It was two years ago today...

[slingshot]

In this case the dealers have a better idea of the actual problem. And they are not using one die to have multiple values. In other words, they have a better grip on the reality of the question.

You "1/11 guys" still don't understand how you are misinterpreting simple English.

I guess when you take probability classes they forget to teach how to understand the English language.

I gave you the question that would have an answer of 1/11.

One die is a fixed parameter, the other is variable.

[RS__]

In this case the dealers have a better idea of the actual problem. And they are not using one die to have multiple values. In other words, they have a better grip on the reality of the question.

You "1/11 guys" still don't understand how you are misinterpreting simple English.

I guess when you take probability classes they forget to teach how to understand the English language.

I gave you the question that would have an answer of 1/11.

You're back peddling. The only reason you brought up the dice crew is because you thought they have some kind of authority or expertise on the subject. But, that's clearly not true. So now you're saying they just understand or "have a better grip" on the question than......people who actually use probability to make a living.

You're a reporter. Stick with reporting instead of arguing yet another case you're absolutely wrong in.

[mickeycrimm]

I ran another sample space of 100 decisions this morning. The other die was a two 13 times in 100 decisions. So now we have a sample space of 300 decisions. The other die was a two 32 times. That's an average of once very 9.375 decisions. Are the numbers now regressing towards 1 in 6, or did the solid four just catch some positive variance in the third sample space.

I have some driving to do today and some slot parlors in a couple of small towns to sweep through. I'll be in a different hotel tonight and run some more sample spaces.

[arcimede$]

Alan has already admitted that if the question is worded one way the answer is 1:11. Hence, the argument here is what is the wording of the question. Alan needs to show everyone the precise difference in wording that would yield 1:11 vs. 1:6 and explain why.

[regnis]

Alan.....dealers, floor people, and pit bosses are generally not experts on probability. To say they are experts on dice is like saying the cooks at McDonalds are expert chefs.

Hell, one time my boss backed off our biggest bettor because he was winning.....he always played the same way: Hop hard ways, regular hard ways, horn bets, etc. for the max he could, and play until he was stuck $20k.....he could be up $40k but he'd still lose it all back, if it took 1 hour or 10 hours.

I asked the other dealers I was dealing with the same question, word for word. Three dealers total. One almost instantly said 1/6 because the other die had 6 sides. Another waited a few moments, his brain working, and said 1/36 because that's the chance of a 2-2 being rolled. The other was still thinking, said 1/12. I asked why 1/12 and he said because you could roll a 1-2, 2-2, 3-2, 4-2, 5-2, 6-2, 2-1, 2-2, 2-3, 2-4, 2-5, 2-6. Then thought about it for a second more and said no, it's 1/11 because he double counted 2-2.

I asked a boss and he just said "it's random, dice are random". I said yes they're random but what do you think the probability is or chance? Like flipping a coin and it landing on heads is 50% or 1/2. Again, he said its random.

I asked them if you are dealt a blackjack, what's the probability the first card is a ten or face card. The guy who said the dice prob was 1/6 said it was 4/13 for the BJ problem, because 4 of 13 cards are tens. The other dealer had some convoluted math and came up with an answer worse than Rob could come up with. The one who said the dice are 1/11, that there's a 1/2 chance your first card is a ten if you have a blackjack, because there are 2 combinations to get a BJ, either Ace+Ten or Ten+Ace. He was 2 for 2.

I asked a few other probability questions, riddles, etc. as did they. It became apparent the guy who said the dice probability is 1/11 actually knew how to do math, while the other two were a little slow, to say the least.

The fact you think dice dealers and floor people are considered "experts" is a bit telling.



I'd be careful about asking a group of math professors any question and accepting (sort of) the answer from just one. I had a computer science professor who gave us a homework assignment that was literally impossible in the language we were using. I don't remember the specifics now, but he wanted us to write a function which would use pass-by-reference which, done the way he wanted, was impossible (per the book and any expert or beginner). I asked for an example of code which would be sufficient, and the code he gave did not meet the criteria in the assignment (pass by reference). I ended up getting a 100% on the assignment, but only after many emails back and forth as well as getting the head of the department involved. The head of the department said something like, "This assignment was impossible. The language simply doesn't work that way."

