Betting system explained on one example:



We allways start with betting 4 units on T and we also bet 4 units on H, if T(first flip) falls, we than bet 3,998 units on T and we also bet 3,998 units on H. If another T(second flip) falls, we than bet 3,996 on T and we also bet 3,996 on H. If another T(third flip) falls, we than bet 7,988 on T.
This is just example, we bet looking at the table above, basically how next H/T falls. After 4th bet. We go to bet no. 1 again, and repeat this to infinity.
Hope is it clear now?


I do not know how to write a simulation. I think that we are calculating some probabilities wrong. Not visible with our eyes offcourse. Very small difference, but I think it is there. Maybe if we do it like this(in our system): no. of combinations/ all combinations we just gave average estimate (very very close to real), but not exact number. And most certainly, that will explain a lot of things in general math also.

If I would think that this system is roullete beatable or anything else beatable I would not publish it here for sure. As mentioned before, small differences...

I replied to Aaron W how betting system works. Hope is it clear now? Maybe it is a bit confusing because I choose 8 combinations for winning ones out of 16. My system would be winning one also if we would just bet on all the combinations that has 2H and 2T.(6 combinations)...

Also, what this means?: "this is a goal post shift."

If anybody see at least small chance that what I am saying is correct (I understand how "crazy" this sounds) and is willing to write a simulation(and share it with me or here) for betting system, which I describe here, that would be amazing (I would assume not all the RNG are good?). If anything is still unclear how betting system works, please ask me. I am not paying anything to anybody (and if it turns out that my theory is not correct: you will doing it all for free and you will waste a bit of a time also). If it turns out that this system is a winning system, than this is game changer at maths and it is huge thing (and you will be first one to test it). If a person who will do a simulation, will find out that this is a winning system, please do not clame this as your discovery (I have this covered allready).

This example is not understandable. I still can't even figure out what you are betting on. Write out exactly what you do step by step. Explain it like you are explaining it it to 4th graders.


I cannot figure out what you are trying to say. But i'm perfectly willing to bet a lot of money on the house's side in a roulette game at any major casino if you want to bet against me.

Wanna add(just for better understanding):

Let us say that we have result for simulation: THTTTHHHTTTTHTHTTTHH.... We look at the groups of 4 coinflips. We check first group of 4 coinflip, win or loss(does not matter), we go to the next group of 4 coinflips. That is in this case: THTT(1. fr.),THHH(2. fr.),TTTT(3. fr.),HTHT(4. fr.),TTHH(5 fr.). We would win our bet in 3 our of 5 in this case. That is 60% of winnings. Winning frequences are 3,4 and 5.
The frequence that I bolded is not winning for us THTTTHHHTTTTHTHTTTHH..

Did you read everything what I said? Please people read whole post.

I quote myself:
I quote you:
???
Again: My betting system is not beating roullete or beating anything else in the casino. It is not aprox. 3 percent house edge beatable... Maybe my system is beating the game that I meantioned at first post of this thread.

Wanna add:

If bold number in the upper quote, will turn out to be more than 50% in the simulation, that would be proof that for example:
GTO is not superior strategy in poker(not allways) vs some other strategies... I see you people debate this a lot. I also see that some of very smart people think that some other strategy is better.... Maybe somebody is interesting in simulation result, because of a reason mentioned in this post.

Hey PIMP did you get charged extra for your 23andMe testing?

I think I might get it. You are basically betting that the 4th flip in sequences of 4 flips will land in such a way as to make the 4 flip sequence one of your 8 favored sequences. So you essentially pass on the first 3 flips of the sequence (or bet both sides if you must bet), and then risk your money on the 4th flip betting that it produces a favored sequence of 4.


So 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

HHT you bet T

TTH you bet H

HTH you bet T

THH you bet T

HHH you bet H

Or more simply, you bet that the 4th flip of a 4 flip sequence makes the sequence either all Heads, all Tails, or exactly 2 Heads and 2 Tails.


Is that the basic idea of your system?



PairTheBoard

This example is saying that when three consecutive coins fall the same, then bet that the next one will be the opposite. That is classic gambler's fallacy.

Your other unclear explanations all seem to rely on the same concept, that past flips dictate what coin to bet on next. This even a betting system as the examples all use flat betting. It's merely betting on what you think is "due" to come.

Please explain how this is not what you are doing.

This kind of sounds like you're saying that if the simulation doesn't go your way, you're just going to tell me that my RNG isn't good enough.

This is what is meant by goal post shifting.

you: if X is true, then my theory is right
me: proves X is false
you: ok, but X is not the right thing, actually if Z if true then my theory is right
me: proves Z is false
you: ok but Z wasn't really the right thing, we have to look at A
and so forth

No. You have not replied to me about how the betting system works.

I am asking you to describe your wagering system in the following manner:

You have not done this.

I think I understand the system. He decides which to bet on by which one will get him to one of the endpoints that he wants. He wants to do 4 flips, ending either with 2 heads, or with 4 heads or 4 tails. See PairTheBoard's post.

It *sounds* like for bets 2 and 3 that he bets both sides. I don't understand why you'd do this. Maybe not betting is not optional in this scheme.

Then on the 4th bet you bet on the one that gets you to one of "our" sequences.

He laid out the amounts to bet each time
1st bet: 4 on T
2nd bet: 3,998 (on both?)
3rd bet: 3,996 (on both?)
4th bet: 7,988 on whichever meets the criteria

(I *really* wish he would settle on a 1:1 payout instead of 1000:999 so we don't have this decimal nonsense above)

Okay, I think I see that part.

