Do The Math!

[hung]

Hopefully this will help those that are not conversant with probability and statistics.

A fair coin flip should produce a 50 50 chance of heads or tails, over a large number of flips. If you flipped the coin
three times and got heads, what are the chances that if you flipped it again a head would appear? Well, it is 50%.
The coin holds no prior history of the previous tosses and each toss has a 50 50 chance of coming up heads.

Wrong.
Chances for a head in a single flip: 1/2 = 50%
Chances for 2 heads in second flip : 1/2*1/2 = 25%
Chances for 3 heads in third flip : 1/2*1/2*1/2 = 12.5%
The chances that heads would appear in the fourth flip after 3 heads had prior appeared in the first 3 flips is:

1/2*1/2*1/2*1/2 = 1/16 or 6.25%

A simple statistics problem.
Not even a simple math calculation serves the skeps to appear credible?

 

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[Rudy(CA)]

Hopefully this will help those that are not conversant with probability and statistics.

A fair coin flip should produce a 50 50 chance of heads or tails, over a large number of flips. If you flipped the coin
three times and got heads, what are the chances that if you flipped it again a head would appear? Well, it is 50%.
The coin holds no prior history of the previous tosses and each toss has a 50 50 chance of coming up heads.

Wrong.
Chances for a head in a single flip: 1/2 = 50%
Chances for 2 heads in second flip : 1/2*1/2 = 25%
Chances for 3 heads in third flip : 1/2*1/2*1/2 = 12.5%
The chances that heads would appear in the fourth flip after 3 heads had prior appeared in the first 3 flips is:

1/2*1/2*1/2*1/2 = 1/16 or 6.25%

A simple statistics problem.
Not even a simple math calculation serves the skeps to appear credible?

If your reading comprehension was a little better, you would have realized two things:

1. I was discussing finding or not finding the gold target, not coin tossing. At least have the courtesy to not
change the problem in your riposte.

2. I was discussing the probabilities in the outcome results of four trials. If you noticed, I said that the probability of
one test is 50 50, or 50%. Your probability for four heads in four coin flips is EXACTLY the same as what I wrote.
Your previous (two and three heads in two and three tosses) are totally different and I didn't cover them. I (pay
attention here, you might learn something) specifically mentioned the probability of getting three heads in four tosses
WHICH IS TOTALLY DIFFERENT FROM THE THREE HEADS IN THREE TOSSES you made an issue about.

I purposely stayed away from mentioning that such problems are of a class known as a binomial distribution
since I was only trying to convey the methodology.

But since you seem to at least be partially interested, a binomial distribution is a rather easy one to manipulate with
a little algebra, as follows:

Using S for Success and F for failure, wether you are talking about tossing coins or finding the gold, the success and
failure are mutually exclusive and are the only possible outcomes. Therefore,

(S+F) = 1 Meaning the probability of success plus failure must add to 1 or 100%.

If you do it twice,

(S+F)*(S+F) = (S+F)^2 = 1

If you do it "n" times then you have

(S+F)^n = 1

If you expand the binomial, the first term (which is S^n) is the probability of n successes in n attempts. The next term
(which is n*S^(n-1)*F) gives the probability of n-1 successes in n trials and so forth.

So Hung, I hope you now understand it a little better than before.

 

[hung]

Don't dodge or twist this with blah blah blahs.
I don't care about your theory of LRLs.
What I discuss is your statement:

'If you flipped the coin
three times and got heads, what are the chances that if you flipped it again a head would appear?Well it's 50%.'

You are clearly stating that four flips happen. One after another and then you make a mistake by saying that the probability is 50% in the fourth flip.
IT'S WRONG.
I already demonstrated it is 6.25%.

Whether you made this mistake unconciously or not it does not matter. It was an unfortunate example for sure.
It's a mistake and simply recognize that you comitted a mistake.
But if you keep insisting in twisting this fact, then yes, it will turn really bad for you.

 

[aarthrj3811]

~Rudy~

1. I was discussing finding or not finding the gold target, not coin tossing. At least have the courtesy to not
change the problem in your riposte.

2. I was discussing the probabilities in the outcome results of four trials. If you noticed, I said that the probability of
one test is 50 50, or 50%. Your probability for four heads in four coin flips is EXACTLY the same as what I wrote.
Your previous (two and three heads in two and three tosses) are totally different and I didn't cover them. I (pay
attention here, you might learn something) specifically mentioned the probability of getting three heads in four tosses
WHICH IS TOTALLY DIFFERENT FROM THE THREE HEADS IN THREE TOSSES you made an issue about.

So--Now Carl is wrong about Ransom Chance... With LRLs and dowsing, "random chance" applies to randomized blind tests, not to field use. A randomized blind test does 2 things that a field test cannot do. First, it eliminates outside influences that might alter performance results, such as observable clues. Second, it provides a baseline from which to compare results, namely guessing.