During a dispute at the craps table I once made them call the gaming board agent on to the boat (in Illinois we originally had to have our casinos on big boats). After it became clear that he didn't have a clue and was just a typical government employee, I made a point to embarrass him by asking him to tell me what the proper payoff on a nine was. He was unable to do so.

I did used to take great pleasure in delaying the game for about 45 minutes over a minor amount of money. These casinos and their employees don't seem to understand that every roll, every spin, every deal is $$$ and that they should never let the game slow down. So they could argue with me for 45 minutes over a few dollars and it costs them hundreds.

[redietz]

Alan has already admitted that if the question is worded one way the answer is 1:11. Hence, the argument here is what is the wording of the question. Alan needs to show everyone the precise difference in wording that would yield 1:11 vs. 1:6 and explain why.

Arci, good to see you! I appear to have inherited your mantle as Rob's most beloved poster, only he wants me to put my driver's license online. That'll be the day. At least he believed you were you!

Anyway, arci and I disagree on this, as it is the responsibility of the writer to make clear the math of the answer. If the way a question is written leads a large number of reasonably educated readers to the wrong answer, then the writer is more at fault than the reader. Math may be about finding the correct answers, but writing is about making the correct answers understandable.

[quahaug]

Alan has already admitted that if the question is worded one way the answer is 1:11. Hence, the argument here is what is the wording of the question. Alan needs to show everyone the precise difference in wording that would yield 1:11 vs. 1:6 and explain why.

Arci, good to see you! I appear to have inherited your mantle as Rob's most beloved poster, only he wants me to put my driver's license online. That'll be the day. At least he believed you were you!

Anyway, arci and I disagree on this, as it is the responsibility of the writer to make clear the math of the answer. If the way a question is written leads a large number of reasonably educated readers to the wrong answer, then the writer is more at fault than the reader. Math may be about finding the correct answers, but writing is about making the correct answers understandable.

The question couldn't be clearer. You say it's poorly written. Please explain why that is. And please don't count Alan in as a reasonable person.

[redietz]

Alan has already admitted that if the question is worded one way the answer is 1:11. Hence, the argument here is what is the wording of the question. Alan needs to show everyone the precise difference in wording that would yield 1:11 vs. 1:6 and explain why.

Arci, good to see you! I appear to have inherited your mantle as Rob's most beloved poster, only he wants me to put my driver's license online. That'll be the day. At least he believed you were you!

Anyway, arci and I disagree on this, as it is the responsibility of the writer to make clear the math of the answer. If the way a question is written leads a large number of reasonably educated readers to the wrong answer, then the writer is more at fault than the reader. Math may be about finding the correct answers, but writing is about making the correct answers understandable.

The question couldn't be clearer. You say it's poorly written. Please explain why that is. And please don't count Alan in as a reasonable person.

First of all, your last sentence reminds me of everybody with a doctorate who thinks they can write. Just because something is clear TO YOU doesn't mean it's clear to a general population. Write a different variation of it that makes it clear and doesn't allow a good chunk of the readership to draw an erroneous conclusion. That's the writer's job. YOU are not the general population. As a writer, your job isn't (1) to be tricky, (2) to show how smart you are, or (3) to dichotomize the readership into those who get it and those who don't.

When this was first posted two years ago, one of the posters described the rules of writing concerning conditionals and tense uses. I am not going to go back and review it because (1) I'm not an expert on it and (2) I remember my ex-girlfriend (who is an editor at Penn State) describing the same rules. From what he said, however, there is a problem with it as presented that leaves open two interpretations. I leave it to those with doctorates in technical writing to have at it, because I was lost in the middle of the second sentence.

All I will contribute is this. Looking at the dice under the cup is, in reality, a sequential act. An actual human being's eyes process one die before the other by darting from area to area. One die will be processed before the other. This makes it a sequential act. An actual person is not, technically and actually speaking, drawing the conclusion about what is on which die simultaneously. It is sequential. Therefore, when a person sees a 2 under the first die, he has very possibly not yet processed the second die. If he immediately reports that he has seen a 2, that does not necessarily mean he has seen the second die. If he processes the first die and it is not a 2, then he processes the second die. Mickey's experiment does not technically fulfill the wordage of the trick question because he is reporting the sighting of the dice as if it's simultaneous, not sequential.

