Why does he need to send anything to a third party? What does it matter if he changes things midstream? Once your interaction is complete you either have a unique, determinitistic solution that depends ONLY on the questions asked, who they are asked of, and the answers given, or you don't. Hymie is free to change whatever he wants, as long as his final choice of assignments are consistent with the answers provided to the questions asked.

In essence, he starts out with every possible path through the decision tree available to him and, at each step he gets to choose his answers so that so as to prune as few of those paths as possible (or, more to the point, to keep paths that give him the most flexibility).

At the end of the day, as long as he can show that there is at least one assignment of roads and roles that results in you getting the answers he provided to the questions you asked while also resulting in you picking the wrong road, then he has successfully demonstrated that your algorithm is flawed.

Note that the reverse is NOT the case -- if Hymie can't come up with an assignment that makes your solution incorrect for the questions asked and answers provided, that does NOT prove that your algorithm is correct, only that it is capable, at least under some circumstances, of providing a correct result. But your algorithm is a solution to the problem only if it provides a correct result under ALL circumstances.

He needed to contact the third party because I made that condition and no explanation is required. This is a simple implementation of a "contract" between two parties. Both parties must agree to the terms (they didn't in this case) or there is no contract.

From a less litigious perspective... I am not sure that you read all of the posts. My "algorithm", when I left thinking about it, was flawed as I was going through all possibilities and I would find some paths where I couldn't solve it, but many where I could. If that is not clear to everyone, I can so state without hesitation.

I left it (thinking about it) when I realized that the solution is a simple extension of the very old problem. See my post #36 and the identical question/solution stated again in #39...and a slightly different question/solution first stated in #35 (and pronounced the solution by the TS).

The "gyp" commentary stems from a belief (and one that I don't care to explain or elaborate on further) of a lack of an operational definition of lie and truth when applied to a compound question, which the extension relies upon.

I hope this clears up the Psychology behind my behavior to your satisfaction and no matter if I am T, L or R...if it doesn't clear it up for you....at least I tried .

 

He needed to contact the third party because I made that condition and no explanation is required. This is a simple implementation of a "contract" between two parties. Both parties must agree to the terms (they didn't in this case) or there is no contract.

I'm merely curious as to what purpose that condition served. I'll stipulate that no explanation is required, but that doesn't mean that no one is allowed to inquire. Of course, when one can't/won't provide a rationale for making purposeless conditions part of a contract, others are left to conclude, in the resulting vacuum, why that might be the case. Initially I assumed that you didn't realize that it serves no purpose, but now I have to reevaluate that assumption and decide if a different motive -- a motive that you want to keep hidden -- is more likely.

Now, before you point out that it doesn't really matter what conclusion I do or don't draw, I will cheerfully stipulate that point a-priori.

 

I'm merely curious as to what purpose that condition served. I'll stipulate that no explanation is required, but that doesn't mean that no one is allowed to inquire. Of course, when one can't/won't provide a rationale for making purposeless conditions part of a contract, others are left to conclude, in the resulting vacuum, why that might be the case. Initially I assumed that you didn't realize that it serves no purpose, but now I have to reevaluate that assumption and decide if a different motive -- a motive that you want to keep hidden -- is more likely.

Now, before you point out that it doesn't really matter what conclusion I do or don't draw, I will cheerfully stipulate that point a-priori.

It's not that it doesn't matter at all what conclusion you do or do not draw, it's that it doesn't matter very much to me.

Your writing, however, might suggest something of a a compulsion...."when one can't/won't provide a rationale", "I assumed that", "I have to reevaluate", "a motive that you want to keep hidden". Alternatively, you may just feel like doing a little insulting about a post written a week ago in a thread that is several weeks old and that you did not participate in until now. For all I know, you just had a rigid sigmoidoscopy. I can't explain to you why your concerns have given rise to such inquiries but I am distinctly comfortable not knowing the reasons.

