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

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Originally Posted by RS__

I would just love to know -- why aren't any of the simulations giving us an answer around 1/6?

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In engineering terms, computer simulation is the final and least resource intensive aspect of any project. After all of the manual research and set up.

A computer can do only what it's instructed to do. Any biases carry over. Simulation is the easy part.

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Originally Posted by RS__

The Wizard wrote a simulation in C++. I did one in Excel as well as PHP. Others have written simulations in Excel and other languages (not that Excel is a language).

All of the simulations are giving the same answer: Approximately 1/11 or 0.090909.

I would just love to know -- why aren't any of the simulations giving us an answer around 1/6?

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Maybe it's because you aren't asking the correct question?

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Originally Posted by Alan Mendelson

If we are talking about a throw of a pair of dice then the answer to the question is 1/36.

If one of the two dice is known to be a two, then it is the "second die" and that is 1/6.

Your answer of 1/11 still does not apply to this question.



Yes it does, because if a 2 shows up on one die you can't change the value of that die to fit your 1/11 answer. With a 2 on one die, only 6 faces remain on the second die.



And that's your problem -- it doesn't apply to the condition of the original question.

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Please, stop trolling me already :)

If you decide to actually read and think, then by all means share your thoughts. Otherwise i don't really see any point for you to post in this thread - disregarding all simulations, examples and thoughts which don't suit you and then out of the blue post some nonsense is not the way adults communicate.

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Originally Posted by kewl

"What is the probability of a fair throw of two standard dice showing 2-2 given that at least one of the dice shows 2?".

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The problem with the 1/11 answer is the "at least one of the dice shows 2", which equates to "one or more show a 2". The or part of this.

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Originally Posted by kewl

Simple enough, and there is no ambiguity about any human interference.

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But still this, if you want to define a way in which 1/11 and 1/6 say the same thing. The truly interesting and joining part of this with the two envelopes problem, where one might similarly ask about how it's right answer and wrong answer can be the same.

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Originally Posted by kewl

What the 1/6 supporters fail is - they believe one 2 showing makes it equal to "we have one certain die as a 2 and are now asking whats the odds on the second die to be 2"

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Certainly not what I've professed. If the first die looked at is not a 2, then do not have the one or more 2's. Remove those possibilities.

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Originally Posted by OneHitWonder

Certainly not what I've professed. If the first die looked at is not a 2, then do not have the one or more 2's. Remove those possibilities.

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Don't understand what the hell are you talking about.

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Originally Posted by kewl

Please, stop trolling me already :)

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Perhaps, he should ban himself?:)

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Originally Posted by kewl

Don't understand what the hell are you talking about.

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And me too?

At least one of us is confused. Guess who.

Allow me to ask a simple question: why does it matter which die shows a 2 in a two dice problem?

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Originally Posted by Alan Mendelson

Allow me to ask a simple question: why does it matter which die shows a 2 in a two dice problem?

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It doesn't. What matters is there are certain(real, physical) probabilities either one shows 2. In the same throw.

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Originally Posted by OneHitWonder

Perhaps, he should ban himself?:)

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Perhaps he should at least try and listen to the opposite side. And not only himself.

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Originally Posted by Alan Mendelson

Allow me to ask a simple question: why does it matter which die shows a 2 in a two dice problem?

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1/6 is about a specific roll; 1/11 is about the overall sets (or sums, and's of column and row) of rolls given the simultaneously possible forms of one 2 and two 2's. A specific roll is a question of and between two dice only; and looked at or rolled consecutively.

The or of this question focuses on - and makes sense with - the specific roll only.

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Originally Posted by OneHitWonder

1/6 is about a specific roll; 1/11 is about the overall sets (or sums, and's) of rolls given the simultaneously possible forms of one 2 and two 2's. A specific roll is a question of and between two dice only; and looked at or rolled consecutively.

The or of this question focuses on - and makes sense with - the specific roll only.

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Wrong.
Are you saying that 1/6 probability for a single die to show, for example, 6 is somehow different if we are talking single roll or many rolls?

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Originally Posted by OneHitWonder

There are two types of or: inclusive; and exclusive... this isn't an inclusive-or problem.

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Dead wrong! This most certainly is an inclusive-or problem. (Your mistake, buddy.)

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Originally Posted by kewl

Are you saying that 1/6 probability for a single die to show, for example, 6 is somehow different if we are talking single roll or many rolls?

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No. Only that asking 'or' of two dice isn't the same as summing the row and column of one-2 rolls with the one roll of 2-2. To get the 1/11, you must add the row and column with the one roll of 2-2 (and invert). Addition takes place, not the pick and choose of 'or'.

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Originally Posted by kewl

It doesn't. What matters is there are certain(real, physical) probabilities either one shows 2. In the same throw.

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Maybe. But not in this question.

In this question it doesn't matter which die shows a 2 or even if both dice show 2. The answer is always 1/6 faces on one die.

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Originally Posted by indignant99

Dead wrong! This most certainly is an inclusive-or problem. (Your mistake, buddy.)

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Why do you insist on heavy-handed responses w/o any attempt at correction; let alone clarification of your own stance if any???

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Originally Posted by Alan Mendelson

Maybe. But not in this question.

In this question it doesn't matter which die shows a 2 or even if both dice show 2. The answer is always 1/6 faces on one die.

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Read the question one more time.
It is 1/6 on one die, yes. But what this has to do with the question?
You throw two dice.

Now we have the "geniuses" arguing with each other. :) Theories flying all over the place.

Yeah, who cares. Let's just go win money!!

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Originally Posted by Rob.Singer

Now we have the "geniuses" arguing with each other. :) Theories flying all over the place.

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If you think this is bad, read the blackjack forums!

You throw two dice. There are eleven ways they can land as 2-x.

Why would you even consider one of the dice to determine your probability?
Don't you see there is so many ways you can arrive to 2-x, that your 1 face out of six is no longer relevant? Don't you see that when the blue die is 2, there are 6 ways the red die can land and vice versa? Don't you see that these possibilities are intrinsic to every single throw?