It was two years ago today...

[Alan Mendelson]

Eddy... you keep on bringing up Rob's comments that favored the answer of 1/11. He explained that, as I have. Yes, 1/11 is an appropriate answer until you look at the specifics of the question we are considering. Rob has recognized the fine point of the question which is something you still can't do. Regnis has also recognized this fine point. Redietz has also recognized this fine point. This is why the answer is 1/6.

[mickeycrimm]

the only conditional fact is that one die is identified as a 2. that changes the entire problem so there is one answer: 1/6

Which die is showing the 2?

[mickeycrimm]

Eddy... you keep on bringing up Rob's comments that favored the answer of 1/11. He explained that, as I have. Yes, 1/11 is an appropriate answer until you look at the specifics of the question we are considering. Rob has recognized the fine point of the question which is something you still can't do. Regnis has also recognized this fine point. Redietz has also recognized this fine point. This is why the answer is 1/6.

Which die is showing the 2?

[Alan Mendelson]

Which die is showing the 2?

I've been telling you, regnis has been telling you.... it doesn't matter. You won't accept that. Now, why don't you tell us why it does matter? Please be specific. Please refer to two real physical dice. In fact, using two real physical dice please carefully explain step by step why it matters which of the two dice is identified as a 2?

All of you who believe the answer is 1/11... please explain why it matters which of the two dice is showing a two when we know at least one of two dice is showing a 2?

[mickeycrimm]

Which die is showing the 2?

I've been telling you, regnis has been telling you.... it doesn't matter. You won't accept that. Now, why don't you tell us why it does matter? Please be specific. Please refer to two real physical dice. In fact, using two real physical dice please carefully explain step by step why it matters which of the two dice is identified as a 2?

All of you who believe the answer is 1/11... please explain why it matters which of the two dice is showing a two when we know at least one of two dice is showing a 2?

It has been explained to you over and over again in this thread and you still don't get it. What will one more explanation do for you?

[a2a3dseddie]

Eddy... you keep on bringing up Rob's comments that favored the answer of 1/11. He explained that, as I have. Yes, 1/11 is an appropriate answer until you look at the specifics of the question we are considering. Rob has recognized the fine point of the question which is something you still can't do. Regnis has also recognized this fine point. Redietz has also recognized this fine point. This is why the answer is 1/6.

As long as one of the dice is a 2 the 1/6 answer applies. It doesn't matter which or even if both show 2. And that is the same thing you OnceDear said you would unconditionally agree to. Saying that at least one die shows a 2 and setting aside one die as a two means the same thing in the language I speak.

I understand how you get 1/6. I've also read most of these monster threads where people have explained it much better than I have.

Throughout the course of these threads, I can see where you originally thought the bets proposed by the people at the Wizard's site were good bets.

I also see where you realised it wasn't.

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?

When you mimic this question exactly as written your 1/6 answer just doesn't hold up. You realise that or you wouldn't have warned coach belly against it twice in this thread.

It DOES hold up if you re-roll the second die as you've suggested. It does if you just fix one specific die as a 2 and roll a second die. I feel this changes the parameters of the original question, but I see you don't.

Which die is showing the 2?

I've been telling you, regnis has been telling you.... it doesn't matter. You won't accept that. Now, why don't you tell us why it does matter? Please be specific. Please refer to two real physical dice. In fact, using two real physical dice please carefully explain step by step why it matters which of the two dice is identified as a 2?

All of you who believe the answer is 1/11... please explain why it matters which of the two dice is showing a two when we know at least one of two dice is showing a 2?

Do we agree that in the question, that both dice are rolled together, and there is no mention of re-rolling any die? Also, if want to "set aside" 1 die after they've BOTH been rolled that's fine. Believe it or not, that actually doesn't make a difference if you don't re-roll any dice.

You understand how there are 11 possible combinations of two dice where at least one of them is a 2. When you "fix" one die to always stay on a 2 leaving the only variable the other die, of course the chances of that die landing on 2 is 1/6. By fixing one die to stay on 2, you've eliminated 5 of the 11 combinations that could appear. That's how it gets narrowed down to 1/6.

