The Wizard will bank this bet: 1/6 vs 1/11

[Alan Mendelson]

This is starting to get stupid. Now we are arguing about who said what first and what the original question is? Here is the original question, copied from the WOV forum:

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?

There is only ONE roll of the dice. For the Wizard and for miplet to rotate the die with a 2 to justify their 1/11 claim when there is only ONE roll of the dice and one of the dice rolled is showing a 2 is just WRONG.

[kewl]

There is only ONE roll of the dice.

WHEN do you determine a probability? Before the roll or after?

After the roll is made there is no probabilities, there is just an outcome. Don't you get it?

In your video you made a blatant mistake. You rolled the dice and THEN you start examine faces and determine odds. There is no such thing as 1 in 6 at that point.

Read the basics of probability and then comment things.

[Alan Mendelson]

Here we go. Kewl now admits that the 1/11 folks are ignoring the question because he says "when do you determine a probability? Before the roll or after?" And then he goes on to say after the roll is made there is no probabilities, there is just an outcome." EUREKA -- THEY HAVE FOUND IT!!

They have been making this error the entire time. They are talking probability to come up with the 1/11 answer and those of us who say it's 1/6 are looking at the actual problem.

Kewl: this question is not going to be answered by imagining the different combinations of two dice containing a 2. The question is answered by the conditions being presented: you have one die showing a two so what will it take to have 2-2?? That is 1/6 and that is determined by the conditions of the question.

[redietz]

Part of the trick is that in the version of the question referenced by Alan, you have a description of an event in present tense. The use of present tense lends itself to a possible interpretation that the event in question is just one of many such events. That, however, is not stated, so deciding that this is one event of many requires drawing an unmerited conclusion.

All we do know, based on this description, is that there was one event.

If the question had been put in past tense ("rolled the dice" and "peeked"), then it would be more likely to be interpreted by most readers (and editors) as a single event.

The bottom line is that if the author wanted to be clear, and intended to describe multiple throws of the dice, one would assume he would say exactly that. Instead, he does not, which leaves the verbiage open to multiple interpretations if you're trying to be tricky. Most people are not trying to be tricky, and editors do not like this kind of being tricky.

From the question as stated, we can infer there may have been or be more than one throw of the dice, but that's speculative. All we definitely know is that there was one throw.

[RS__]

You guys keep saying it's a trick question. I'm not sure why you think that.

[OnceDear]

[QUOTE=redietz;28167]From the question as stated, we can infer . . .[QUOTE]

Guys, Guys, Guys,

The thread has flown off course.

Please, let's stop all this bickering about some question from long ago. Look at the title of this thread. Look at post 1 and look at post 5.

A real wager has been offered where Alan believes the odds are 1/6 and where the Wizard (and I) would pay out at 1/9.

Doesn't that get anyone's interest? The amount you can stake is massive and by implication, you can wipe out the Wizard, and if you wish, you can wipe out my pension fund.

Not one taker on that bet. Really? I'm not counting Alan, because he would only bet Lunch and has not yet materialised that bet.

Alan only asks you to agree or disagree whether the bet is a good one. No need to mess around with arguments or insults.

From post 5...

Let me answer your questions specifically and I am sure this will be the understanding:

1. Two dice are in a cup or other device, shaken and in the cup placed on the table.
2. A witness will peek. If a 2 is shown the bet is on.
3. If a 2 is not shown, there is no betting.
4. In both cases, the cup will be removed and the dice can be viewed. This will prevent the original dice from showing 2-2 and the witness lying.
5. With one deuce the bet is on (#2) and if there is not a second bet the "player" will lose their bet.
6. With one deuce the bet is on (#2) and if there is a second deuce the "bank" will pay either 9-to-1 or 9-for-1 (the Wiz doesn't care.)

My own personal thought: I can't imagine why the Wizard agreed to this? There is a 1/6 chance that when one die shows a 2 that the other will also be a 2 yet he is willing to pay 9-for-1 or 9-to-1.

Is it possible he misread this bet the same way I suspect he misread the original question? Somebody wake me up from this (bad) dream.

Does this forum support polls? Maybe after all the debate, someone could create one with three options such as "No. This is a bad bet for the player, Yes. This is a good bet for the player, Yes.This is a good bet for the player and I've contacted Wiz or Oncedear to arrange taking it up for serious money.

[Alan Mendelson]

Let me return to the wager: I said no. And the reason why I said no is that I do not make bets against individuals. Yes, I play in casinos -- but my parents taught me not to make bets against individuals, friends, relatives, co-workers, etc. because they can lead to bad feelings.

I did, however,agree to bet the Wizard lunch of up to $50. I did try to meet the Wizard to have this bet a couple of weeks ago but I got into Vegas too late to hook up with Mike and I had to leave in the morning for a meeting with a client and then the drive back to LA. I am more than happy to have the meeting again and the lunch wager.

Now, there were some others who said they wanted to make more substantial bets with the Wizard, but they dropped out for whatever reason.

The bet I have with the Wizard calls for a limited number of dice rolls and frankly I don't expect to win because of the way the bet is structured -- but it doesn't matter I think it will be fun to have lunch with Mike.

But frankly the bet is a separate issue. What's more important is the truth about the actual question and the actual solution. You 1/11ers have corrupted the question and manipulated the information to come up with your answer. Sorry -- just gotta tell it like it is.