On the other hand, consider this: maybe pR1 <> pR2, when it is decided by a person instead of a random process. If so, how could one increase their chances (in the situation represented by the "contract") without having any other information about the problem? It might be as difficult for you to think about that question as it is for me to not think about that question.

Or maybe it is just that you are driven to see a signal where there is only noise. Maybe I don't even remember why I said whatever it is that I said. Maybe I was just having fun in a thread on a forum that is meant to be enjoyed.

I don't know the answers that will soothe your discomfort except to note that there is apparently no end to the injustice that you must endure.

 

Raymond, I'm not trying to start a fight and I certainly didn't mean to insult you. As I said, I was merely trying to inquire about why you felt something was needed when it serves no purpose. I saw two possibilities -- you thought it WAS needed, in which case you might appreciate learning that it wasn't (clearly I was wrong on that latter part), or else it really WAS needed, in which case I would appreciate learning why it was. But it would seem that now only are you willing to explain why you believed it was necessary, but just asking is somehow an insult. So I apologize for insulting you.

Now, since you asked me to consider pR1 <> pR2, I hope that you won't take insult if I proceed to do that. I have no problem at all thinking about that question, so let's think about it. Why would the relative probabilities matter at all, provided you have a correct algorithm to solve the problem? Let's say that you know, a-priori, that there is a 99% probability that R1 is the road you want. So what? If your algorithm is a correct solution to the problem, it doesn't matter -- it must still correctly identify the road you want 100% of the time or it is not a correct solution to the problem. The probabilities would ONLY matter if your algorithm itself was probabilistic.

 

Raymond, I'm not trying to start a fight and I certainly didn't mean to insult you. As I said, I was merely trying to inquire about why you felt something was needed when it serves no purpose. I saw two possibilities -- you thought it WAS needed, in which case you might appreciate learning that it wasn't (clearly I was wrong on that latter part), or else it really WAS needed, in which case I would appreciate learning why it was. But it would seem that now only are you willing to explain why you believed it was necessary, but just asking is somehow an insult. So I apologize for insulting you.

Now, since you asked me to consider pR1 <> pR2, I hope that you won't take insult if I proceed to do that. I have no problem at all thinking about that question, so let's think about it. Why would the relative probabilities matter at all, provided you have a correct algorithm to solve the problem? Let's say that you know, a-priori, that there is a 99% probability that R1 is the road you want. So what? If your algorithm is a correct solution to the problem, it doesn't matter -- it must still correctly identify the road you want 100% of the time or it is not a correct solution to the problem. The probabilities would ONLY matter if your algorithm itself was probabilistic.

WBahn, I accept your apology for insulting me.

Since you are persisting with your inquiries, I will attempt to explain, again, why I think you may be doing what you are doing. Please understand that I am only speculating and only doing so because you are persistent (well, maybe I am enjoying doing it a little bit).

What I said:

“On the other hand, consider this: maybe pR1 <> pR2, when it is decided by a person instead of a random process. If so, how could one increase their chances (in the situation represented by the "contract") without having any other information about the problem? It might be as difficult for you to think about that question as it is for me to not think about that question.”

Notice that there is only one question mark in the paragraph because there is only one question in the paragraph. That question is clearly, “If so, how could one increase their chances (in the situation represented by the "contract") without having any other information about the problem?”

What you wrote:

“Now, since you asked me to consider pR1 <> pR2, I hope that you won't take insult if I proceed to do that. I have no problem at all thinking about that question, so let's think about it.”

You completely ignored the question I posed in order to set up an answer to a question that was not posed, but that you wanted to address…

“Why would the relative probabilities matter at all, provided you have a correct algorithm to solve the problem? Let's say that you know, a-priori, that there is a 99% probability that R1 is the road you want. So what? If your algorithm is a correct solution to the problem, it doesn't matter -- it must still correctly identify the road you want 100% of the time or it is not a correct solution to the problem. The probabilities would ONLY matter if your algorithm itself was probabilistic.”

Your response does, indeed, support my speculation that “It might be as difficult for you to think about that question as it is for me to not think about that question”.

