If the first 3 flips of the 4 flip sequence is:



TTT you bet T on the 4th

HTT you bet H on the 4th

THT you bet H on the 4th

HHT you bet T on the 4th

TTH you bet H on the 4th

HTH you bet T on the 4th

THH you bet T on the 4th

HHH you bet H on the 4th

If we hit our sequence we get +1. If we lose sequence we get -1.

Or like this:We get +1 if next group of 4 coinflip sequences are "ours" and we get -1, if next group of 4 coinflip sequences are "not ours".

But important: not working for us: if a sequence from second to 6th coinflip is "our" sequence, we do not get 1+. So, just next 4 sequences we are interested in.

@Aaron W.

I think now it is clear, if you look what I wrote(no need to bet first 3 sequences; for easier understanding; but really just in this betting system in this case).
TNX for calculating. But I am saying that we are maybe calculating some things wrong. I mean sure our calculations are allmost close to real number, but what if calculating like this (at binomial;at least in some cases): Calculating probabilities with method: no. of combinations/all combinations is wrong in at least some cases and this is just average number. Like mentioned, real results will be very close to real. But what if this are not exact numbers?

Here are some interesting readings:

- https://www.smithsonianmag.com/smart...112-180949559/
- r. von mises,.. what is he saying about randomness
-,...

TNX, but what if calculating like this, we get close to real numbers, but not exact numbers?

Oops. The bold part is not true. Instead of sequences it should be written flips.

To sum some of the things:

I am not a man that take for granted everything that I hear. I think this is correct way. I need evidences. No evidences: I do not believe it... As for this is maths(and I think in this forums there are a lot of smart people), you can prove my "theory" to be wrong (simulation will be very helpfull).

Also this:
let us say we have 3 numbers:
1. number: 0,33
2. number:0,33
3. number: 0,34

Total is 1,

so average is 0,3333333. This does not mean that all our numbers are 0,333333. I mean it is close. But not exactly. We can not just say all of our numbers are 0,333333.
This is the same method that is used in some binomial calculations.

I can paraphrase question:
Give me an evidence that binomial calculations(at least with my betting system) are not average numbers(numbers from my system).

For example I got a number 51,6% with normal approximation. Maybe there is a error there. So, maybe exact number is 50,5%. Tell me why is this wrong?

It is also true that this number will be overlooked by every single stats report, if we would not know what we are looking for. And maybe will be overlooked also due to variance factor.

Prove me wrong?

Thanks...

Ops, mistake. Offcourse the bold part is wrong. It should be three, or it should be written: from second to 5th. or so on...

He's still going strong and will quite often pop up in reddit/stackexchange threads to defend his theories.

Juk

That was me. I only suggested that because the default RNG in a lot of programming languages are especially poor for probability simulations (specifically the use of "Linear Congruential Generator" pRNGs):

Juk

I would probably either use mersenne twister or a hardware random source. But what would the point be? I already know the outcome. It would not convince him.

You say "we" but really, you're the one who is calculating something wrong. Forget all of the fancy calculations that you clearly don't understand and try to focus on the things that you do.

Let me strip my calculation back to skip the first coin flip, and you tell me EXACTLY what you think is wrong.

If TTT you bet T on the 4th
-- 50% of the time the 4th flip is T and you get +1
-- 50% of the time the 4th flip is H and you get -1

HTT you bet H on the 4th
-- 50% of the time the 4th flip is H and you get +1
-- 50% of the time the 4th flip is T and you get -1

THT you bet H on the 4th
-- 50% of the time the 4th flip is H and you get +1
-- 50% of the time the 4th flip is T and you get -1

HHT you bet T on the 4th
-- 50% of the time the 4th flip is T and you get +1
-- 50% of the time the 4th flip is H and you get -1

TTH you bet H on the 4th
-- 50% of the time the 4th flip is H and you get +1
-- 50% of the time the 4th flip is T and you get -1

HTH you bet T on the 4th
-- 50% of the time the 4th flip is T and you get +1
-- 50% of the time the 4th flip is H and you get -1

THH you bet T on the 4th
-- 50% of the time the 4th flip is T and you get +1
-- 50% of the time the 4th flip is H and you get -1

HHH you bet H on the 4th
-- 50% of the time the 4th flip is H and you get +1
-- 50% of the time the 4th flip is T and you get -1

This is a 0 EV game. What part of my analysis (not YOUR analysis) is wrong? There are no standard deviations here. There are no approximations. There is no binomial vs normal. This is *YOUR* assumption that it's a 50-50 coin flip. These are just the raw basics.

Edit:

We *KNOW* precisely what's exact and what's not in your calculation. You've been told and shown the exact statement in the wikipedia post why it's wrong. You've been shown why your normal approximation is wrong.