I'm just going to assume we sit out bets 2 and 3 because why bet both sides and lose money?

I'm just going to do type up this whole thing with a 1:1 payout, since it's not obvious at all what the 0.001 does except make it a -EV game. The same strategy should do better if the payout is better.


1.HHHH = +4
-- 1st (Bet 4 on T, lose) = -4
-- 4th (Bet 8 on H, win) = +8
2.HHHT = -4
-- 1st (Bet 4 on T, lose) = -4
-- 4th (Bet 8 on H, lose) = -8

3. HHTH = -12
-- 1st (Bet 4 on T, lose) = -4
-- 4th (Bet 8 on T, lose) = -8
4. HHTT = +4
-- 1st (Bet 4 on T, lose) = -4
-- 4th (Bet 8 on T, win) = +8

5. HTHH = -12
-- 1st (Bet 4 on T, lose) = -4
-- 4th (Bet 8 on T, lose) = -8
6. HTHT = +4
-- 1st (Bet 4 on T, lose) = -4
-- 4th (Bet 8 on T, win) = +8

7. HTTH = -12
-- 1st (Bet 4 on T, lose) = -4
-- 4th (Bet 8 on H, lose) = -8
8. HTTT = +4
-- 1st (Bet 4 on T, lose) = -4
-- 4th (Bet 8 on H, win) = +8

9.THHH = -4
-- 1st (Bet 4 on T, win) = +4
-- 4th (Bet 8 on T, lose) = -8
10.THHT = +12
-- 1st (Bet 4 on T, win) = +4
-- 4th (Bet 8 on T, win) = +8

11. THTH = +12
-- 1st (Bet 4 on T, win) = +4
-- 4th (Bet 8 on H, win) = +8
12. THTT = -4
-- 1st (Bet 4 on T, win) = +4
-- 4th (Bet 8 on H, lose) = -8

13. TTHH = -4
-- 1st (Bet 4 on T, win) = +4
-- 4th (Bet 8 on T, lose) = -8
14. TTHT = +12
-- 1st (Bet 4 on T, win) = +4
-- 4th (Bet 8 on T, win) = +8

15. TTTH = -4
-- 1st (Bet 4 on T, win) = +4
-- 4th (Bet 8 on T, lose) = -8
16. TTTT = +12
-- 1st (Bet 4 on T, win) = +4
-- 4th (Bet 8 on T, win) = +8

And so in the end, it looks like a 0 EV game is, in fact, 0 EV.

Well, right, but for some reason he thinks probability doesn't work the way everyone else thinks it works. Refer to his notions about using the normal approximation, etc.

I'm reminded of a story I once heard about a guy who claimed to be able to square a circle. (I doubt this is a true story.) But back in the days that recreational math was a thing, some guy claimed to have a really clever method, and mathematicians had a hard time explaining the flaws to him. He insisted that he was right, and would not let it go at their explanations.

So eventually, they just had him do it. And then they measured the sides and told him that it didn't work out. Then he finally accepted the conclusion.

I don't know what the moral of the story is. But I just measured the sides of this square.

If your calculation of 51.6538 % probability for one of your 8 designated 4-sequences were correct then you clearly would have found a way to beat a 0 EV game of independent trials by betting on every 4th flip (since for every 3-sequence there is a possible 4th flip that can make one of your 8 designated 4-sequences).


The mistake you made was to jump to the hope that you might actually have found a way to beat a 0 EV game of independent trials. Instead you should have immediately concluded that you had incorrectly calculated the 51.6538 % probability. nickthegeek explained to you in post #10 that the Normal is a poor approximation to the Binomial for small n like your n=4. And Aaron W. showed you in post #11 that your method of calculation could also be used to get several different answers for the probability you calculated.


However, there is something you can be happy about. You discovered an alternative way to show that the probability for one of your 8 designated 4-sequences happening is 50%; By noticing every 3-sequence has a 50% chance of completing to one of the 8 designated 4-sequences. Of course, just noticing that each 4-sequence has 1/16 chance of happening is easier, but still.



PairTheBoard

Even if the 51 percent was not obviously wrong, all the sequences have to have a matching pair that would be 49 percent, which the system could equally bet against. So, misusing the normal distribution should still have some sequence at 49 percent, for symmetry, unless I am totally off base, which is possible.

What's wrong with all of you?

This sounds like the infamous "John Gabriel" (see the link I added above, or just search google for "John Gabriel maths" / "John Gabriel calculus").

Juk

I've never heard of this guy. Must be evidence of the conspiracy against him.

But my sense of the story was that it was a early or mid-1900s event.

Yes.Exactly what you wrote. I was trying to explain how betting works on every coinflip. Offcourse it is optimal if we do not bet until 4th(just in this case): not betting in flip no. 1, no. 2 and no.3..
I am trying to prove that many -EV can go to +EV(that is why I bet on every flip), but for easier explanation in this case(only in this example at this betting system), this is fine also and a lot easier for everybody to understand.
Thanks for this.

Please read what I wrote.

If TTT: in this system we bet T(on 4th)...
How is this opposite? Or "evening" the game?

Maybe. But it was more of a question because somebody in the other thread said that I should learn doing simulations and that not all RNGs are good for testing(if I understand it correctly. That is why I asked.)

TNX for explanation of goal post shifting.

Let us not complicate. In my example we can also do this (for easier understanding and really only in exactly this betting system and only in this case;otherwise we must start betting at coinflip no.1):


If the first 3 flips of the 4 flip sequence is(we are sit out 1st, 2nd, 3rd flip):


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