THis is not true, this is the gambler's fallacy.
The odds of a fair coin being head or tails is 50/50, every time, no matter what the previous x flips were.
If you ALREADY flipped 10 heads, NOW the odds of getting 11 in a row are 50/50 because you ALREADY did the hard part of getting 11 in a row, getting 10 in a row.
You are stating the EV is not positive and is the same. (correct)
You are stating ROI % that implies a positive EV (contradictory and incorrect)
Suppose you make 1,000,000,000,000 rolls and got all heads, for the next head assuming the game to be a fair one, the odds are 50%, and for the tails the odds are 50%.
I think you are taking it in a way where in a probability distribution of say 1000 rolls, ~500 are heads and ~500 are tails, and if you get 100 heads, the next flip would most likely land a tail. This concept DOES NOT apply in this case. Because the distribution you are talking about is INFINITE. Even if the probability distribution happens to be evenly distributed (is it?) say in centillions (tending towards infinity to be stated properly) of hash combinations, it still gives you an astronomically insignificant effect (1/infinity tending to 0)
I understand what you are saying guys but you fail to see the perspective.
Let's look at "life". All life expectancy is negative because everybody will die eventually.
So by your logic nobody can be a billionaire in his lifetime because his life has a negative expectancy, but that is obviously not the case.
So you can have local positive expectancy, while the overall one is negative.
I tend to see probability as a collective of local ones, so the total negative expectancy of a gambling game, is composed of local positive expectancies + local negative expectancies, where the local negative dominates, but that doesnt mean that the positive cannot happen.
Take the inverse for example, if you win 1000 times in a row in a 50% probability dice game:
- did you played agains overall negative expectancy: Yes because the payout ratio was < 1x
- did you had a local positive expectancy: Yes, because you won 1000 in a row. Otherwise you could not have the trend. It was lucky, but it was still a trend.
So if you can jump on a local positive expectancy train, you can win locally, but if you "force" your luck, you will eventually lose.