ton of evidence to support it. Not saying that it answers every question that can be posed yet, but it's got enough evidence to be the accepted model for the birth of the universe.

 

Step 1: Look up examples of neutron stars.

Step 2: Observe them.

Step 3: Stop being stupid.

 

I looked at a damn neutron star. Now prove it to me EXPERIMENTALLY.

 

Then, please prove EXPERIMENTALLY that if you toss a coin and call Heads or Tails there is a 50% chance to get Heads. I will say it again EXPERIMENTALLY. And if you get 10 Heads and 11 Tails, that's a failure.

[Guest Chaos Pudding]

I simply said that although math proves it' date=' there is no way it can be proven experimentally.

[/quote']

 

In the sense that anything can be proven experimentally, it can.

 

Prove the Big Bang theory EXPERIMENTALLY. Prove the existence of a neutron star EXPERIMENTALLY.

 

Theories don't or can't be proven. They can only be disproved with evidence. Otherwise, they would be facts. That being said, the Big Bang model has a metric ton of evidence to support it. Not saying that it answers every question that can be posed yet, but it's got enough evidence to be the accepted model for the birth of the universe.

 

Step 1: Look up examples of neutron stars.

Step 2: Observe them.

Step 3: Stop being stupid.

 

I looked at a damn neutron star. Now prove it to me EXPERIMENTALLY.

 

Then, please prove EXPERIMENTALLY that if you toss a coin and call Heads or Tails there is a 50% chance to get Heads. I will say it again EXPERIMENTALLY. And if you get 10 Heads and 11 Tails, that's a failure.

 

Question: Do neutron stars exist?

Hypothesis: Neutron stars exist

Method:

1. Research what a neutron star is.

2. Research examples of neutron stars.

3. Observe said examples for evidence of neutron star characteristics.

Results: Observed star was a neutron star.

Conclusion: Neutron stars exist.

 

There. Do this experiment, and you've proved that a neutron star exists "EXPERIMENTALLY". Now stop being an ass.

 

And, truth be told, no coin has an exact 1:1 heads to tails rate, because no coin is created perfectly. But the average flip rate of an average coin is, rounded, 50%.