Question for your Christmas Dinner Guests

[Alan Mendelson]

If you listened to what Mike said in his video he said what I said. There are 11 combinations of two dice showing 2s.

But why are you considering two dice? This is something no one in the 1/11 camp has explained.

There is no reason to consider two dice.

Some of you said you consider two dice because you don't know which die the peeker has seen to truthfully tell you that at least one die is a two. The fact is, it doesn't matter which of two dice is showing a 2 in a two dice problem.

If you know that there is a two on one die then it's simple: one of six sides on the other die will give you another two.

Mike admits to double counting. Why double count?

If I'm at a craps table and one die lands on a two and the second die is spinning the chance for another two is 1/6 and not one out of eleven. If I'm on the phone and talking to you from the craps table and I tell you that one die landed on the two and the second die is spinning, are you going to tell me the chance of another two is 1/11?

[coach belly]

There is no reason to consider two dice.

What is the significance of the peeking?

For the purposes of the bet...can't the dice be rolled so that the results are visible to both players?

Any roll showing no 2s is a push and any roll showing exactly one 2 pays 1-1.

Then, how much should a 2-2 pay?...the true odds so that neither player has an edge.

Does one player peeking and hiding the results from the other change the odds somehow?

[Alan Mendelson]

Coach you need to read the original post on the WOV site. It was a post by one poster who never posted again. I think the post with the setup and the spoiler were meant to cause confusion.

[tableplay]

But why are you considering two dice? This is something no one in the 1/11 camp has explained.

There is no reason to consider two dice.

How will you know that one dice is showing the same number as the other, if you are only considering one die ? For there to be a comparison, there must be two entities. Comparisons, by definition, must occur between two or more entities. So there is a reason to consider two dice - so that a comparison can take place.

[Alan Mendelson]

But why are you considering two dice? This is something no one in the 1/11 camp has explained.

There is no reason to consider two dice.

How will you know that one dice is showing the same number as the other, if you are only considering one die ? For there to be a comparison, there must be two entities. Comparisons, by definition, must occur between two or more entities. So there is a reason to consider two dice - so that a comparison can take place.

There is no need for a comparison. Thats not the question. The question simply asks if at least one die is a two what's the probability that the other die is also a two?

Why do you insist on making this so complicated?

It's a simple question that turned into a Rube Goldberg answer.

[a2a3dseddie]

The question simply asks if at least one die is a two what's the probability that the other die is also a two?

NOPE.

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?


Why do you keep changing the question?

[a2a3dseddie]

I'm still waiting for someone to act out the problem. If you act out the problem you will see its a one die problem AND you won't be able to rotate a die like the Wizard did.

Really, where is it allowed to change the face of a die?

The original question is simply the same as rolling two dice with one landing on the 2 and the second die spinning.

So, rotating the die to demonstrate that any of the 11 combinations could be under the cup is not okay, but having the second die defy physics and continue to spin under the cup after it is slammed down on the table WHERE THE RESULT is hidden, IS okay?

[Alan Mendelson]

No Eddie. It's just a way to illustrate the problem/question.

And if you read what I wrote it's similar to a spinner on a craps table -- not under a cup.

[Alan Mendelson]

The question simply asks if at least one die is a two what's the probability that the other die is also a two?

NOPE.

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?


Why do you keep changing the question?

The answer is still 1/6. Why do you insist on rotating a die after it has landed on a 2 to prove your 1/11 answer?

I'm still waiting for someone to explain why you rotate that die?

[a2a3dseddie]

But why are you considering two dice? This is something no one in the 1/11 camp has explained.
There is no reason to consider two dice.

Why? Because that is the only information the non-peeker is given:

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


BEFORE he is asked:

What is the probability that both dice are showing a 2?


And using what YOU YOURSELF have said:

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.

The non-peeker HAS to consider all 3 scenarios.

[a2a3dseddie]

Alan, we are in agreement that there are 11 possible combinations of 2 dice where at least one of the dice is a 2. Can't any one of those 11 be under that cup when the peeker says at least one of them is a 2?

The odds of winning the Powerball lottery are 1 in 292,201,338. Do you need to see all the combinations before you'll believe it?

[Alan Mendelson]

But that doesn't change the answer. When you know one of two dice is a two it's a 1/6 chance that both dice have a two. That's all. There is no need to go thru the mental gymnastics of considering the 11 faces on two dice with at least one two showing.

You guys have taken a solution to a probability question concerning all of the faces (11) contains a two and applied it (incorrectly) to a question about one die.

[Alan Mendelson]

Alan, we are in agreement that there are 11 possible combinations of 2 dice where at least one of the dice is a 2. Can't any one of those 11 be under that cup when the peeker says at least one of them is a 2?

The odds of winning the Powerball lottery are 1 in 292,201,338. Do you need to see all the combinations before you'll believe it?

I think there are 36 different combinations that could be under the cup. Why stop at 11?

But the next question is do you consider 5-4 to be different from 4-5?

But this next episode of mental gymnastics still doesn't answer this simple, one die question.

[a2a3dseddie]

But why are you considering two dice? This is something no one in the 1/11 camp has explained.
There is no reason to consider two dice.

Why? Because that is the only information the non-peeker is given:

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


BEFORE he is asked:

What is the probability that both dice are showing a 2?


And using what YOU YOURSELF have said:

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.

The non-peeker HAS to consider all 3 scenarios.

No response to this Alan?

[Alan Mendelson]

Why? Because that is the only information the non-peeker is given:

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


BEFORE he is asked:

What is the probability that both dice are showing a 2?


And using what YOU YOURSELF have said:

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.

The non-peeker HAS to consider all 3 scenarios.

No response to this Alan?

There is no need to know all three combinations: 2-X, X-2, 2-2. That info doesn't affect the question or its answer.

If you have 2-X then X=1/6
If you have X-2 then X=1/6
If you have 2-2 showing under the cup then the answer for either die is 1/6.

[a2a3dseddie]

I think there are 36 different combinations that could be under the cup. Why stop at 11?

How could your partner peek under the cup, and tell you, truthfully, "At least one of the dice is a 2." then?

Are you changing the problem again?

[a2a3dseddie]

If you have 2-2 showing under the cup then the answer for either die is 1/6.

Does anyone here know what Alan means?

[a2a3dseddie]

Alan, you've said numerous times that "you can't rotate the die under the cup".

How can you even show 1/6 if you can't rotate any of the dice?

[Alan Mendelson]

If you have 2-2 showing under the cup then the answer for either die is 1/6.

Does anyone here know what Alan means?

Let me make this clear: if the peeker tells you that at least one die is a two then even if the second die is in fact a two the 1/6 answer still applies because that die has six faces.

[Alan Mendelson]

Alan, you've said numerous times that "you can't rotate the die under the cup".

How can you even show 1/6 if you can't rotate any of the dice?

Now you're getting desperate. But since I won't stoop as low as you I will give you an answer. You don't have to rotate the second die to know it has six faces. These are standard dice.

Try something else.