Despite intentional attempts to mislead people, random chance doesn't apply to field use. You can't ask, "What are the odds of digging 10 holes in a park and recovering a gold coin?" There is no way to calculate that, because there is not enough information*. But in a randomized blind test, it is quite easy to calculate the odds. Depending on the design of the test those odds can vary, so it is not a fixed number that applies to every test, but it's not a "moving target" either.

 

[aarthrj3811]

~EE~

What needs to be known about treasure hunting?
And while you're at it, since you claim to be such a big treasure hunter, I'm sure you brought your camera and video recorder along on all those big hunts. So show us some of your expeditions and huge booty hauls. (Not the Tic-Tacs under the plastic eggs, or silver dollars under the napkins.)
I can't wait to see all of them!

Replies by Skeptics two days ago at Detected, Located and Dug.

That one was actually entertaining. They needed 8 or 9 people, cameras rolling, all for a little old earring. It's not like it was staged . The lady just maybe, sort of, possibly kept hinting she knew what and where it was. Notice how the shovel had to be stood on for a couple of the digs and the other side it slipped right into the dirt? Almost like the dirt had previously been dug. I almost expected Art to jump out from behind a bush.

What a bunch of suckers.

dug it up, or that it didn't detect the woman's ring, ear rings and
other gaudy jewelry she was wearing.

Now if Gaucho1961 popped up out of that hole I would have been impressed. I guess he's still too shy to simply admit he was screwed by Mineoro. Big talker, couldn't back it up. Just like all of the others.

Right, there are so many ear rings lost in forests. Did they find any high heels to go with them?

Nonetheless, they will certainly graduate from cheap ear rings to Carl's $25,000.00 award next. So what will the date of that be? I'm sure there will be videos, and I don't want to miss that!

It would make no difference to the Skeptic Cult…Art

 

[Rudy(CA)]

Hung,

I know science can be difficult for you and I don't want you to get stressed out. Let's try again, in small steps.

'If you flipped the coin
three times and got heads, what are the chances that if you flipped it again a head would appear?Well it's 50%.'

Absolutely correct! Give Hung a lollypop.

You are clearly stating that four flips happen. One after another and then you make a mistake by saying that the probability is 50% in the fourth flip.
IT'S WRONG.

You are wrong Hung. If you flip it a fourth time, the odds that the fourth flip comes up head is 50%.

I already demonstrated it is 6.25%.

Whether you made this mistake unconciously or not it does not matter. It was an unfortunate example for sure.
It's a mistake and simply recognize that you comitted a mistake.
But if you keep insisting in twisting this fact, then yes, it will turn really bad for you.

What your 6.25% number, which is the same as my 6.25% is "the average probability of getting four successes is 1/16 or 6.25%."
The key is four successes in four tosses. In other words, you flipped it four times and all four times came up heads.

In other words, the combined probability of getting heads on the first toss AND the second toss AND the third toss AND the fourth toss is 6.25%.

Comprende?

 

[pronghorn]

Chances for a head in a single flip: 1/2 = 50%
Chances for 2 heads in second flip : 1/2*1/2 = 25%
Chances for 3 heads in third flip : 1/2*1/2*1/2 = 12.5%
The chances that heads would appear in the fourth flip after 3 heads had prior appeared in the first 3 flips is:

1/2*1/2*1/2*1/2 = 1/16 or 6.25%

A simple statistics problem.
Not even a simple math calculation serves the skeps to appear credible?

You are joking, right?



It doesn't matter if a flipped coin lands heads up three times
in a row, 100 times in a row, or 99999 quintrillionbillionmillion
times in a row, there is still only a 50% chance the
next roll will be tails.

Credibility is at the top of a high mountain and you just
fell to the bottom, again. Pick yourself up, dust yourself
off and start the climb again, you can do it.

This is funny! Any of you promoters want to verify
hungover's odds or math?

 

[Rudy(CA)]

<deleted irrelevant content>

Now, lets do an experiment. Suppose we have an LRL with an experienced operator, an observer/recorder, an assistant,
two identical containers, a gold coin and a junk target. A wall separates the LRL operator from where the boxes are.

So, the assistant goes behind the wall where the two boxes and the two targets are and he places one target in each box,
then leaves the area. The observer and the LRL operator then enter the area where the boxes are and the LRL operator, using
his trusty LRL selects the box he feels has the gold. The box is opened by the observer/recorder and the results are written down.

A short digression. The above is a double blind test. Neither the observer nor the LRL operator know in advance which box has
the gold and the assistant that put the targets in the boxes left the area and can't communicate his actions to the other two.

