Mind Melters

[Taylor57]

Ok, I just looked up your Wikipedia link.
A veridical paradox

Now I got something to get me to sleep other than recanting and recounting my last 9 holes of lousy golf today!

 

[Handlebars]

...because Monty would never reveal the prize and ruin the show. He has knowledge of where the prize is and so he will not open that door.

So you guys are telling me that if the can of spaghetti, shows up and Monte offers me the switch, and it's played out enough times to be significant, I lose if I keep my original bet?

Yes, you double your probability of winning if you switch upon learning where one of the joke prizes is. That's why I use the naming of positions, the "You" and "Not You".
I call it like this: I'm taking the Not You. The winning part of the Not You. That's only if you don't change.

 

[Taylor57]

I just cant get over how close it is to a coinflip. In the Wikipedia you do notice that there are some variables based on how Monte behaved during the new offers, but it's almost like a whatever the guys name is Mindfreak trick!

 

[Sierratim]

Life is stranger than we can imagine. Here's to Strangerester!

Ride On!

EDIT - Strangerester is to Weird as Fasterest is for the color red is to Speedyerester for any thing else, just to be clear.

 

[Taylor57]

Life is stranger than we can imagine. Here's to strangnester!

Ride On!

• A veridical paradox produces a result that appears absurd, but is demonstrated to be true nonetheless. The paradox of Frederic's birthday in The Pirates of Penzance establishes the surprising fact that a twenty-one-year-old would have had only five birthdays had he been born on a leap day. Likewise, Arrow's impossibility theorem demonstrates difficulties in mapping voting results to the will of the people. One version of the Monty Hall paradox demonstrates that a decision which has an intuitive fifty–fifty chance is in fact heavily biased towards making a decision which, given the intuitive conclusion, the player would be unlikely to make. In 20th-century science, Hilbert's paradox of the Grand Hotel and Schrödinger's cat are famously vivid examples of a theory being taken to a logical but paradoxical end.

 

[Taylor57]

I try not to Google when my girlfriend asks me sports questions on the NY Times crossword.

 

[Taylor57]

And you know what Yogi Berra said many years ago:

"When you come to a fork in the road, take it"

 

[Sierratim]

I just cant get over how close it is to a coinflip. In the Wikipedia you do notice that there are some variables based on how Monte behaved during the new offers, but it's almost like a whatever the guys name is Mindfreak trick!

It blew me away as well in a friendly debate with my sons. I do hate losing these debates! Who do these people think they are? Right, my (well educated) sons with (still) open minds. I yielded to their logic and poured more wine...

 

[Handlebars]

I went through this with my (enginering) sons recently. What seems intuitive is wrong; your odds of success do improve with switching your selection. I even took Stats 201! We are not smarter than piegons...

Now that I think about it, I question whether the humans were given a setup with actual doors to choose from as the pigeons undoubtedly had presented to them.

 

[Taylor57]

It blew me away as well in a friendly debate with my sons. I do hate losing these debates! Who do these people think they are? Right, my well educated sons with (still) open minds. I yielded to their logic and poured more wine...

I found a great Pinot from Napa yesterday.

 

[opimax]

Next you wil tell me I can use regen and power my bike indefinitely while going up hill !

 

[Sierratim]

Next you wil tell me I can use regen and power my bike indefinitely while going up hill !

Well, it depends on the hill...

 

[Handlebars]

Here's your next Mind Melter. It is very similar to the Monty Hall problem but it's easier to wrap your mind around before it melts.

There are 2 coins tossed simultaneously by an honest gambler. After flipping them the honest gambler tells you that one of the coins is "heads". He asks you if you want to bet for or against both coins being "heads".
What do you think the odds are that both coins are "heads"?

 

[Sierratim]

It does seem similiar to the Monty Hall problem. In this case there are 4 possible out comes with 2 coins;

Toss A - H..H
Toss B - H..T
Toss C - T..H
Toss D - T..T Where H = heads & T = tails.

With 1 coin being revealed as heads (H) means that the 'honest gambler' has thrown either Tosses A, B, or C. Toss D is eliminated as neither coin can be revealed as heads (H). So, should you bet for or against both coins being heads (H) with the possible combinations of;

H..H
H..T
T..H ?

Looks like the best bet is against the H..H combo with 2:1 odds. This is true, because like the Monty Hall problem, the outcome is determined once the game has started.

In an actual game of 'chance' each roll of the dice is independent upon the former, i.e. the outcome has get been determined.

 

[Handlebars]

If the weather channel hour by hour says for today under every hour, there is a 50% probability of rain that hour, what is the probability of rain today?

 

[Sierratim]

If the weather channel hour by hour says for today under every hour, there is a 50% probability of rain that hour, what is the probability of rain today?

Nearly 100% at some undefined point during the day.

 

[Handlebars]

Nearly 100% at some undefined point during the day.

If thinking of the 24 hours of 50% probability in each hour, would the probability of "no rain" be considered analogous to the probability of 24 coin tosses in a row, all heads?

 

[opimax]

“0” weather report always wrong here !

 

[Handlebars]

 

[Sierratim]

A good explaination of the "Monty Hall" problem;

Why You Should Always Switch: The Monty Hall Problem (Finally) Explained - By Steven Pinker - Behavioral Scientist

The infamous problem even professors and mathematicians got wrong comes down to one unintuitive inference—in the Monty Hall problem, Monty Hall is God.

behavioralscientist.org