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

[OnceDear]

The peeker said one is a 2. The other one has 6 faces. Can we please drop this nonsense.

Try it. You can be peeker and tosser.
Remember now. Rob Singer is a supporter of Alan's, But even he says this... And even he asserts that this bet is a 1/11 proposition.

But, if as I suspect, we don't get to see which die has the original 2 until after the bet, then 9-1 is a punk bet because two 2's, after knowing half the outcome at that point, is an 11-1 event in this case.

[redietz]

I have three questions for both the 1/6 camp and the 1/11 camp. What percent of an audience of general readers do you think would arrive at 1/6 after reading the original question as written? Not after 50 posts and commentaries and coaching, but after reading the original question. What percent of a general audience do you think would arrive at 1/11 after reading the original question as written? Do you think that a jury of your peers in a US courtroom would vote that the 1/11ers have proved their case beyond a reasonable doubt?

This is not an equation. It is a piece of writing. This is all about the writing, not the reading.

[OneHitWonder]

Unfortunately I'm afraid that the experts in this field will fail to read English and will not correctly reason the question.

I'm not the least bit bit afraid. Here's that word least again, lol.

Those guys are sharks when it comes to semantics. With them, it's not a matter of agreeing with each other, whichever camp, so much as with the correct answer. And, they go at it until it is unanimously resolved however long it takes.

BTW, the correct answer is almost invariably more complex and complicated (to the remainder of us) then the wrong answers.

[OnceDear]

I have three questions for both the 1/6 camp and the 1/11 camp. What percent of an audience of general readers do you think would arrive at 1/6 after reading the original question as written? What percent of a general audience do you think would arrive at 1/11 after reading the original question as written? Do you think that a jury of your peers in a US courtroom would vote that the 1/11ers have proved their case beyond a reasonable doubt?

This is not an equation. It is a piece of writing. This is all about the writing, not the reading.

Not putting percentages to it. The original post was on a maths subforum of a gambling website. Of the readers there, there was a mix of opinions. However after an absolute wealth of explanation, only about three members on wov still believe the correct answer, after clarifying the peeking rules, would still assert 1/6. I pity a nation where Alan could sit on a jury. Even amongst his friends here he is not listening at all to any proofs or arguments.

[kewl]

Regnis they cannot drop their nonsense because they were not taught to think in real terms and only theoretical terms. Wizard proved this in his video when he rotated the die with a two. They cannot deal with the question in a real, physical world.

I believe you are quite wrong here.
The real problem for you is you think the people able to perceive 1/11 are deluded theorists and not "grounded" like yourself.
What the situation actually is, is that you are unable to see further than your nose and the people you're accusing in being theorists are just the ones who have been there where you are now long time ago and see no real benefit to go down to your level and explain things like to a child, because they can see it all from a higher perspective than you and see exactly what your thought process is.
They just see the things clearly and can shift through the levels as they like if they want. You can't.
I'm no theorists nor mathematician by far, but was able to understand "the grounds" of the problem.
Its a shame people like you would fire someone just for being up the level you are.

[Alan Mendelson]

I've read their arguments on the WOV forum over semantics and they get ridiculous making up their own definitions sometimes.

Had I been with the Wizard when he shot that video and he started to rotate that die with the two I would have stopped him right there.

[Alan Mendelson]

Kewl in the real physical world you cannot rotate that die showing a 2. Deal with it.

[kewl]

Please address my example of one die.

Again--cards are different because removal of a card leaves the other options. Removal of a die removes the other options.

You are not allowed to remove one die. You only know "at least one of the dice" is 2. That makes it possible for any die to be 2. If you go ahead and remove one die , you don't see the problem in full.
The example with the cards is EXACTLY the same as the original question.
You draw a card and the peeker tells you it is 2-x. Period.

[redietz]

Not putting percentages to it. The original post was on a maths subforum of a gambling website. Of the readers there, there was a mix of opinions. However after an absolute wealth of explanation, only about three members on wov still believe the correct answer, after clarifying the peeking rules, would still assert 1/6. I pity a nation where Alan could sit on a jury. Even amongst his friends here he is not listening at all to any proofs or arguments.