I believe that this is an example of rigid thinking in which the person is inhibited from seeing the question posed. We all engage in that at times and some “brain teasers” even rely on that process.

You interpreted my asking you to consider something (pR1 <> pR2) as the question that followed (…how could one increase their chances…). But, I don’t think it was careless or accidental, instead, I think it was willful ignorance because it is unlikely that you are incapable of reading and understanding that short paragraph. It is much more likely that you chose a misinterpretation that, in your mind, would justify being able to express the point that it does not matter if one has the solution.

In so doing, you also ignored the terms of the “contract” presented in my post #30. Those terms specified a single trial resulting in what basically amounts to a “yes, you got it” or a “no, you got squat”. Given a p=.5 for either answer, the risk:reward for choosing either road is even. If pR1<>pR2, the ratio changes and, as I said, “It might be as difficult for you to think about that question as it is for me to not think about that question”.

Your predisposition was not to “see” the contrived scenario accurately (a game that might offer an edge) and, instead, only see it as “it must still correctly identify the road you want 100% of the time or it is not a correct solution to the problem”. Clearly, the terms of the proposed “contract” only had to choose the road once.

Further, since it was already stipulated to you that I did not have the “solution” (as per my post #41) and ignoring, for obvious reasons, the “trick” solution in my post #36, I suspect that it is not at all curiosity that drives your inquiry - “I'm merely curious as to what purpose that condition served“. Instead, you want to extract a “pound of flesh” for what you perceive as the injustice of having a flawed analysis.

This brings me to another question and one that we will likely never answer: If we sat down at the poker table, which one of us would leave without their shirt?

 

The answer to your question, "If so, how could one increase their chances (in the situation represented by the "contract") without having any other information about the problem?" is: They couldn't. Why would the relative probabilities matter at all, provided you have a correct algorithm to solve the problem (which is what you were claiming to have at the time that you stipulated that condition to the contract)? Let's say that you know, a-priori, that there is a 99% probability that R1 is the road you want. So what? If your algorithm is a correct solution to the problem, it doesn't matter -- it must still correctly identify the road you want 100% of the time or it is not a correct solution to the problem. The probabilities would ONLY matter if your algorithm itself was probabilistic and this problem calls for a deterministic algorithm as its solution.

Now, since you are doing little beyond going out of your way to impune my motives and character, I see no point in even attempting to discuss this with you further. Good day.

 

The answer to your question, "If so, how could one increase their chances (in the situation represented by the "contract") without having any other information about the problem?" is: They couldn't. Why would the relative probabilities matter at all, provided you have a correct algorithm to solve the problem (which is what you were claiming to have at the time that you stipulated that condition to the contract)? Let's say that you know, a-priori, that there is a 99% probability that R1 is the road you want. So what? If your algorithm is a correct solution to the problem, it doesn't matter -- it must still correctly identify the road you want 100% of the time or it is not a correct solution to the problem. The probabilities would ONLY matter if your algorithm itself was probabilistic and this problem calls for a deterministic algorithm as its solution.

Now, since you are doing little beyond going out of your way to impune my motives and character, I see no point in even attempting to discuss this with you further. Good day.

This is not an instance where I would say: don’t go away mad, just go away. While nobody here has to respond to any post, I hope you will read my response.

You [finally] got to the crux of the biscuit (not always the apostrophe) and answered the question. “The answer to your question, "If so, how could one increase their chances (in the situation represented by the "contract") without having any other information about the problem?" is: They couldn't.”

By a preponderance of evidence, you are wrong.

The situation in question (the “contract”, not the initial problem) clearly and pointedly required a person (the TS) to choose the left or right road as the road to heaven. I would argue, and with a large body of supporting data, that the choice a person makes is not random.

Therefore, if one knows the biases that people engage in, one can, potentially, increase the likelihood of determining the choice they made - without any information about the problem.

