Seven out of seven people were asked to use the Thought Dial to determin the winner of the 2013 Super Bowl. All seven picked the Ravens to win . No one picked the 49ers.
Firstly, what are the odds that everyone would be in agreement and what are the odds that the Ravens, I'm told are the underdogs, would win?

The odds against 7 people randomly picking the same side of a 2-option proposition are 63-1 against. The Ravens' underdog status is harder to say, because the betting odds aren't intended to reflect actual odds (which are impossible to determine to a certainty), but rather reflect public perception. It's probably most accurate to characterize it as a consensus opinion of the betting public. That being said, that consensus opinion is that the Ravens have about a 36% chance of winning.

So this is about a 3 to 1 underdog ?

Ok. So it actually happened. Seven out if seven people using paranormal methods predicted the outcome of the Super Bowl !!!!!

Nice!

It's 2 to 1 that they would lose if the probability is 1/3 that they'd win.

When you ask "in agreement", do you also include the case that they all chose 49ers (they would all be in agreement then), or do you only mean the case where all agrees that Ravens would win?

Is the Thought Dial some mentalist prop and/or something woo-woo people thinks actually works? I quickly googled it but it did not help.

/Tomas

Tomas is one of my favorite mentalists.

Not sure why you'd be name calling here on the Café?
Especially since our current guest of honor uses the Thought Dial himself?????
And Woo Woo or not ..IT WORKS!!!!

Sooo, a magic prop? I don't even know what it does, but it sounds like something you use as a prediction in performance. By "works", do you mean in the same sense that a dove pan "works"?

By woo-woo I meant if this is something superstitious people use themselves to predict the future. I realize that one doesn't exclude the other, which is why I had the "and/or" in the original question. I thought it might be something like an ouija board, which can be a game, a tool for superstitious people, or a magic prop.

I'm still not sure, so I'd love to hear any clarifications or what a Thought Dial is and what it is used for.

/Tomas

Slim King, your post about the guest of honor led me in the right direction to understand a bit more. The guest, Jerome Finley, indeed uses it in performance to knowingly fake psychic phenomena. Still, it looks like it originally was made for the woo-woo market. Is that correct, or was it intended as a mentalist prop originally?

/Tomas

I use it for REAL as an experiment and twice now it has yielded fantastic results. Amazing really. I think it is bigotry to label people with any name because you don't agree with them. The same people who called blacks the N-word also call believers Woo Woo ... It's really insulting in my eyes.(Maybe it's different in Sweden)

I've never used the Thought Dial to knowingly fake psychic phenomena. All the experiments were done and published way before the event for all to see or hear.

That's why I'm asking for the real odds.

To clarify, on the Ghost and Demon Hunter radio show both the hosts were Thought Dialed on the air a week before the game. People were contacted during the show. Five more were Thought Dialed soon after the show and their names and contact information were recorded ( I included myself as always). Each and every one who was Thought Dialed chose the underdog Ravens. No one was turned away and no one chose the 49ers.

It was almost a mirror image of what happened in 2010 when we used the Thought Dial on the internet and the Dark truth radio show( one person used dowsing rods)... all done and published before the game. In that situation it was determined the odds were determined to be 2186 to 1 if memory serves me correctly. Martin Gardner was even consulted!

It had produced two amazing results for you since at least 2010? Do you even care wether what you believe is true or not? If not, keep using it without trying to find out. If you care, test it blindly against a control.

This isn't about not agreeing. You are claiming something exceptional here, and need to prove that the effect exists (not _how_ it works). The guest you cited uses it as a prop to cleverly sell faked phenomena in performances, which you seemed unaware of.

It's not wrong to not care about what you believe is true or not. It's wrong if you start selling books, courses, seminars or other services in regards to it.