Put some percentages on it. Where the original post appeared is irrelevant. I could argue, after all, the other way -- that the fact it appeared on a math subforum means the readers there are lousy writers and don't know anything about effective clear writing.

So let's put those alleged IQs to work. What do you think the percentages are for a general audience arriving at 1/6? What are the percentages for arriving at 1/11?

The key element to this question, partly because it's a piece of writing and not an equation, is how and where it guides an audience. So where do you think it guides what percentage of a general audience?

[kewl]

Kewl in the real physical world you cannot rotate that die showing a 2. Deal with it.

You don't have to. The only thing you need to comprehend is the experiment begins with the throw of pair of dice. All consecutive probabilities stem from there.

Not with setting one die and now throwing a second die. Where do you guys get this from?
Try to deliver your logic while holding pair of dice before the throw. Not holding one die. If the question was what are the odds for a single die it would say so. it would read: Look, you have one die and the other is not of interest.

[regnis]

Any die is a 2--but one of them is, and it can't change its spots. Sheesh---the mysterious chameleon dice again. Where can I get me a pair of those.

That's why I tried to make it easy for you and I only used 1 die. You refuse to address my one die example.

[OneHitWonder]

What percent of an audience of general readers do you think would arrive at 1/6 after reading the original question as written?

Surprisingly, in my opinion, the ones who think about this the least (for whichever reasons) or the most will come to a 1/6 chance answer.

"At least one die is a 2" has more of a one-die and consecutive nature or flavor to it than does "one or the other die is a 2". If the first die of a specific roll under the requirement of "at least one die is a 2" is a 2, then the requirement has already been met. If it's not a 2, then ""one or the other die is a 2" would be the requirement required to justify looking at the second die.

As well, we could get into how restrictive the possible or's are. The unannounced, general case of no restrictions when the "peeker" just looks at the first die, or randomly chooses one of the dice to look at. The least restrictive case when the "peeker" looks at both, and announces the smaller or larger dice-number, and discloses his own variation. And, the most restrictive case when a dice-number is chosen in advance, and the "peeker" follows suit.

What percent of a general audience do you think would arrive at 1/11 after reading the original question as written?

If you rush to judgment as the Wizard did, or have a broader but still simpler notion of probability questions as seen or heard of before, then you are more likely to arrive at the 1/11 chance answer.

If you go online and look for other instances or form of this exercise, you'll see the same rush to judgement by the same sorts of persons. A lot of the math fellas forget the general case of 1/6 chance, and fail to specify their dice number from the outset with the 1/11 chance answer. I guess this is what Allen might be afraid of with the math guys; but I would point out the other things brought up here and there. Many of the internet experts don't take the time to exhaust every little thing brought up. Scientific specialists in the field who do the actual research and reporting of results in the journals do but tend to stay where they are.

With the 1/11-ers, it's that Mark Twain quote over and over again which I noted earlier. Makes the Wizard's forum so very boring after a while. Nobody is getting rich at blackjack; or having any fun bickering with other players and the casinos. Old news. Yet seemingly idiotic experts who sell useless gambling books and offer advice about online casinos try to dig up some other way, like Markov chains, to relate one random distribution to another, to exactly determine how one might go ahead by 300 units while flat betting. The rest is all canned stuff. Nobody with half a brain and a life is ever going to sit there at a blackjack table year after year to wait for any stretch of wins to amount to 300 units while flat betting. Secondly, no one is going to actually write down and reduce those specific Markov chain probabilities. The real experts care only that it can be done in the theory. The suckers off the streets want rationales they don't want to understand to convince themselves that they can keep losing ridiculously but still come out ahead.

Do you think that a jury of your peers in a US courtroom would vote that the 1/11ers have proved their case beyond a reasonable doubt?

Of course not. There are so many untraveled avenues even with the usual number of dead ends.

In my opinion, court procedure and administration is crazier than even poker. Math is a game of checkers. So, where do the gambling forums fit in?

I have noticed that gamblers are concerned with distinctly but simplistically defined notions of now, and past/future. So too, their forums. Everything has to be a quick and easy fix or "road to riches". Insults are poorly implied and inferred, and topped off with the mentality of "nuking" or parading offenders. Here, a bit of sensationalism with Alan, who is a well-known celebrity in the area.