Math people assume the writing is easy to grasp because, what the hell, it's only writing. Do you see how arrogant and self-referential that is?

[regnis]

Arci, good to see you! I appear to have inherited your mantle as Rob's most beloved poster, only he wants me to put my driver's license online. That'll be the day. At least he believed you were you!

Anyway, arci and I disagree on this, as it is the responsibility of the writer to make clear the math of the answer. If the way a question is written leads a large number of reasonably educated readers to the wrong answer, then the writer is more at fault than the reader. Math may be about finding the correct answers, but writing is about making the correct answers understandable.

The question couldn't be clearer. You say it's poorly written. Please explain why that is. And please don't count Alan in as a reasonable person.

First of all, your last sentence reminds me of everybody with a doctorate who thinks they can write. Just because something is clear TO YOU doesn't mean it's clear to a general population. Write a different variation of it that makes it clear and doesn't allow a good chunk of the readership to draw an erroneous conclusion. That's the writer's job. YOU are not the general population. As a writer, your job isn't (1) to be tricky, (2) to show how smart you are, or (3) to dichotomize the readership into those who get it and those who don't.

When this was first posted two years ago, one of the posters described the rules of writing concerning conditionals and tense uses. I am not going to go back and review it because (1) I'm not an expert on it and (2) I remember my ex-girlfriend (who is an editor at Penn State) describing the same rules. From what he said, however, there is a problem with it as presented that leaves open two interpretations. I leave it to those with doctorates in technical writing to have at it, because I was lost in the middle of the second sentence.

All I will contribute is this. Looking at the dice under the cup is, in reality, a sequential act. An actual human being's eyes process one die before the other by darting from area to area. One die will be processed before the other. This makes it a sequential act. An actual person is not, technically and actually speaking, drawing the conclusion about what is on which die simultaneously. It is sequential. Therefore, when a person sees a 2 under the first die, he has very possibly not yet processed the second die. If he immediately reports that he has seen a 2, that does not necessarily mean he has seen the second die. If he processes the first die and it is not a 2, then he processes the second die. Mickey's experiment does not technically fulfill the wordage of the trick question because he is reporting the sighting of the dice as if it's simultaneous, not sequential.

Math people assume the writing is easy to grasp because, what the hell, it's only writing. Do you see how arrogant and self-referential that is?

I've got to step in here. There is no place on this Forum for such an intelligent and well thought posting.

[a2a3dseddie]

Alan has already admitted that if the question is worded one way the answer is 1:11. Hence, the argument here is what is the wording of the question. Alan needs to show everyone the precise difference in wording that would yield 1:11 vs. 1:6 and explain why.

Hey arcimede$ how have you been?

Here's the original question to which Alan says the answer is 1/6:

You have two 6-sided dice in a cup. You shake the dice, and slam the cup down onto the table, hiding the result. Your partner peeks under the cup, and tells you, truthfully, "At least one of the dice is a 2."
What is the probability that both dice are showing a 2?

And here's Alan's version of a question that he says would lead to a 1/11 answer:

For those of you who want the answer to be 1/11 here is your question:

Given two dice, with a 2 showing on at least one of the two dice, what are the odds that both dice will show 2-2?

The answer to this question is 1/11.

I am not smart enough to see the difference between these 2 scenarios.

[Count Room]

Redietz: I'm not going into a long dissertation over this, but it still doesn't matter at all whether your partner peeked under the cup and looked at the dice sequentially or not.

Yes, some of the time it would only be necessary for the partner to look at one die and other times it would be necessary for the partner to see both dice in order to say, "At least one of the dice is a 2."

The fact that the partner does not reveal to us that s/he had to look at one or both dice truly keeps the odds at 1/11.

If the partner explicitly reveals to us that he only looked at one die would the odds become 1/6. The whole point of this exercise is that he does NOT say this to us.

Moreover, if the partner DID tell you that it was necessary to look at both dice in order to say, "At least one of the dice is a 2", the odds of both dice being a 2 given that information would become:



This whole dice problem is a beautiful illustration of conditional probabilities based on limited information. It does not need to be worded any differently at all.