/Tomas

Slim King,
Returning to your original question. I am not certain that the odds of such a problem can be computed particularly well. For instance, were the people who were interviewed (I have no idea what a thought dial is, so I'm assuming instead that they simply told you who they thought would win) followers of either of the two teams? If not, then there is a good reason that they would psychologically choose the underdog to win:

• People like watching 'classic' matches which will be memorable.
  
• If an underdog wins they feel less bad that their own team wasn't in the game (belief that if their team was there, then they'd have won).
  
• Betting people stand to gain a lot more money for choosing the underdog.
  

Likewise, however, there are equally as compelling reasons to choose the favourite (after all, they are the favourite...). Obviously these things are highly personal, so we cannot really choose the odss of all the people to be the same.

So, let b_i, I = 1,...,7, be the 'belief' of person ''i'' (here we're assuming there are 7 people, as in your question). Now the belief of each person is going to be a number between 0 and 1
b_i = "the certainty of person I that the Ravens would win."
So if b_i = 1 then person number 1 is 100% certain that the Raven's would win. If b_i = 0 then they're certain that they will lose.

Now there are two ways to model the situation, again: not knowing what a thought dial is I don't know which of the following best describes the experiment.

• Perhaps the people made their choice by taking into account their lack of certainty.
  For somebody with b_i= 0.5 then they are sitting on the fence and have no preference. In this case it seems reasonable that they'd randomly choose a side. Accepting this as a reasonable approach, we could also apply it to somebody who has b_j= 0.55. Again, they're not so certain so it seems that picking randomly is a good idea. The way to do this is to sample a uniform number between 0 and 1, if it is less that 0.55 then they choose the Raven's, if it is bigger than 0.55 they choose the 49ers. But now we can extend this even to the extreme cases. So in general, for each of the people I = 1,...,7 independently sample a number between 0 and 1. If person i's number is less than b_i they choose the Raven's. Otherwise the 49ers.
  In this situation, the probability that they all chose the Ravens is the product of the b_i
  
  Probability that all choose the Ravens = b_1 x b_2 x ... x b_7.
  This is known as the multinomial distribution.
  
  
• Perhaps more realistic is that if somebody has a belief which is more than 0.5 then they always choose the Ravens. So now the probability that the Raven's would be chosen by everyone is the probability that all the beliefs are bigger than 0.5.
  
  Probability that all choose the Ravens = 1, if b_i > 0.5 for all I = 1,...,7. Otherwise it is 0.
  

The whole problem is that we have no access to what the b_i are since they are personal to the individual. The study of Bayesian statistics tries to answer this question: given some data which depends on the people's beliefs, can we reconstruct what their beliefs are. In this case, however, we only have one experiment which isn't enough to reconstruct any information about the b_i.

Right. That might have been completely irrelevant... As I said, without knowing what the Thought Dial does (I have searched but I couldn't find an obvious and clear description of it) I cannot analyse the situation all that well.

Hope that helped in some way.

Owen

Good observation, Owen. If this is tightly connected to Numerology, which is deterministic in nature, i.e. when applied to the same word or date it will give the same result to anyone using the procedure, it might be a huge probability that many people get the same result, so the only important probability is in fact for the event itself.

/Tomas

Hi Tomas, Slim King, and co.

So from my understanding the thought dial 'method' is that you ask for some random numbers from a person, apply some sort of reasoning to this (a formula?), and then get an answer based on those random numbers.

For simplicity (and since I don't know the details of Thought Dial). I'll assume it works something like this: I ask you for any three numbers between 1 and 50. These now get put through some procedure, and I get returned the answer Y or N... where in this situation

Y = "Ravens will win"

For simplicity again, I'll assume that the order of the three chosen numbers doesn't effect the formula (these assumptions don't make a qualitative difference). So in total there are 50^3 different numbers that could have been arrived at. Since each set of numbers (a,b,c) (i.e. person chose the numbers a, b, and c) gives a deterministic answer, we can consider the set of numbers which lead to the answer Y

A = { (a,b,c) : ThoughtDial(a,b,c) = Y }
(this is the collection of all triples which give the answer Y when put through the Thought Dial procedure).

