Do you know the correct answer?

[Boatbum]

y
the new york times leans very slightly left* l

* and let's be honest, in today's world reality has a liberal bias

OK, but I do disagree with the NYT. They are more than slightly left. They picked up the party line of Russian disinformation on the Hunter Biden Laptop for 18 months before finally (but not formally) conceding that the contents were legitimate.

Also they buried an attempted assignation of a Supreme Court Justice in the middle of the paper.

Here was the front page news that was more important.....

June 8 https://static01.nyt.com/images/2021...tpage/scan.pdf

Seizing money US retaliates for Cybercrime
FDA Approves new medication for Alzheimer's
Jail for Women shut for abuses in New Jersey
Arrival of FEMA aid widens racial disparities
In Guatemala Harris discourages migration
Arizona's Vote audit is scorned. Republicans Press on anyway
One House Two Families and the struggle for East Jerusalem
Hot, Fresh and Machine-made
For Belfast, a tense summer
At Yale, a law school divided
Democrats seek path forward
Arrest in 1972 cold case


June 9 https://static01.nyt.com/images/2021...tpage/scan.pdf

Talks Collapse on Biden Plan for Rebuilding
Global FBI Sting nest 800 arrests
Richest in US pay all but nil in Income Tax
Back to Normal? Not for many Asian Americans
Countering China, Senate unites on a bill to pour aid into Tech
After a Campaign Uprising, Morales presses on
Subway leaps back to life
Bill opens gun makers suits
A fight of French Identity
Stolen election crisis in Israel.

[L.W. Baxter]

some people take disagreement as insult.

[Tom Montgomery]

.
Here is the simplest table I have found that shows all the possible outcomes. The assumption is the contestant initially chooses door #1.



This was the table created by Marilyn vos Savant and published in Parade Magazine to show how always choosing to switch is the best strategy.

[Decourcy]

I might be wrong, but I recall that you joined the forum 'rather hot.' Perhaps it was not just your thoughts, but your tone, that influenced responses.

I have no issues supporting my position against opposition, and some of my ideas go against the standard opinions here. So was i “hot” or was my not modifying my ideas when met with vitriol just considered to be “hot”?

Some of my first interactions were met mostly with “troll” and “sock puppet” and I have been told such things as I am “not fit to live amongst civilized people” and similar to people who shoot children in schoolyards.

I think, personally, that I’ve remained rather calm. Other than the one time I challenged another member to a duel of course.

My tone became what it is through the responses of members here. Distain will be met with like. Friendliness with friendliness.

[David G]

The psychology of all this is informative - for all of us. Wed to certain outcome, 'just absolutely sure' we are right - it's hard to ask 'is it possible that I'm wrong?'.

On the first page, we saw a similar blowback from actual math/statisticians, who had to re-evaluate what they 'knew' to be true - that wasn't.

No wonder society can't get together to solve problems. 'I could agree with you - but then, we'd both be wrong'.

Great thread.

As I mentioned earlier - the difference between Type1 and Type2 thinking.

What makes it so dramatic an example is that the setup makes 'stick' SO strongly (and seductively) intuitive. And it also makes 'switch' so strongly counter-intuitive... requiring a strong leap into slow thinking with a strong follow-thru required as well. That's why so many mathematicians were confused back in the day. Even minds adept and trained at making that leap could be seduced by such a strong Type1 'obviousness'.

[CWSmith]

Yes, it's so simple that it's wrong. It fails to account for one door being opened. I've already done it correctly on the first page. You can disagree, but the fact that you present this as in any way relevant is surprising.

It also demonstrates why Savant is wrong.

.
Here is the simplest table I have found that shows all the possible outcomes. The assumption is the contestant initially chooses door #1.



This was the table created by Marilyn vos Savant and published in Parade Magazine to show how always choosing to switch is the best strategy.

[David G]

if only tom montgomery had presented the solution to us in an authoritative british accent

IKR. Sheer malfeasance on his part.

Unless (can we inject some conspiracy theory here?) he's secretly out to dethrone you as 'most prolific troll'???

