Maybe something that has "betting odds" at 6/16, can happens in exact:604/1600...

My simulation merely determines whether your chosen flip after the first 3 came in more than it was supposed to (no, it didn't). I ignored cases where you had TTT or HHH after 3 flips, which is why it came up to 37.5%

I'm not going to come back to this thread any more. You can waste your own time if you want, but not mine.

Your betting system is designed to win 10 units if the 4 sequence comes up 2H-2T and lose 6 units otherwise. Therefore it is equivalent to just betting 6 units at 10-6 odds on the 4-sequence coming 2H-2T. By Rusty's simulation you know you will win that bet as close as you wish to 6 out of 16 times if you make the bet enough times. That's why we say the probability is 6/16.



PairTheBoard

And did you calculate your EV? It looks to me that your EV is exactly 0, just as one would expect under the assumption that this is a 0EV game with every single decision at every single decision point being 0 EV.

This has been discussed already.

It's *possible* but that would be due to the nature of the coin being flipped and having nothing at all to do with the calculations you're thinking that you might be doing.

@RustyBrooks

TNX for clarifying.

@PairTheBoard, Aaron W.

Yes, thanks for explanation both, but this is exactly what I am trying to say that we are maybe doing wrong. I calculated EV for my game(sure it is EV0 game by calculations). I understand how "crazy" is what I am trying to say(hope the people that are giving me amazing replies are not thinking that I am trolling): -EV,-EV,-EV,-EV=+EV(I know this is "impossible" by our understanding of maths:I know that this is like basic rule of a math). Like you both mentioned I am also not the most schooled-man (sometimes I am not using correct terms and I am not english native) for a job(but I do not think I need PHD for trying to do something).

I have been reading about randomness for about 2 weeks now. There are a lot of really smart people that think that we do not understand randomness complety. For example: if not understanding randomness completly is maybe a problem(a lot of smart people think that), I think one possibility is that we are doing something wrong with probability calculations. So, why not try to solve this problem(I know how "crazy" "problem" I am trying to solve), but since I am allready reading a lot about this, why not give it a try. I do have one theory(if this one is not correct:Not big of a deal, but at least I tried(but I actually think It may work); If this one will not be correct I will just move on and never wrote about "exploit random" theories and not think about it either).

I think it is pretty cool that I am trying to do something(trying to make a difference in the world;and than debating with smart people about it: like for example you both are and many others here), even if theory is turned out to be wrong one. I think this is a lot better than just troll, like some posters do(not reffering to you both; you are both very helpful and some other posters also; TNX for this). I will be happy also with this: Maybe somebody that is reading this thread, will find out something usefull in this thread and maybe use info from this thread in some matter that is not related to this..

This paradox is very interesting for me:
Parrondo´s paradox:
https://en.wikipedia.org/wiki/Parrondo%27s_paradox
Especially the game under this tittle(aprox. middle of mentioned site):
A simplified example

This has nothing to do with the sum of the EV of events. If we are calculating probability wrong, that would affect the EV of every single event. It would not affect how you add up the sum of those EVs. That is simple addition.

So your thesis is that a coin flip is not 50/50. As has been said, that is possible with physical coins, but it is not possible with a truly random virtual coin flip. And it is not possible to calculate this wrong. Two equally possible events have a 50% chance, period. No way to argue that unless we don't know how to divide by 2. I think we do.

Maybe.
_____________________
I opened new thread about theory (Exploit Random Theory) that I have been talking lately(I think it deserves it). Not same theory as from this thread´s first post. Here it is link:
https://forumserver.twoplustwo.com/4...es-no-1720209/

The difference with Parrondo's paradox is that the game itself changes between wagers. That's not what the repeated coinflip problem is.

Ironically, you want to believe that there's something Parrodo's paradox, which is based entirely on probability theory, while simultaneously thinking that there's something inherently wrong with probability theory.

Furthermore, there *are* philosophical questions surrounding randomness. But those are philosophical and not mathematical. So if you want to come at it with a problem, you're going to have to raise philosophical objections and not mathematical ones.

Ultimately, you're in a position where you can believe whatever you want. Distrust probability calculations even though it has been thoroughly tested both empirically and theoretically for a few hundred years. Whatever. It's all in your head anyway.

Also, you should read the full wikipedia page. The actual name os "parrondo's apparent paradox" because there's not actually a paradox. This appearance of a paradox happens because you're using math that works for independent events on events that aren't independent.

And p isn't 50%