Similarly we can define the set of numbers that give the answer N
B = { (a,b,c) : ThoughtDial(a,b,c) = N }

Let #A be the number of triples that are in A, and #B the number of triples in B. Then since every triple gives us an answer: #A + #B = 50^3.
Depending on the formula, ThoughtDial, the sizes #A and #B might not be the same.

Ok, so now we're in a position to answer your question better. Under the assumption that the chosen numbers are really random (by which I mean uniformly distributed... so the number 1 is chosen as often as the number 43, etc.), and are independent (i.e. my choice of first number doesn't effect my choice of the later numbers, and likewise the choice of second number doesn't effect the final number), then the probability that an individual gets a Y when doing the thought dial experiment is

#A / 50^3.

And then, if we do this for 7 spectators independently, and they all choose the numbers according to the assumptions above, then the probability that all of them get a Y is

(#A / 50^3) x (#A / 50^3) x ... x (#A / 50^3) = (#A / 50^3)^7.

Right. So now for some important comments.

• Presumably the person who set up the experiment chose which way round Y and N are given... by this I mean the following: suppose the numbers (a,b,c) are in A. Then whatever the question is they always give the answer Y. So now consider the following two questions
  " Will the Ravens win?"
  " Will the Ravens lose?"
  Depending on which question was asked the sets A and B switch around. So the person controlling the experiment has a large influence here. Suppose they know that #A is much larger than #B. They can then influence people to answer positively to the question "Will the Ravens win". On the other hand, if #A is much smaller than #B. He can similarly influence people to conclude that the Raven's will win by getting the answer N to the question "Will the Ravens lose".
  
  So what we see is that depending on how biased the Thought Dial answers are (i.e. how much bigger/smaller #A is than #B) the person controlling the experiment can bias the outcome heavily. If in fact #A is approximately the same as #B then #A/50^3 will be approximately 0.5, and under the independence and uniformity assumptions, the probability that everyone chose the Ravens is 0.5^7 = 0.007 (i.e. less than 1% chance of happening).
  
  
• We must also think about these assumptions: i.e. that all the numbers in 1,...,50 are equally likely, and that they are chosen independently. This isn't really all that fair. Here are two examples pointing out an error each assumption:
  
  Uniformity. Most people have a lucky number, and normally this will be between 1,...,10. One would expect people might include this lucky number in their set of three numbers. Therefore there is a bias towards lower value numbers. Humans are remarkably bad at choosing random numbers. Here is the first link I could come across to some data of this type (it isn't a huge sample size but it makes a point). If the people had chosen numbers uniformly all the bars would be roughly the same length. [If you want to know more about people's inability to choose random numbers PM me and I can tell you about some interesting phenomenon... which aren't relevant to this post].
  
  Independence. Suppose I ask you to name a number between 1 and 50. Now I ask you for a second one. Are you really likely to say the same number again? No, most likely you wont. Whats more, you probably won't choose a number which is 1 more or less (or even 2 or 3 more or less), since psychologically you will want to choose your numbers broadly across the whole range. So this means that the configurations that come up do not have the independence we want. As an example of the effect of this, suppose you pick the numbers (a,b,c) and you assume that neither b or c is equal to a-1, a, a+1, and further that c is not equal to b-1, b,b+1. Then there are approximately 50 x 47 x 44 possible numbers. Doing some quick calculations, you have now ruled out approximately 1/5th of all possible numbers... so the lack of independence has had a drastic effect on our number sets.
  

So what can we conclude from all of this.

• If the thought dial gives a deterministic formula, then this can be controlled by the person setting the questions.
  
• To be able to work out the probability that a person gets the answer Y (to whatever the question might be) we need a good understanding of the distribution of how often a given triple (a,b,c) is chosen.
  
• Based on a lack of independence/uniformity, finding this distribution is not easy, and would need a lot of statistical data... which to the best of my knowledge just does not exist.
  