Dr. Rudy,

May I see your test design?

I'll show you mine if you show me yours.

 

[Rudy(CA)]

<deleted irrelevant text>

Note from the above sequence of 4 tests, the average probability of getting four successes is 1/16 or 6.25%.
If instead we insisted that there'd be no more than 1 failure, then the probability would be 5/16 or 31.25%.

Of course, if we used sequences with more tests, we can produce even smaller probabilities of success from purely
random chance.

However, if we do this test only once, then we can't rule out that it may have been an accidental quirk that produced
the results obtained. To eliminate, or at least quantify the probability of a quirk producing the results, we would need to run
the experiment multiple times, each time recording the results obtained.

If enough of these 4 test trials are run (from sampling theory and the Central Limit Theorem, 30 or more sequences of tests
should suffice), we can assure ourselves of approaching the random chance probabilities with some suitably small confidence
interval, as well as determining if the LRL produced results that are statistically significant and different from random chance.

Let me get this straight.
4 "tests" consisting of 4 attempts each = 1 experiment
If we ran this experiment 30 times, as you suggest, that would be 480 total attempts.
Are you saying that in 480 coin tosses, the average overall success (heads up) rate would be 50%?

You are clearly stating that four flips happen. One after another and then you make a mistake by saying that the probability is 50% in the fourth flip.
IT'S WRONG.

You are wrong Hung. If you flip it a fourth time, the odds that the fourth flip comes up head is 50%.

I already demonstrated it is 6.25%.

Whether you made this mistake unconciously or not it does not matter. It was an unfortunate example for sure.
It's a mistake and simply recognize that you comitted a mistake.
But if you keep insisting in twisting this fact, then yes, it will turn really bad for you.

What your 6.25% number, which is the same as my 6.25% is "the average probability of getting four successes is 1/16 or 6.25%."
The key is four successes in four tosses. In other words, you flipped it four times and all four times came up heads.

In other words, the combined probability of getting heads on the first toss AND the second toss AND the third toss AND the fourth toss is 6.25%.

Comprende?

So you are saying the test subject has a 6.25% probability of having 100% success rate in performing a single trial of 4 attempts?

No what I am saying is that random chance would produce on average a probability of success of 6.25% over many repeated trials of 4 attempts each.

 

[hung]

Hung,

I know science can be difficult for you and I don't want you to get stressed out. Let's try again, in small steps.

'If you flipped the coin
three times and got heads, what are the chances that if you flipped it again a head would appear?Well it's 50%.'

Absolutely correct! Give Hung a lollypop.

You are clearly stating that four flips happen. One after another and then you make a mistake by saying that the probability is 50% in the fourth flip.
IT'S WRONG.

You are wrong Hung. If you flip it a fourth time, the odds that the fourth flip comes up head is 50%.

I already demonstrated it is 6.25%.

Whether you made this mistake unconciously or not it does not matter. It was an unfortunate example for sure.
It's a mistake and simply recognize that you comitted a mistake.
But if you keep insisting in twisting this fact, then yes, it will turn really bad for you.

What your 6.25% number, which is the same as my 6.25% is "the average probability of getting four successes is 1/16 or 6.25%."
The key is four successes in four tosses. In other words, you flipped it four times and all four times came up heads.

In other words, the combined probability of getting heads on the first toss AND the second toss AND the third toss AND the fourth toss is 6.25%.

Comprende?

You've made your choice that is to make it appear really bad for you.
Your native language is english. So there is no excuse possible to type what you posted in bold and then try to change somehow the meaning and the result. Math is an exact science. The fouth flip after getting heads in 3 previous flips is not 50%. It's 6.25%. There is no possible argument on that.

It would have caused less damage by just admiting you've made a mistake in your comparison. It would probably hurt your ego but would keep your honesty intact.

 

[aarthrj3811]

Hey hung..They have to do something when somebody punches holes a in one of their favorite day dreams..

 

[Rudy(CA)]

You've made your choice that is to make it appear really bad for you.
Your native language is english.

Quien the dijo que mi lengua nativa es ingles?

So there is no excuse possible to type what you posted in bold and then try to change somehow the meaning and the result. Math is an exact science. The fouth flip after getting heads in 3 previous flips is not 50%. It's 6.25%. There is no possible argument on that.

It would have caused less damage by just admiting you've made a mistake in your comparison. It would probably hurt your ego but would keep your honesty intact.

Math is indeed exact.

Each flip is a separate event whose outcome is not dependent on prior events. Each coin flip has a 50% probability. 6.25% is
the probability of getting 4 heads (or 4 tails) in exactly four flips.

If you can not grasp that concept, then you should go back and take a remedial course in statistics for pseudo scientists.

 

[Rudy(CA)]

I'll show you mine if you show me yours.