But the dice are rolled together in the cup!

In English, the statement "at least one of the dice is a 2" means that either Die A or Die B is a 2 or Both Die A and Die B are showing a 2.

So would you agree that either Die A or Die B or BOTH could be 2 under the cup?

If you agree, that's 11 possibilities that could be under the cup isn't it?

[arcimede$]

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?

This is why you look so foolish, Alan. Nothing in the question identifies the value of either die. Only someone who could write the absolute nonsense you just wrote above would think that it does.

Nothing identifies the value of either die, Arc? Are you insane or just senile?

Alan, assume one die is red and the other green. After the toss and verification that at least one die is a 2, tell us the value of the red die.

Notice how Alan refused to answer this question. Absolute proof he knows he is wrong.

[Alan Mendelson]

I hear you loud and clear: you are saying it has to be 1/11 because you don't know which of the two dice is showing a 2.

I am asking you to explain why it matters which of the two dice is a 2?

You haven't answered my question.

I've told, regnis has told you, Rob has told you that:

if the green die is the 2, the red die is 1/6
if the red die is the 2, the green die is 1/6

if the left die is the 2, the right die is 1/6
if the right die is the 2, the left die is 1/6

For us it makes no difference.

Why do you say it makes a difference?

Please explain and describe it so that when I have two dice in front of me, I will see why it matters.

Again, please explain and describe it so that when I have two dice in front of me, I will see why it matters.

[Alan Mendelson]

Arc asks: "Alan, assume one die is red and the other green. After the toss and verification that at least one die is a 2, tell us the value of the red die.which die is the 2?"

Arc, if the red die is the 2, the green die is 1/6. If the green die is the 2, the red die is 1/6.

That's the answer to your question.

[Alan Mendelson]

eddie I warned Coach against the bet, because the bet is not the same as the question in the two dice problem. I can understand the difference, you cannot. You have a reading comprehension problem. I'm sorry, but some of your synapses are not connected.

[a2a3dseddie]

I hear you loud and clear: you are saying it has to be 1/11 because you don't know which of the two dice is showing a 2.

I am asking you to explain why it matters which of the two dice is a 2?

You haven't answered my question.

I've told, regnis has told you, Rob has told you that:

if the green die is the 2, the red die is 1/6
if the red die is the 2, the green die is 1/6

if the left die is the 2, the right die is 1/6
if the right die is the 2, the left die is 1/6

For us it makes no difference.

Why do you say it makes a difference?

Please explain and describe it so that when I have two dice in front of me, I will see why it matters.

Again, please explain and describe it so that when I have two dice in front of me, I will see why it matters.

When you fix the green die as a 2, the red die is 1/6. I agree.
When you fix the red die as a 2, the green die is 1/6. I agree.

Because either die (or both) could start out as the 2 (since you are rolling them at the same time and only counting rolls that contain at least one 2) any of the 11 two dice combinations that contain at least one 2 could be under the cup.

[mickeycrimm]

I hear you loud and clear: you are saying it has to be 1/11 because you don't know which of the two dice is showing a 2.

I am asking you to explain why it matters which of the two dice is a 2?

You haven't answered my question.

I've told, regnis has told you, Rob has told you that:

if the green die is the 2, the red die is 1/6
if the red die is the 2, the green die is 1/6

if the left die is the 2, the right die is 1/6
if the right die is the 2, the left die is 1/6

For us it makes no difference.

Why do you say it makes a difference?

Please explain and describe it so that when I have two dice in front of me, I will see why it matters.

Again, please explain and describe it so that when I have two dice in front of me, I will see why it matters.

Combinations don't disappear. They can only be eliminated from possibility. If all you know is one die is a two then the answer is 1 in 11. If you know the red die is the 2 then you can eliminate five combinations from possibility. If you know that the green die is a 2 then you can eliminate five combinations from possibility.

I've told you that.
Eddie has told you that.
RS has told you that.
Count Room has told you that.
Dan Druff has told you that.
Arci has told you that.
Quahung has told you that.