I asked everyone to do a video explaining your methodology and the videos PROVE your methodology corrupted the question. This should not have been treated as a question of probability -- but only as a simple math problem: You have one die showing a 2 was fact number one, and you have a second die with six sides which was fact number 2. You only had six sides to choose from -- and not eleven. As soon as you turned that die showing a 2 to expose five more faces you corrupted the question. Shame on you.

[Alan Mendelson]

You guys keep saying it's a trick question. I'm not sure why you think that.

It's not exactly a trick question. But the question was framed to mislead, and then the way the question was actually worded, left open all sorts of interpretations. Let's face it -- not only are we arguing over whether the answer is 1/11 or 1/6 but over on the WOV forum they're arguing over whether or not the "peeker" has seen one or both dice.

If you wanted a question about probability it should have been written as a question about probability. If you wanted a question about dice combinations, it should have been written as a question about dice combinations. And when you frame the question as it relates to the "two coin problem" it immediately raises the issue of how you are supposed to come up with the answer.

So, it's the confusing nature of how the question was written that is "tricky."

[Alan Mendelson]

About polls -- yes, if you start a new thread you can choose the poll option.

[RS__]

It's not exactly a trick question. But the question was framed to mislead, and then the way the question was actually worded, left open all sorts of interpretations. Let's face it -- not only are we arguing over whether the answer is 1/11 or 1/6 but over on the WOV forum they're arguing over whether or not the "peeker" has seen one or both dice.

Because you brought it up. ?

If you wanted a question about probability it should have been written as a question about probability. If you wanted a question about dice combinations, it should have been written as a question about dice combinations. And when you frame the question as it relates to the "two coin problem" it immediately raises the issue of how you are supposed to come up with the answer.

Aaaaaand...probability and the number of combinations are the same thing (well, they lead to the same answer).

You have yet to answer how the two-coin problem is significantly different than the 2-dice puzzle.

So, it's the confusing nature of how the question was written that is "tricky."

No. It's people who get the answer wrong then later on blame their wrong answer on "the question being tricky". You (and your rob-singer friends) got the answer wrong and are making an excuse.




We can find the answer to this question quite easily -- via simulation. However, the anti-math people tend to naysay simulations and their results.

Quick question (naysayers will likely get it wrong or refuse to answer) -- If I do a simulation (say 100 million rounds) of dice throws/tosses and gather a sufficient sample size, and one of the events in the simulation occurs 1 out of 11 times. Now on my own, not part of the simulation, I throw the dice once and they meet the standards in the simulation (ie: at least one die a deuce), what is the probability or chance that both dice are deuces?

[Alan Mendelson]

RS__ I didn't use the word "tricky." Redietz did. I was offering an explanation on how the question was problematic. There is no doubt the question is problematic. You are also problematic and I am tired of you and your ridiculous comments -- not to mention your cursing which left a very bad taste in my mouth and makes me not want to communicate with you. Go back to the WOV forum -- you fit better there.

[RS__]

I'm sorry. Did it taste salty?

[Rob.Singer]

I told you Alan, with these people you have to interpret their brain teasers exactly as they do. When you don't and you clearly explain why by exposing a geek-fault, the agitation sets in and the results are vulgarity & insults. They do that over there and the sensitive admins immediately suspend them. You also experienced what occurs when someone outside the gay math club brings up an important point about a posted problem that none of them thought of before you. Who'd of thought to solve this issue by using situational reality, when WoV wisdom demands you use probabilities & theory??

"It's not whether you made a 'good' bet; it's whether you win or lose"

[Alan Mendelson]

Who'd of thought to solve this issue by using situational reality,

I am sure that those of us who came up with 1/6 got that answer because we visualized two dice. The "probabilities crew" probably visualized that chart of 11 dice combinations. This is why I asked them to use real, physical dice because if they had (and didn't alter the conditions of the problem) they would have seen for themselves the answer was 1/6. But, lo and behold, they manipulated the dice just to fit their probability chart again.

To compound their corruption, first the Wizard and then one of the WOV visitors on this forum starts talking about the 36 dice combinations of which only one is 2-2 and they start using that for some evidence of whatever.

And they make up their own rules such as: we don't know which of the two dice is a 2 so let's figure the problem by switching the 2 from one die to another. And that's the only way they can come up with 1/11. Anyone who looks at two dice with one die showing a 2 knows there are only six combinations for that 2. But at the WOV they have their own rules, don't they?

Meanwhile over at the WOV they're still fighting among themselves over what the problem says and they're still quoting what's posted here.

[OnceDear]

You also experienced what occurs when someone outside the gay math club

I'm offended by your childish name calling.

[Rob.Singer]

Exactly right. They keep tossing in so many varying events of probabilities because when frustration takes over, obfuscation results. And that constant arguing among themselves now is "pure gold"....

The wiz should be shutting it down soon. It's becoming an embarrassment for him.

[Rob.Singer]

I'm offended by your childish name calling.

And I, even more so, by you spelling MATERIALIZED incorrectly. Please use the host country spelling.

[OnceDear]

I'll spell materialise and colour, etc. any way I damned well choose. I owe you no courtesy, Rob.

[OnceDear]

About polls -- yes, if you start a new thread you can choose the poll option.

I suggest you create that Poll. It would carry your authority and none of us 'Maths' people could bias it with 'overthinking' or 'trickiness'

[Alan Mendelson]

I suggest you create that Poll. It would carry your authority and none of us 'Maths' people could bias it with 'overthinking' or 'trickiness'

Why don't you write it up and PM me. My first concern is that the poll questions might not be clear. But let's give it a shot.