So in conclusion, we cannot really answer your question of how likely it was that all 7 people got the answer Y. There are too many variables.

A more interesting question to me, and of more interest to magicians, is the question of the respective sizes of the sets A and B... Depending on the bias here the performer could have a very strong ability to influence the outcome of a spectators 'random' decision. Since I do not know the formula I cannot speculate as to whether this is really practical though.

Owen

Owen. You really need to find out what the thought dial is and how it works... You are unfortunately spinning your wheels a bit too much. I appreciate your energy level though !!!!!

Except for the first 2 people who did the THOUGHT DIAL live on the radio, no one knew the outcome of the others choice. And the choices made were often contrary to their personal beliefs!
We will discuss this amazing experiment on the GHOSTMAN AND DEMON HUNTER SHOW. Tomorrow at 7:30 EST...

Call in or join the chat room.

I have quite clearly said in both of my posts that I would like to know how it works, but cannot find any suitable sources where the procedure is explained. So perhaps it would be useful for you to explain it for those of us who do not know what exactly the procedure involved is... Since you insist that this is not a magic effect I am sure it will not be an issue to explain how the final answer is arrived at from the chosen numbers (even if you do not provide a specific formula, knowing what form this takes (i.e. is it deterministic or random) would be very useful... So I will look forward to hearing from you with some details.



I'm not too sure what you are implying with this. You asked people here to calculate the odds of something. I am trying to explain to you that these odds are not really calculable from a mathematical perspective. If you were interested in having an answer with a genuine mathematical description of the odds, then that is exactly what I have given you. So, when you say it is "unfortunate" how much effort I put in, this appears to be suggesting that the calculations I have given are irrelevant... But this couldn't be further from the truth...

... I do not want to join in the debate as to whether the thought dial works from the esoteric point of view. You asked us to give you the odds of your experiment, by which we assumed you want the odds that are obtained without the help of the thought dial, or in the case that the thought dial doesn't work... Presumably so that when you talk to people about the experiment you can point out how unlikely the outcome was. So this is exactly what I have given you: an explanation of the odds under the assumption that the thought dial does nothing. Unfortunately, as I point out, there are too many variables to give you a specific number at the end.

If you were wanting the odds under the assumption that the thought dial works, then this is easy... with probability 1 they will all have chosen the same (correct) answer.

So, in all, I'm curious to know what you mean by saying how unfortunate my thought process is...

Regards

Owen

Owen. Please don't be offended I certainly appreciate all the hard work you've put in. In 2010 I used a college professor to figure the odds for the xperiment. I think they are almost exactly the same but I'm double checking everything to be sure.
The Thought Dial was invented by Sidney OMARR back in the 50 as a Divination tool. It reportedly worked quite well for certain radio stars of the time for determining hoarse racing results. I thought I'd follow the exact procedure and it has truly been amazing.

I think I understand now how the Thought Dial works, but am missing some details in your execution. Is this correct:

You ask people to send you three numbers from the set {0,1,2,3,4,5,6,7,8,9,22,11} and you take the digital root (dropping nines) of their sum. This number from 0 to 8 (or maybe you have 1 to 9) gives you a list of words which you try to associate with either Ravens or 49ers.

If this is close to how it's done, was it the person that named the numbers who got the list of words to make his own association with team, or did you do it?

If you did the association, did you in advance, before anyone sent you their numbers, look over the 9 lists of words to decide which of them would mean Raven and which would mean 49ers? If so, which lists did you assign to Ravens and how many did you assign to 49ers?

What 7 numbers did the 7 people end up on? I assume some was the same. If they were the ones deciding which team to accociate with the word list, did you eventually send all lists to them? Perhaps all of the 9 lists would easier be associated with the Ravens than the 49ers?

Assuming you have used this for a while on people, do you have any statistics on how often people end up on the nine different end numbers?

/Tomas