[Alan Mendelson]

Unfortunately when I look at two dice in front of me, and one die is a 2, the second die only has six possible combinations.
When the peeker truthfully tells me that at least one die is a two, it is the same thing as me seeing one die is a two and still the second die only has six possible combinations.

Whenever I know one die is a two, I know that the second die has a one out of six chance to show 2-2 on both dice.

You still have not told me, shown me, or explained to me, why it matters which die is a 2.

Frankly you can't.

I will say it again: you can't.

You guys have a reading comprehension problem. You are missing the point that one of two dice has settled on a 2.

Yes there are 11 combinations showing at least one 2 on dice. But as soon as you tell me that one die is indeed showing a 2, the chance for 2-2 becomes 1/6.

You are missing this step.

[a2a3dseddie]

eddie I warned Coach against the bet, because the bet is not the same as the question in the two dice problem. I can understand the difference, you cannot. You have a reading comprehension problem. I'm sorry, but some of your synapses are not connected.

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?

This is a new bet and quite frankly I like it.

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 deuce 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.)

How does this bet you posted not conform to the original question? I guess I do have a reading comprehension problem.

Please explain why they aren't the same.

[Alan Mendelson]

When you fix the green die as a 2, the red die is 1/6. I agree.
When you fix the red die as a 2, the green die is 1/6. I agree.

Because either die (or both) could start out as the 2 (since you are rolling them at the same time and only counting rolls that contain at least one 2) any of the 11 two dice combinations that contain at least one 2 could be under the cup.

You just contradicted yourself. Exactly what I expected.

Now, think again what you wrote and this time remove the word "fix" and instead use the phrase "when the green die settles on a 2..."

You see eddie, this is a two dice problem, and if the peeker tells you at least one die is a 2 then either one of the two sentences is correct.
In fact, if both dice are showing a 2, either one of the two sentences is still correct because you are still considering one die.

It makes no difference which die is the 2 when there are only 2 dice in the problem.

Try to grasp this concept. Apparently it is very difficult for you.

[Alan Mendelson]

Eddie I know that the "bet question" is not the same as the question about looking at the second die. If you can't see the difference you have a problem with the English language.

I said I liked the bet because it was close to the question but it was not the question.

I'll say it again, I like the bet because it was close to the question but it was not the question.

The question about the peeker and two dice and at least one die shows a 2 is very specific. Very specific. I'll say it again: it is very specific. I am really sorry that you don't understand this.

[a2a3dseddie]

Eddie I know that the "bet question" is not the same as the question about looking at the second die. If you can't see the difference you have a problem with the English language.

I said I liked the bet because it was close to the question but it was not the question.

I'll say it again, I like the bet because it was close to the question but it was not the question.

The question about the peeker and two dice and at least one die shows a 2 is very specific. Very specific. I'll say it again: it is very specific. I am really sorry that you don't understand this.

I'm sorry too Alan, could you please explain it to me? How does that bet you posted not match the original question? I missed where it specified which die was the 2.

[redietz]

Let me just say this. If people don't come to the proper conclusion from an equation, the assumption is that the people "reading" the equation are wrong. If these same people come to a wrong conclusion from a verbal summary, the fault does not necessarily or even most likely lie with the readers, but with the writer. The writer has a responsibility to be clear, just as the "writer" of an equation has a responsibility to use a left-to-right format and not something right to left (that's a salute to Alan in case he reads Hebrew).

The responsibility to guide lies with the writer. If the readers are of average or above intelligence, and their conclusions are generally wrong vis-a-vis the material, the writer has failed.

[jbjb]

The bet and the puzzle are EXACTLY the same. Two dice will be rolled. If AT LEAST ONE DIE is a 2, the player will be paid 8 to 1 if BOTH DICE are a 2. If only one 2 shows, the player pays 1 to 1. Any other result is a push.

[Alan Mendelson]

The bet and the puzzle are EXACTLY the same. Two dice will be rolled. If AT LEAST ONE DIE is a 2, the player will be paid 8 to 1 if BOTH DICE are a 2. If only one 2 shows, the player pays 1 to 1. Any other result is a push.

Please explain your piles of spades and hearts. Still waiting.