The purpose of the brain (the CNS to be more accurate) is to produce behavior – that is what it does. The output of the brain, in this case picking R1 or R2, is never truly random. There are always internal and external factors that influence the choice. Whether the influence is conscious, unconscious, genetic, related to dominance (right-brain or left-brain; right-handed or left-handed, whatever) or related to prior experience, is another matter. That they exist is the important point in the instant discussion.

As a mathematician by training, you undoubtedly have a good deal of experience with inferential statistics. We know that such statistical methods never state with absolute certainty that an outcome cannot be due to chance alone. Instead they give you a likelihood of the outcome being due to chance alone and when that probability is low enough (p<.05, p<.01, P<.0001 and so on) the result is deemed statistically significant. If you spend just a few hours reading the substantial amount of literature in this regard, you cannot escape the preponderance of data that converge on the conclusion that such biases exist in humans.

Not only is the brain unprepared to produce random choices, it seems to go deep into the available data to avoid them, if the choice matters at all (see http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.825.3945&rep=rep1&type=pdf for an example).

Take for example, a study that asks subjects to simply produce sequences of numbers between 1 and 10 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3899545/ . Statistically and scientifically significant biases are observed and furthermore, in this case, they are age-related. There are literally hundreds of such studies.

What does the marketing profession think about choosing to turn right or left (https://retailminded.com/the-invariant-right-how-people-move-around-stores/ http://www.unc.edu/courses/2008spri...qualities/Boston Review consumption issue.pdf) - they seem to believe pretty strongly in the concept of the “invariant right” (although they could have done without the word “invariant”).

Many years ago, when state lotteries first became popular, I remember seeing hucksters hawking systems to beat the lottery. What hogwash, I thought. How are you going to beat a random process (not to mention beat the process enough to overcome the paltry 50% return that a lottery typically offers)? But, they were not pure hogwash. They were, in principle, quite sound. They simply exploited biases in the numbers people chose. Choosing the winning numbers is random, but choosing the numbers to play is not. Since jackpots are divided among winning tickets, it actually does (or at least did) make sense to choose numbers that were least preferred. Of course, the difference was never going to be enough to overcome the 50% take, but it was, at least potentially, better than choosing preferred numbers or even choosing randomly.

I am not going to apologize if you feel that you have been insulted, because explaining that someone’s character is predictable is true for everyone and, in this case, was not pejorative.

Hopefully, I have made a valid point and you (and others) can see that now – if you can’t, well “tough grit, mac”, it’s just how I see things, I don’t demand that you or anyone else see them in the same way.

Finally, I came across a quote the other day (Thomas Schelling, Nobel laureate, economics) that is relevant here…. “One thing a person cannot do, no matter how rigorous his analysis or heroic his imagination is to draw up a list of things that would never occur to him.”

 

The bystanders could also be subjected to perception bias.

 

Hi,

So what was the final answer?

It's interesting a little bit that if you ask the 'random' guy the same question over and over, it is unlikely but possible that he will answer just like one of the other two every time you ask, even though he is giving a random answer. That's because a random variable can yield a 'run' that is very long.
Of course more probable is that the answer will change mid stream, but that stream can be very long sometimes.

I see you guys like logic problems. I'll see if i can find a few more from my old books.

 

The correct solution was given by Tesla23 in post #35

 

How does one ask two people a question......and get three answers? Post #35 makes no sense.

 

Tesla23 wrote in response #35:-

Ask all three
"if you ask your two colleagues: 'is R1 the road to heaven?' is it possible that they will both say YES?"

Once two of the responses are in agreement (regardless whether one of the respondents is random) – the solution is known.

Again, Tesla23 has explained this.

 

Hello again,

Ask all three:
"If you are the one that does not lie ever, determine which road is the one to heaven and then tell me so".


Hire an assistant, ask him to determine which road is the right one any way he wants to

Ask the first guy to go down one road and return, ask the second guy to go down the other road and return. The one that comes back not burnt went down the road to heaven

 

You know what......I'm just glad there is no math test required for Heaven.