[regnis]

Alan--I guess you are going to have to change your line to "Alan simply can't get past a die having 12 sides".

[Alan Mendelson]

It's really amazing that intelligent people can't see the actual wording of the question and interpret it accordingly.
They are reading a question and then responding to a different question, and I can't believe that so many are doing it.

Look guys, would you all agree that if I threw two dice down a table and one die came to rest on a two and the second die was a spinner, that the odds of the spinner settling on a 2 were 1/6?

Do we all agree on that?

Well, that's the closest analogy to the original wording of the question. If you do not believe the "spinner analogy" is the closest to the original question, what is your analogy?

Are you telling me that the original question tells you to rotate both dice to see 11 possible results containing a 2 on at least one die? If so, how do you reach that conclusion?

(thank you regnis and redietz.)

[redietz]

Redietz: I'm not going into a long dissertation over this, but it still doesn't matter at all whether your partner peeked under the cup and looked at the dice sequentially or not.

Yes, some of the time it would only be necessary for the partner to look at one die and other times it would be necessary for the partner to see both dice in order to say, "At least one of the dice is a 2."

The fact that the partner does not reveal to us that s/he had to look at one or both dice truly keeps the odds at 1/11.

If the partner explicitly reveals to us that he only looked at one die would the odds become 1/6. The whole point of this exercise is that he does NOT say this to us.

Moreover, if the partner DID tell you that it was necessary to look at both dice in order to say, "At least one of the dice is a 2", the odds of both dice being a 2 given that information would become:



This whole dice problem is a beautiful illustration of conditional probabilities based on limited information. It does not need to be worded any differently at all.

I didn't say it mattered. What I did say is that mickey's demonstration starts from the presupposition that it does not matter, and since the physical processes for the two things are different, the demonstration presupposes the conclusion. The experiment does not recognize that the processes are different.

If you don't immediately see the difference in the two processes, you have a blind spot when it comes to running a proper experiment. It's also possible you have blind spots regarding word usage. Should I now say, "Gotcha? You're an idiot!"

If the writing leads a large chunk of readers to the wrong conclusion, then it's a bad piece of writing. This whole "gotcha" mentality is like some Saturday afternoon Mensa get-together. It serves no purpose. Just rewrite the damn thing so it's clear what's going on. But that wasn't the purpose. It was a word game to generate a gotcha. I saw this thing 20 or 25 years ago. I know the proper "answer." It's a stupid exercise in trickeration of which Don King would be proud.

There's probably a reason the disparate group of Mendelson, Singer, regnis, and Dietz all found fault with the exercise. Unless I miss my guess, these are probably the folks who have done the most writing for the public or for use in court.

[Count Room]

Look guys, would you all agree that if I threw two dice down a table and one die came to rest on a two and the second die was a spinner, that the odds of the spinner settling on a 2 were 1/6?

Do we all agree on that?

Well, that's the closest analogy to the original wording of the question. If you do not believe the "spinner analogy" is the closest to the original question, what is your analogy?

I have a question for you, Alan. If your partner is looking at a resting die with a "2" and the other one is a spinner, does he show you this or tell you this fact? Again, this situation would be exactly the same as if your partner telling you s/he only needed to look at one die to tell you "At least one of the dice is a 2". Yes, at that point the odds truly become 1/6.

It's not a good analogy for the original problem, though.

[Count Room]

I didn't say it mattered. What I did say is that mickey's demonstration starts from the presupposition that it does not matter, and since the physical processes for the two things are different, the demonstration presupposes the conclusion.

If you don't immediately see the difference in the two processes, you have a blind spot when it comes to running a proper experiment. It's also possible you have blind spots regarding word usage. Should I now say, "Gotcha? You're an idiot!"

If the writing leads a large chunk of readers to the wrong conclusion, then it's a bad piece of writing. This whole "gotcha" mentality is like some Saturday afternoon Mensa get-together. It serves no purpose. Just rewrite the damn thing so it's clear what's going on. But that wasn't the purpose. It was a word game to generate a gotcha.