Gambling can be a boring yet ever more addicting grind of a life, both mentally and physically. To have to come somewhere anonymously and spend also the remainder of one's time then talking about it is a whole new level. So many things to talk about in a more productive manner in the forums, even about gambling, yet so few are barely broached. So many PhD studies, yet no such PhD's on the gambling forums.

This is the only forum I've come across where no one seems to be locked into the gambling thing. And, few seem "to have something to prove".

This is not an equation. It is a piece of writing. This is all about the writing, not the reading.

formal logic
n
1. (Logic) Also called: symbolic logic the study of systems of deductive argument in which symbols are used to represent precisely defined categories of expressions. Compare philosophical logic
2. (Logic) a specific formal system that can be interpreted as representing a fragment of natural argument

http://www.thefreedictionary.com/formal+logic

[Zedd]

That's why I tried to make it easy for you and I only used 1 die. You refuse to address my one die example.

Okay…

I'm going to try to make this real easy AGAIN!!!

I roll one die. It is a 2.

What were the odds that it was going to be a 2----1 of 6.

What are the odds that it is a 2----100%.

It is all about understanding plain simple english.

Yes, 1/6 and 1/1 are the correct answers to those questions. Now try this one…

I roll two dice until at least one of them is a 2.

What were the odds that it was going to be 2-2?
What are the odds that it is 2-2?

It is all about understanding plain simple conditional probability (and knowing English helps as well).

[regnis]

This is not the original question that started this whole mess. If you can't see this there is no use talking any further.

The original question referred to one roll where a 2 was showing on 1 die. It made no mention of numerous rolls being made until there was a 2.

[Alan Mendelson]

I roll two dice until at least one of them is a 2.

What were the odds that it was going to be 2-2?
What are the odds that it is 2-2?

to answer your first question: 1/36
to answer your second question: 1/6

[Zedd]

This is not the original question that started this whole mess. If you can't see this there is no use talking any further.

The original question referred to one roll where a 2 was showing on 1 die. It made no mention of numerous rolls being made until there was a 2.

Read the very first post on this thread. It was agreed that the dice are rolled until there were a 2.

to answer your first question: 1/36

Correct

to answer your second question: 1/6

Wrong

[Alan Mendelson]

Actually, it's not wrong. It's the same thing we've been arguing about. One die is known to be a two, and the question is what is showing on the six sides of the second die.

[Zedd]

Actually, it's not wrong. It's the same thing we've been arguing about. One die is known to be a two, and the question is what is showing on the six sides of the second die.

Indeed, it is the same thing we’ve been arguing about (unlike the questions that regnis proposed).

So regnis (and others)…can you answer it?

I roll two dice until at least one of them is a 2.

What were the odds that it was going to be 2-2?
What are the odds that it is 2-2?

[regnis]

I am only interested at this point in Redietz' question about the odds after Arci looks down the waitress' dress (and I don't even know if that was part of this thread anymore). The rest of this discussion has been exhausted.

[kewl]

Any die is a 2--but one of them is, and it can't change its spots. Sheesh---the mysterious chameleon dice again. Where can I get me a pair of those.

That's why I tried to make it easy for you and I only used 1 die. You refuse to address my one die example.

I did address it, I believe.
You roll one die - the odds of it to stop on 2 is 1/6. When it stops at 2 it is a 2 for eternity.

Now, add another die. Same thing - the odds of it to stop on 2 is 1/6. When it stops at 2 it is a 2 for eternity.

Now, what is the probability (see, we have combined probability now) of pair of dice to come 2-x?
And what is the probability to come 2-2?

The original question referred to one roll where a 2 was showing on 1 die. It made no mention of numerous rolls being made until there was a 2.

If you perceive this as if a single roll is made and it happens to be 2-x, then the answer would be 1/6. But that's not the case. The case is it has to be a 2-x.
Because if the roll happens to be a 6-4 for example, there wouldn't be any question to be asked and no answer. This was cleared long ago for the purpose of the old discussion and here on the first page and in many,many answers on WoV and here as well.