I don't have one. 8)

No what I am saying is that random chance would produce on average a probability of success of 6.25% over many repeated trials of 4 attempts each.

How many repeated LRL trials would it take to reach the 50% mark, Dr. Rudy?

How many repeated coin toss trials would it require to reach that same mark?

I don't understand your question. The 50% mark of what?

Just to be clear, in the example I gave I was just trying to show how the compound probabilities would
build up by showing a string of 4 tests. Later, when explaining to Hung, I said that the result is really
a binomial distribution. So, if we were doing the test for real, I wouldn't recommend doing sequences
of 4 tests, instead it would be smarter to do "n" tests, where "n" is picked to drive the probability of success
"P" due to random chance down to an acceptable level.

Doing it this way, would then allow the simple calculation of the mean and standard deviation of the binomial
distribution. The mean is μ= n * P
and the standard deviation is σ = sqrt[ n * P * ( 1 - P ) ]

Since in our test, there is a 50 50 of success for each trial so the standard deviation
becomes σ = sqrt[0.25n] = 0.5*sqrt(n)

If we set n to 16 (the number of tests), then the
Average expected result is μ=16*0.5 = 8 successful detections
with a standard deviation of σ = 2
And the probability of detecting the gold all 16 times without fail is 0.5^16 or 0.0015258789063%

Assuming the binomial distribution with 16 trials is close enough to the normal (gaussian) distribution,
then 99.6% of all attempts at taking the test sequence should fall within ± 3σ of the mean, so 99.6%
of the tests should fall in the interval of μ ± 3σ

In other words, 99.6% of the test sequence results will yield from 2 to 14 successes in 16 trials.
Conversely, only 0.4% of the test sequence takers will have results that lie on the tail of the distribution.
0.2% in the 0 & 1 success interval and 0.2% in the 15 & 16 success interval.

So, the odds of successfully detecting the gold target 16 times in a row is 0.0015258789063%
and the chance of it happening randomly is less than 0.2%

 

[hung]

Each flip is a separate event whose outcome is not dependent on prior events. Each coin flip has a 50% probability. 6.25% is
the probability of getting 4 heads (or 4 tails) in exactly four flips.

Dude, with only one idependent event you get 50%.
But when you have 4 successive flips being that in the 3 previous flips you got heads and you want one more head, obviously this is the same as wishing exactly 4 equal results for heads. And this probability is 6.25%.

For a probability result of 50%, only if you flipped all four coins simultaneously.

Why are you exposing yourself to ridicule like that?

 

[hung]

Flip a coin until you obtain a second head. What is the probability that the coin be flipped 4 times?

 

[EE THr]

What is mixing up some people is the difference between someone guessing, and nobody guessing.

If the experiment is done only by seeing when one particular side comes up, that's not a "guessing" experiment.

But if the experiment is done by someone trying to guess which side will come up, that's different.

If the experiment is done by trying to guess, heads or tails, for the entire four flips, the odds will be a certain percentage for guessing correctly for all four of the flips.

But if, on the fourth flip, someone makes a side bet, the odds will be 50-50 on that one flip bet, even though the odds for the full set of four-correct are different.

 

[aarthrj3811]

But if, on the fourth flip, someone makes a side bet, the odds will be 50-50 on that one flip bet, even though the odds for the full set of four-correct are different.

Great exlanation EE...So what does flipping coins and side bets have to do with Treasure Hunting ?

 

[hung]

But if, on the fourth flip, someone makes a side bet, the odds will be 50-50 on that one flip bet, even though the odds for the full set of four-correct are different.

You contradicted yourself in your own sentence.
Do you really know what a binomial distribution means?
I could read what you posted through Art's quote.

Try to answer my probability question to Dr. Rudy in my post above. Let's see what you get.

 

[EE THr]

But if, on the fourth flip, someone makes a side bet, the odds will be 50-50 on that one flip bet, even though the odds for the full set of four-correct are different.

Great exlanation EE...So what does flipping coins and side bets have to do with Treasure Hunting ?

Read the topic title.

 

[EE THr]

But if, on the fourth flip, someone makes a side bet, the odds will be 50-50 on that one flip bet, even though the odds for the full set of four-correct are different.

You contradicted yourself in your own sentence.
Do you really know what a binomial distribution means?
I could read what you posted through Art's quote.

Try to answer my probability question to Dr. Rudy in my post above. Let's see what you get.

No, the odds for "guessing" a set of four flips are different than guessing a single flip.

But the odds for merely counting the "heads," without anyone "guessing" are 50% whatever the number of flips are. However, the more flips, the closer the actual results will be to the odds.

Remember, there is a difference between probability and actual results.

And there is a difference between "correct guesses" and "heads counting."

Have you been skipping breakfast again?