There's probably a reason the disparate group of Mendelson, Singer, regnis, and Dietz all found fault with the exercise. Unless I miss my guess, these are probably the folks who have done the most writing for the public or for use in court.

Redietz: OK, fair enough. How would you re-word this problem to satiate the masses, yet keep the information limited enough to have the same answer as originally intended (1/11)?

[a2a3dseddie]

Look guys, would you all agree that if I threw two dice down a table and one die came to rest on a two and the second die was a spinner, that the odds of the spinner settling on a 2 were 1/6?

Do we all agree on that?

Are you telling me that the original question tells you to rotate both dice to see 11 possible results containing a 2 on at least one die? If so, how do you reach that conclusion?

This isn't close to the original wording of the question at all.

You do not see any of the 2 dice. Your partner does.

Your partner peeks under the cup, and tells you, truthfully, "At least one of the dice is a 2."

In your analogy, you KNOW for certain which of the dice is a 2.

Let's say we use coloured dice. One is red and one blue. If you see that the red die is 2, of course you can eliminate all of the combinations where the blue die is 2. That would be 1/6

But you do not know which die is 2, so you cannot eliminate any of the combinations.

Therefore any of the 11 possible combinations where "At least one of the dice is a 2." could be under that cup. Hence 1/11.

[redietz]

I didn't say it mattered. What I did say is that mickey's demonstration starts from the presupposition that it does not matter, and since the physical processes for the two things are different, the demonstration presupposes the conclusion.

If you don't immediately see the difference in the two processes, you have a blind spot when it comes to running a proper experiment. It's also possible you have blind spots regarding word usage. Should I now say, "Gotcha? You're an idiot!"

If the writing leads a large chunk of readers to the wrong conclusion, then it's a bad piece of writing. This whole "gotcha" mentality is like some Saturday afternoon Mensa get-together. It serves no purpose. Just rewrite the damn thing so it's clear what's going on. But that wasn't the purpose. It was a word game to generate a gotcha.

There's probably a reason the disparate group of Mendelson, Singer, regnis, and Dietz all found fault with the exercise. Unless I miss my guess, these are probably the folks who have done the most writing for the public or for use in court.

Redietz: OK, fair enough. How would you re-word this problem to satiate the masses, yet keep the information limited enough to have the same answer as originally intended (1/11)?

I have no idea, but you bring up an interesting question. Why make this a word game? Why not just a paragraph lecture on conditional probability so everyone learns something? The only reason for the dice example is to create a gotcha. Unless the dice example has some real world application of some kind, which I doubt.

I don't know why the information has to be limited or what reason there is to format the information into a word game. Cleverness isn't everyone's raison d'etre. Dr. Michael Starbird at Ut-Austin does probability lectures for the masses. I'd ask him.

[a2a3dseddie]

In this case the dealers have a better idea of the actual problem. And they are not using one die to have multiple values. In other words, they have a better grip on the reality of the question.

You "1/11 guys" still don't understand how you are misinterpreting simple English.

I guess when you take probability classes they forget to teach how to understand the English language.

I gave you the question that would have an answer of 1/11.

One die is a fixed parameter, the other is variable.

This is true... for the partner who peeks under the cup. We don't know which die is "the fixed parameter" so we must consider all possible combinations.

[RS__]

It's really amazing that intelligent people can't see the actual wording of the question and interpret it accordingly.
They are reading a question and then responding to a different question, and I can't believe that so many are doing it.

Look guys, would you all agree that if I threw two dice down a table and one die came to rest on a two and the second die was a spinner, that the odds of the spinner settling on a 2 were 1/6?

Do we all agree on that?

Well, that's the closest analogy to the original wording of the question. If you do not believe the "spinner analogy" is the closest to the original question, what is your analogy?

Are you telling me that the original question tells you to rotate both dice to see 11 possible results containing a 2 on at least one die? If so, how do you reach that conclusion?

(thank you regnis and redietz.)

And if I asked what's the probability of rolling a 12 with 2 dice, would you jump and scream saying, "What part of the question has you looking at both dice, looking at all 6 sides on each, to come to your '1/36' conclusion? Heresy! It's clearly 50/50 -- it either happens or it doesn't!"

NOTE: I actually wouldn't be surprised if you said that.