[birlinn]

Once the goat is revealed, there are now two doors; one will have a goat, one a car.
If you choose a door, there is a 50% chance it will have a car.
If you switch to the other door, there is a 50% chance it will have a car.
No gain in switching.

[Beowolf]

The psychology of all this is informative - for all of us. Wed to certain outcome, 'just absolutely sure' we are right - it's hard to ask 'is it possible that I'm wrong?'.

On the first page, we saw a similar blowback from actual math/statisticians, who had to re-evaluate what they 'knew' to be true - that wasn't.

No wonder society can't get together to solve problems. 'I could agree with you - but then, we'd both be wrong'.

Great thread.

I’m my time teaching high school, I found it particularly effective to court misconceptions, tease them out as far as we could, before introducing (sometimes blatantly) the inconsistency in the notion that proves it false. Doing so would provide an opportunity for the students to take the “correct bits” of their notion and assign them to the actual outcome of the event with sound reasoning.

A favorite of mine was teaching Newton’s 1st Law of Motion with a cork suspended in a Mason Jar full of water, tethered to the bottom with a piece of string. Somewhere in our long, drawn out conversation regarding what would happen if the jar were to be pushed across a table, I would accidentally nudge the jar.

That’s when all hell would break loose.

However, as a result of working in that medium all that time, I find that I really have no aversion to being wrong. The opportunity to examine my preconceived notion and reconcile it with a new-found reality is rather enjoyable.

Well… as long as it doesn’t cost me any money.

[David G]

As a conservative, the primary reason I spend any time in the bilge is because there is so much opposition. I want to hear why someone has a different viewpoint as it may move my thinking although I do wish some of the viewpoints had less vitriol laced within them. Even in this thread which is theoretically more objective, people started to get heated and began to accuse others of being Trolls.

I sympathize. This is precisely why I am glad to see new conservative voices here. I'm always hoping for a different perspective that'll keep me honest. What I call an 'honest correspondent' with a different viewpoint. Honing your ideas against opposition is valuable.

as a pinko commie tree hugger i appreciate your participation here, but wish you would find more honest and factual sources of news with which to base your arguments, even if they retain a conservative slant

Just so. One of the many things that I get testy about is when my hoped-for 'honest correspondent' argues on the basis of claptrap. We spend far too much time debunking nonsense. Much of that nonsense comes from following too-slanted sources.

Baxter is halfway there when he says some people take disagreement as insult. I take ill-considered, factually incorrect, agenda-driven, logical fallacy laced disagreement badly. I regard it as thrice an insult. First - that you're willing to waste my time with easily disproven dreck. Second - that you think I'm stupid enough, or ill-informed enough to fall for it. Third - mad that you've held youself out as an 'honest correspondent' when you aren't. To be fair, more than half of my mad in this instance is at myself. Disappointment that I've once more allowed myself to be sucked in... even though I saw the (now all-too-familiar warning signs).

That's a fair comment, are there particular sources I use that you feel are not honest and factual? Also who do you accept as an unbiased and accurate authority?

Another thing that bumps me into GOP territory (Grumph Ol' Phart) is having to repeat myself.

If you want to list your usual sources of news and analysis, I'm happy to rate/critique them. I'm sure others will as well. Meantime... one more time... a rough approximation - in graphic form - of 'good news sources'. Ranked for both ideological slant and factual reliability ---

[Tom Montgomery]

Yes, it's so simple that it's wrong. It fails to account for one door being opened.

Actually it does account for one door being opened. In every case what is offered (the fifth column in the table) is the result of a door being opened revealing a goat. What remains behind the other door is what is offered.

[Beowolf]

Once the goat is revealed, there are now two doors; one will have a goat, one a car.
If you choose a door, there is a 50% chance it will have a car.
If you switch to the other door, there is a 50% chance it will have a car.
No gain in switching.

This would only be true if you brought in a “fresh contestant” after the switch, who is unaware that a deliberate and informed decision was made by the host after the first contestant had selected their door.

There is no getting around the fact that the host added actionable information into the scenario by removing a known goat.

