Question for Math/Gambling/Craps Experts

[redietz]

I can see one of the big issues here. Alan is trained as a journalist and writer. His job has always been to make things clear, to write and explain cleanly and with as little obfuscation as possible. I happen to also be trained as a journalist and writer. We aren't trying to look clever. Looking clever means, basically, that we've failed at our expertise.

The various WoV posters are trying to be clever. They have likely not held positions where clarity and clean writing are essential, and where purposeful confused wordsmithing (first time I've used that word myself) would get you fired. This whole enterprise, as I stated initially, is about bad writing creating confusion. If a description of events is confusing, that's on the writer, not the reader. That is a flaw of the writer, not the reader. Saying "Well, if you read it carefully enough, you can figure it out," is still a failure of the writer, not the reader.

One thing for sure, the pseudo-mensa posters are going to give "old Rob" a run for obnoxiousness ratings.

P.S. I have edited some Army event descriptions. The WoV people may have been the original authors of some of those. When people do not want you to figure out what really happened or what's really going on, this is how they write.

[Rob.Singer]

I especially liked how they were "forced" into putting up a video of Dan losing at live poker in 2009 just because he's an admin. here. And oh, how they must HATE the fact that wizard interviewed me, and found that the guy the pseudo-mensas (love that one red) claim not to be taken seriously by math geeks & statisticians, actually has more "math & statistics" education and related applied work experience than most of their proud array of computer nerds, actuaries, math teachers, and so on. Then for some reason they went after Scoblete even though he hasn't even chimed in. Methinks Shack and/or his foreign owners need to make refresher courses on T-O-L-E-R-A-N-C-E mandatory for all the floating egos they babysit.

[RS__]

Alan, OK, so we agree with the Wizard's Bet there are 10 ways to lose and 1 way to win....which is 1 in 11?

Please explain how this is any different than the original problem.

[Alan Mendelson]

Alan, OK, so we agree with the Wizard's Bet there are 10 ways to lose and 1 way to win....which is 1 in 11?

Please explain how this is any different than the original problem.

Are you really asking that?
I have a question: is the Wizard offering 8 to one or 8 for one?

And since each bet is a one roll bet why isn't he offering 30 to one like the casinos?

[RS__]

Are you really asking that?
I have a question: is the Wizard offering 8 to one or 8 for one?

And since each bet is a one roll bet why isn't he offering 30 to one like the casinos?

Yes, I really asked that.

I don't know if he's offering 8 to 1 or 8 for 1. I'm sure you could ask him.

I assume he's not offering 30:1 because....well....that's not what we're talking about.

[1in11]

Are you really asking that?
And since each bet is a one roll bet why isn't he offering 30 to one like the casinos?

Because his bet has 1 way to win, 10 ways to lose, and 25 ways to push.

2-2 on the hop has 1 way to win and 35 ways to lose.

[Alan Mendelson]

You can make any bet that doesn't necessarily match the question asked. In this case the bet does not match the question asked. But that is what this debate is all about, isn't it? I wonder how an English professor would interpret the question? We know how you "math guys" interpret it.

[Alan Mendelson]

I was being sarcastic when I asked why the Wiz isn't offering 30 to 1, because the bet isn't clear to begin with since we don't know if its 8 to 1 or 8 for 1. I am surprised that the difference slipped by the math guys over on the Wizard's forum.

But if the difference between 8 to 1 and 8 for 1 can slip by the math guys, I guess the phrasing of a question might also slip by.

What is encouraging is that a few on the Wizard's site do concede that if one die were set on 2, the odds would be 1/6 on the roll of a second die. By recognizing that, they should also acknowledge that the answer of 1/6 is not wrong based on the interpretation of the question.

What is becoming clear is while I have been accused of having a closed mind, it is the guys on Wizard's site who have their minds made up and have closed it to the idea that the question itself is flawed. And that's what I pointed out earlier in recounting the story about the flawed SAT question back in the 1960s.

[Rob.Singer]

Alan you know what's going on with these guys. They're frustrated that you made sense in your argument and in how they've now needed to change the problem and question around in order that it more closely simulate their version. And this can be readily confirmed by how insulting these geniuses who got it wrong from the start, now are. And those bets....they keep getting more and more further from the point. Oh how I wish those guys had the courage to face me at a machine.....

[Alan Mendelson]

Actually, the more I think about it, there are only TWO possible answers to the original question:

#1 The 1/6 answer because we know one die is already a 2.
#2 The other possible answer is 1/36 because the chance of rolling 2-2 is always 1/36

The answer of 1/11 is really a "reach." I will concede that it might be the way that mathematicians approach this type of problem, but if you were playing a game with two dice would you really consult an Excel spread sheet?