It's like taking a straight measuring stick but trying to measure a curved line with it, but you're insisting that the line is straight so the ruler must be broken.

TNX for clarifying this.

How do you know this is exact?
Can you prove me this with experiment? I did not see any evidence or proof that this is exact. This is science, so this should be provable with experiment (simulation). I did not see one that I would want to see. The one that I am talking about in first post. As mentioned before, if there is no proof of something: I do not take for granted. I can not just believe, because somebody say something...
Also, not big of a deal if I am wrong, but what if I am correct. I have been reading lately a lot about randomness, there are a lot of smart people that think that we do not understand randomness perfectly. Maybe there is a leak in randomness where I mentioned it...

Can somebody do a simulation?
That would be amazing...(do not feel like arguing about this matter)..
Thanks...

You are basically proposing that flipping the coin is not a 50-50 proposition. For theoretical discussion we assume it is. But suppose the coin is weighted to come up one side more often than the other but we don't know which side is favored. In the extreme cases the coin will either always come up HHHH or always come up TTTT, in which case your system will kill. If your system gets an edge on 1-1 bets regardless of which side the weighted coin favors then I think you have something. Although a simpler system would just be to always bet the next flip matches the last flip.

I leave it a problem for the forum to calculate the success this system has with 1-1 bets for various p values, p=P(Heads).


PairTheBoard

A simulation can not provide an exact result. No matter how many simulations you run, it will never be exact.

So let's say I write a simulation. To avoid, as I said, moving the goal posts, you would have to say in advance exactly what would be required to prove your theory. So, what would that be?

There's a very easy proof if you agree it's a fair coin where P(Heads)=P(Tails)=50%, and that the flips are independent. For every 3-sequence there is exactly a 50% chance the 4th flip makes a winning 4-sequence and a 50% chance the 4th flip makes a losing 4-sequence.


If you deny that then you must either deny that's it's a fair coin or deny that the flips are independent. Which is it?



PairTheBoard

I would say 50,5% plus would do it. And for sure less than 52,5%.

So we flip a coin 3 times. Then we are going to flip the coin a 4th time, but first we bet on either H or T for the 4th flip.

So we have a 50% chance of winning. The chance of the 4th flip being H is 50% and the chance of the 4th flip being T is 50%.

Over how many trials?

It will be really amazing if somebody do a simulation.
If somebody decide to do it...
Please first do a simulation for the mentioned one that I am talking about the whole time(2H2T, TTTT, HHHH).
And than, if this person will be so kind and I hope it is possible also to do the second simulation (you can maybe do this in same simulation; I do not know). Same thing, except without TTTT and HHHH. Exact odds percent for 6/18 to happens is 37,5%. I think more than this can happens. I would really like to see how only 2H2T are doing(4coinflips;like before,...)..

Very much thank you.

I really do not know how this works? Is it harder to make a lot of trials? Like I mentioned, I do not know programming.

6/18 = 0.3 where the "3" is repeating. Just get a calculator and divide 6 by 18. Then multiply by 100. That gets you the percent chance of 6/18. It is 33.3% where the 3 is repeating.

PIMP,

One last thought, and then I'm out.

As has been mentioned previously, each of the flips is independent. There is no causal relationship from any previous flip to any current flip. Without causality you can not have a system of related variables.

After every fair flip, the fair penny is still fair.

Now, I choose not to think you are trolling, but you are enjoying all of this somehow. I think there is a mental problem for you that you can not see that what I and others have pointed out is true. I still do not recommend a simulation because you will always get a noisy answer that leaves you hope and fuels your mental problem.

-Rob

No, but you have to know how many times you're going to repeat each individual "game" in order to make predictions about it.

For example if you repeated the game 1000 times, you'd see 50.5% wins about 15% of the time, just by random chance.

Anyway, I decided to choose a number where getting 50.5% is way outside reasonable chance: I ran it for 1 billion iterations. The result was that you won
50.000415%

I ran it again and you won
49.999897%

Here's the code: https://gist.github.com/rustybrooks/...f7cdbd7921b9a6

It requires a C compiler and CPU that support RDRAND which is a hardware PRNG of high quality.

You run it like
./a.out X Y
where X is the number of times to play and Y is 0 or 1, whether to print the results of each game. (Actually it plays 8*X games, because the random number generator generates 32 bits per call, which is enough for 8 games, and I didn't want to waste any)

So I'd say run it like
./a.out 1 1
which would play your game 16 times and print the result for each one. It prints something like

Try that a few times and you'll see that the logic is right, then try it with something like

./a.out 1000000 0
which will run it a million times and not print each line, just the results. If you print each line it takes a LOT longer to run.