[CWSmith]

This is the logical sleight of hand that has stumped you and Nick, and, initially, most everyone else. The door being opened is irrelevant and does not change the starting probabilities.

If that's true, then you should be able to create a table that proves it. I already did on the first page. Now you show your work.

[Paul Pless]

you should make this your avatar

[CWSmith]

Actually it does account for one door being opened. In every case what is offered (the fifth column in the table) is the result of a door being opened revealing a goat. What remains behind the other door is what is offered.

Okay. This is the first time you have me puzzled.

[rgthom]

If that's true, then you should be able to create a table that proves it. I already did on the first page. Now you show your work.

This is the sticking point. You added the rows for the only "choice" the host has, which goat to pick if the remaining two doors both have goats. But it has no effect! The host could be a robot who only picks a specific door with goat for each case, or it could use a random number generator to pick one of the goats, or it could pick the smelliest goat, but it has no effect on the odds! The only real choices in the game are by the contestant. The first choice of door is the only real random choice, if you know the odds of the game then always take the change and win 2 out of 3.

[David G]

you should make this your avatar

Yeah... how many times you reckon I've posted this sort of chart?

Maybe boatbum is new enough he's never seen it until now???

[Jimmy W]

Get 3 squares of paper. Write car on one and goat on the other two. Fold them to hide the writing. Shake in box, then pick one and set it to the side. Open one of the other two, if it says goat, take it out of play, otherwise take other one out. Try this twenty times, 10 where you keep your original choice and 10 where you switch.
My results were 4 wins out of 10 not switching and 8 out of 10 switching. So I did better than 1/3 and 2/3 both ways, that would likely have changed if I had tried 100 of each.

[Tom Montgomery]

It fails to account for one door being opened.

Actually it does account for one door being opened. In every case what is offered (the fifth column in the table) is the result of a door being opened revealing a goat. What remains behind the other door is what is offered.

Okay. This is the first time you have me puzzled.

The first row of the table shows a Car behind door #1 and a Goat behind both doors #2 and #3. The contestant chooses door #1 which has the Car. That means Monty has the other two doors, both of which has a Goat. Monty opens one door (it makes no difference which one) and shows a Goat and discards it. He then offers to switch his remaining door (a Goat) with the contestant. If the contestant accepts the offer to switch he is left with a Goat. He started with the Car and ended with a Goat.

The second row of the table shows a Goat behind door #1, a Car behind door #2, and a Goat behind door #3. The contestant chooses door #1 which has a Goat. That means Monty has the other two doors: Door #2 with the Car and door #3 with a Goat. Monty opens door #3 revealing the Goat and discards it. He then offers to switch his remaining door #2 (the Car) with the contestant. If the contestant accepts the offer to switch he gets the Car. He started with a Goat and ended with the Car.

The third row of the table shows a Goat behind door #1, a Goat behind door #2, and the Car behind door #3. The contestant chooses door #1 which has a Goat. That means Monty has the other two doors: Door #2 with a Goat and door #3 with the Car. Monty opens door #2 revealing the Goat and discards it. He then offers to switch his remaining door #3 (the Car) with the contestant. If the contestant accepts the offer to switch he gets the Car. He started with a Goat and ended with the Car.

So by always accepting the switch the contestant wins the Car 66.66% of the time (2/3).

Column four of the table shows the results if the contestant never accepts the offer to switch. He only wins the Car 33.33% of the time (1/3).

So by always accepting the offer to switch doors the contestant increases his probability of winning the car from 33.33% to 66.66%.
.

[Decourcy]

Although we think of “contestant” and “host” in the standard game show way, the reality is that the host is the player. He gets the second move, but his moves are limited by the initial choice of the “contestant”. If the “contestant” chooses one or the other goat, the “host” can only make one move, and he will lose if the “contestant” always switches. Only if the “contestant” chooses the car does the host have a choice of goats and can only them hope that the “contestant” will fall for his bluff and switch. One in three chances for the host if the “contestant” always switches.

