Yes, sorry, you are correct. I meant 6/16, same number combinations possible.

OK, I do not know why you are writing here if you do not like me. And most certainly, there is no need to insult me...

Well, then that is the answer. Something that happens with odds of 6/16 happens with a percent chance of 37.5%. 6/16 = 37.5%

Woow. Thanks man. You are the best. Yeah, that is the proof I was looking for. Nothing like I was thinking/hoping.

Also a question, because I do not understand exactly what script is about. Did you write it in a way that the bold part does not count(for winnings and for losings)? For example:TTHT,HTHT..
Only four, than next four and so on(starting with no.1 coin flip)?

It does them in batches of 4. It basically takes a series of 4, then breaks them into a 3-sequence, looks up what we would have bet on for that sequence, and then checks if the 4th matches

TNX for this. This is exactly what I wanted. I can not tell you how much thankful I am, that you took your free time and wrote a simulation and helped me a lot. Really appriciate it.

Yeah. I understand it now. To be honest I was thinking they are "some how" connected = if we group them. But yeah, I know... Thanks for taking your time in this thread and for your every post.

Yeah, I see now(with proof) that our binomial calculations are not aprox.(very close to real), but are exact.

@to all
Thank you everybody for every single constructive post in this thread. Appriciate it a lot. I have learned a lot. I hope every reader or poster that was passing by has learned a lot also.

I was just looking in slighty wrong direction about how to exploit randomness...


I can basically prove this is wrong in the case I mentioned, but instead of 2H2T, TTTT, HHHH, we only take 2H2T(4 flips again). So 6/16 possibilities. We have same betting system(expect it is modified that it does not contain HHHH and TTTT). We start betting at 1st flip.
In this case winning will be more than 37,5%.

Also, I mean offcourse if we calculate in the way everybody is doing right now is just very very close to real(avg) and not exact. And yes we prove this is possible: many -EV into +EV...

And I can prove this without needing any simulation. Just maths....Will post it here soon for debate...
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I just needed to write this here. So, I am the first one to prove this(to make equasion for this). Just in case somebody else is close.

Please no.

Sorry, no. I modified the program above to exclude TTTT and HHHH, ran it twice with a billion iterations, and it came out
37.499160%
37.499758%

If you're going to try to "prove" something you need to start out by clearly stating precisely what that something is you want to prove.

Exactly what do you mean by "is just very very close to real(avg) and not exact.".

When you say "many -EV into +EV" do you realize that EV, by definition, is what the average converges to over many trials? So if that EV is negative (-EV) that is already a statement of what happens over many trials. You lose.

If you want to prove something mathematically I strongly suggest you first study mathematics and lots of mathematical proofs.


PairTheBoard

.

There really is no debate. The math has already been worked out. The only mathematical thing that has happened so far is that you've misused some formulas because you didn't understand what you were doing.

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I guarantee that you cannot prove that something that happens with a 6/16 chance happens with a chance other than 6/16 because if it happens with a chance other than 6/16, then it does not happen with a chance of 6/16.

Nobody else is close.

Hi.TNX for this.
I really do not want to post some wrong theory again. That is why I rather ask before.Anybody else is very welcome to help me also with my questions also.

If you run a simulation like descbribed in this post(for a billion trials)? You allways get a number that is lower than 37,5%, right? Or no?

I also do not know if this method that you used will give same results, as for example if script will be written in this way: new 4 flip seq. every time.. 2H2T/all combinations. Maybe different if like this.. Because this is what I am looking for.

Hi. TNX for your help.

Yes, I know.
I mean that we are maybe calculating probabilities wrong. The numbers that we get with no. of combinations/all combinations are maybe not exact number.

As a physical matter, it's possible that coins are not perfectly balanced for flipping. Depending on the methodology used, it's possible to bias results slightly depending on the way that the coin is manufactured. For example:

* The edges of coins are very slightly beveled so that they release from the mold properly, which slightly biases them if they spin on a table before settling.
* The weight of each face of the coin may vary slightly, causing bias as the coin bounces/spins before settling.
* There may be physical defects for any specific coin that is being flipped that may cause bias.

But none of these physical features will be captured in a simulation. There have been various studies of this bias that you can look up for yourself. These are all dependent upon the specific coin itself.

However, the larger point is that the math is still precise in the sense that once the bias is known (say, 50.5% heads/49.5% tails), the math can be worked out. And the bottom line is that if you have a coin that's biased towards heads, then if the payout is even money you gain an EV advantage by just betting heads ALL THE TIME. All the fancy waiting to see X tosses before making a wager has ZERO impact on the outcome as long as you believe that the coin flips are truly independent of each other (by definition of what independent events are).

All of this is understood under the existing framework of probability. As much as you may want to believe you have some super-clever insight that completely destroys everything we know about probability, the reality is that it's highly unlikely (especially given the depth of knowledge we have in this area) and that it's far more likely that whatever "system" you think you come up with is either wrong or easily explained in the existing knowledge framework.

Edit:

No. The fact that you think two consecutive results that are just below 37.5% (on the order of 0.001%) is a pattern that can be extrapolated is a strong sign that your basic understanding of probability is flawed. There was about a 25% chance of that happening.

It might be worth your time watching this playlist:

https://www.youtube.com/playlist?lis...ar3GQVfZD4SlbX

and lecture 1 of this playlist:

https://www.youtube.com/playlist?lis...Q6ht66KWxbzTIo

and lecture 4 of this playlist:

https://ocw.mit.edu/courses/electric...ideo-lectures/

Juk

No

It uses a new 4 flip sequence every time. We've been over this more than once.

@jukofyork, RustyBrooks, Aaron W.

TNX all of you.

Excellent summary

I really do not want to troll(because you were really helpful), but if you did it like this:
"It does them in batches of 4. It basically takes a series of 4, then breaks them into a 3-sequence, looks up what we would have bet on for that sequence, and then checks if the 4th matches."
and than give out HHHH and TTTT.. This is not correct way. In previous system was possible to bet on only last flip because it has exactly 8/16 combinations.

I modified betting system for only 2H2T:

(I made it for 0EV game, so I think it is easier to understand). Here is example how it works:

We allways start with betting (we allways start with 6 units;we look at the line: on every flip) 3 units on T and we also bet 3 units on H, if T(1. Flip; we have 6 units) falls, we than bet 2 units on T and we also bet 4 units on H. If H (2. Flip; we have 8 units) falls, we than bet 4 units on T and we also bet 4 units on H. If H(3. Flip;we have 8 units) falls, we than bet 8 on T. If T falls(4. flip) we have won 16 units. Offcourse, we can miss a bet at a flip when a line tells us that we need to bet same amount of units on H or T, but because this is example how betting works I did not make any simplicity.
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And as mentioned before, I do not think simulation will be needed. Will post here a bit later...