I guess in an ivory tower you would.

[jbjb]

#1 The 1/6 answer because we know one die is already a 2.
#2 The other possible answer is 1/36 because the chance of rolling 2-2 is always 1/36.

#3 1/11 when you eliminate the 25 other outcomes like 4-3, 3-4, etc without a 2.

[Alan Mendelson]

Be practical for a minute and step out of your ivory tower. The question is this:

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?

Would you really answer the question with this:

#3 1/11 when you eliminate the 25 other outcomes like 4-3, 3-4, etc without a 2.

Or would you say: the other die has six faces, so 1 in six is a 2. Or... would you say the chance of rolling two dice to be 2-2 is always 1/36 ??

[jbjb]

Your not looking at one die when you peek. You look at both. This is the confusing part of the whole question and can see where it's causing fits. Not that complicated. Hell, even when I first read it over there, 1/6 was the first thing I thought too. Took me about half an hour to realize that I was wrong. Also nobody changed my mind either. Again attempt this on your own and you'll see it work out.

[1in11]

Or would you say: the other die has six faces, so 1 in six is a 2. Or... would you say the chance of rolling two dice to be 2-2 is always 1/36 ??

Or would you say how many combinations of the dice satisfy the condition "at least one of the dice is a 2", and how many combinations of the dice satisfy the condition "both of the dice are a 2"?

Alan, with your understanding of the meaning of "At least one of the dice is a 2," can you tell us how many combinations of the dice can satisfy that condition?
Or is it somewhere else in the question that the wording is unclear?

[Alan Mendelson]

Your not looking at one die when you peek.

This is absolutely and totally wrong. We -- the respondents -- are not looking at anything. We are only told that "At least one of the dice is a 2."

That is the only information we have, and because we are told that, we can arrive at the answer that the remaining die is a 1/6 chance of being a 2.

[Alan Mendelson]

Or would you say how many combinations of the dice satisfy the condition "at least one of the dice is a 2", and how many combinations of the dice satisfy the condition "both of the dice are a 2"?

Alan, with your understanding of the meaning of "At least one of the dice is a 2," can you tell us how many combinations of the dice can satisfy that condition?
Or is it somewhere else in the question that the wording is unclear?

Let me take these statement by statement:

Statement #1 how many combinations of the dice satisfy the condition "at least one of the dice is a 2" There are two combinations. 2-2 and 2-X with X being any of the five faces on the second die that is not a 2.

Statement #2 how many combinations of the dice satisfy the condition "both of the dice are a 2"? this is easy, there is only one combination which is 2-2

Statement #3 with your understanding of the meaning of "At least one of the dice is a 2," can you tell us how many combinations of the dice can satisfy that condition? There are two combinations. Die #1 is a 2 and die #2 is any of the six numbers on that die. Or you can reverse this so that Die #1 is any of the six numbers on that die and Die #2 is the 2.

[1in11]

Statement #3 with your understanding of the meaning of "At least one of the dice is a 2," can you tell us how many combinations of the dice can satisfy that condition? There are two combinations. Die #1 is a 2 and die #2 is any of the six numbers on that die. Or you can reverse this so that Die #1 is any of the six numbers on that die and Die #2 is the 2.

Can you tell me out of the 36 ways to roll 2 dice, how many of those ways satisfy the condition "Die #1 is a 2 and die #2 is any of the six numbers on that die. Or you can reverse this so that Die #1 is any of the six numbers on that die and Die #2 is the 2"?

[jbjb]

The cup and person peeking is just an illusion to throw you off. There is no need for them. Surprisingly Frank Scoblete hasn't chimed in on this. Would love to hear his expansion.

[Alan Mendelson]

Can you tell me out of the 36 ways to roll 2 dice, how many of those ways satisfy the condition "Die #1 is a 2 and die #2 is any of the six numbers on that die. Or you can reverse this so that Die #1 is any of the six numbers on that die and Die #2 is the 2"?

All you are trying to do is get me to refer to your 1/11 answer. And I just can't. It's because the original question gives us the value of one die and to answer that original question you figure the second die.

Look guys, if the original question were different your Excel spreadsheets and your 1/11 answer might be appropriate. But I can't and won't use Excel spreadsheets when I know at least one die is a 2 and it's a matter of six possible choices on the second die.

[Alan Mendelson]

The cup and person peeking is just an illusion to throw you off. There is no need for them. Surprisingly Frank Scoblete hasn't chimed in on this. Would love to hear his expansion.

It is NOT an illusion. IT IS THE QUESTION. And you have to respond to the question. And that's the problem with you and the others. You are making up your own rules and your own conditions and you are not responding to the question. When you respond to the question the answer can only be 1/6. Give it a rest already.