[birlinn]

This would only be true if you brought in a “fresh contestant” after the switch, who is unaware that a deliberate and informed decision was made by the host after the first contestant had selected their door.

There is no getting around the fact that the host added actionable information into the scenario by removing a known goat.

If the host knows what is behind each door, then the odds are different, agreed.

[rgthom]

The first row of the table shows a Car behind door #1 and a Goat behind both doors #2 & #3. The contestant chooses door #1 which has the Car. That means Monty has the other two doors, both of which has a Goat. Monty opens one door (it makes no difference which one) and shows a Goat and discards it. He then offers to switch his remaining door with the contestant (a Goat). If the contestant accepts the offer to switch he is left with a Goat. He started with the Car and ended with a Goat..

CW says it does matter which one, but it does not. The two states are identical. CW says show your work. Tom did, in his first table.

[Jimmy W]

The latest version of that Media Bias Chart is here. https://adfontesmedia.com/static-mbc...WebSite_Button

[David G]

The latest version of that Media Bias Chart is here. https://adfontesmedia.com/static-mbc...WebSite_Button

Even better. Thanks!

[CWSmith]

Probability isn't about choices in any humanistic sense, so talk about robots and random number generators (which don't actually exist, but that's another story) are not relevant.

Probability is about actions and outcomes, how many paths lead to a positive or negative outcome.

This is the sticking point. You added the rows for the only "choice" the host has, which goat to pick if the remaining two doors both have goats. But it has no effect! The host could be a robot who only picks a specific door with goat for each case, or it could use a random number generator to pick one of the goats, or it could pick the smelliest goat, but it has no effect on the odds! The only real choices in the game are by the contestant. The first choice of door is the only real random choice, if you know the odds of the game then always take the change and win 2 out of 3.

[CWSmith]

CW says it does matter which one, but it does not. The two states are identical. CW says show your work. Tom did, in his first table.

As I did in post #24. Now, can you explain why one is right and one is wrong instead of just stating which you believe?

[Tom Montgomery]

Even better. Thanks!

Interesting. I it turns out I do not depend on any of the organizations that fall south of the green box for my news, information and analysis.
.

[rgthom]

As I did in post #24. Now, can you explain why one is right and one is wrong instead of just stating which you believe?

It is not my "belief". The two states are identical, they do not create any change in the odds. Follow Tom's table and explain why you believe splitting the two identical goats can change the outcome in any way.

[CWSmith]

The first row of the table shows a Car behind door #1 and a Goat behind both doors #2 and #3...
.

Yes, I understood the table. It's logically the same as your original table, but presented in a more tempting manner. It took me a few minutes to understand why it's wrong.

You need to make a choice. Either you start the game from the very beginning and follow ALL realizations to the end, or you start after the one door is open and recognize it is a new game. You are doing something between the two, starting from the very beginning, but continuing to combine two realizations as if they were one.

[leikec]

Jesus Alou…

Jeff C

[Tom Montgomery]

.
Here is an interesting paper published online by Psychologica Belgica, Journal of the Belgian Association for Psychological Science:
Why Humans Fail in Solving the Monty Hall Dilemma: A Systematic Review.

[Tom Montgomery]

You need to make a choice. Either you start the game from the very beginning and follow ALL realizations to the end, or you start after the one door is open and recognize it is a new game. You are doing something between the two, starting from the very beginning, but continuing to combine two realizations as if they were one.

OK... you've lost me. I do not understand this at all. Could you restate the above in a different way that I might be able to understand?

[Tom Montgomery]

.
Let me ask you a question. Say the contestant chooses one door. Monty Hall keeps the other two doors. Monty Hall looks to see what are behind his two doors and opens a door containing a Goat and discards it. Say that no switch is offered. The remaining two doors are opened simultaneously. What is the probability that the Contestant has the car? What is the probability Monty Hall has the car? Are you under the impression they both have a 50% probability of having the Car?

[Paul Pless]

.
Let me ask you a question.

544 replies!

[George.]

Nope that suggests that Monty's decision affects the location of the car, which is impossible.

No, but it is based on the location of the car.