The probability of probability I am trapped by a logic premise. We know coins have no memory and each throw is a independent event. Thus, after 20 faces, it should not really matter what side you bet.
But there is also a normal distribution, and the probability of getting far to the mean. Isn´t there some sort of statistical tendency for returning to the mean? A black swan or something? The roulette record is 35 reds. If you happen to be in the 36th red in 2016, its exactly the same betting on both colors when you know the casuality is probably not gonna continue? Indeed, ine empirical terms a series of 50 reds in contrast to another random pattern is so unusual that im sure any scientist would believe the roulette is not working well, but all permutations are equally probable in the end. 
Isn´t some kind of marginal probability as soon as you get far from the mean? Is it eqully probable to get a face in the next 5 tries when you are at throw 0 than when you are at 25? 
Is it equally probable a particular random pattern of crosses and faces that 20000 faces in a row? Mathematically, an infinite or infinite -1 series of faces is possible. But whats the probability of not being equally distirbuted after 30,3000,30000 throws?

Dice and coins indeed have no memory; in fact, if I show you a coin, you even don't know how many tosses before there was a "face". Is the coin smarter than you?
Note that if you throw a die 5 times, then the outcome $(4,2,5,1,6)$ has exactly the same probability as $(6,6,6,6,6)$. The normal distribution can be derived purely combinatorially: you can just count how many 6-tuples contain "one six", how many contain "two sixes" etc.
You can check all of your questions and concerns yourself, by running a simple simulation.
Of course, with a real die, if you throw it 10 times and you get 10 times a "six", then it is very likely that the eleventh will be a "six" too, that is, the die is not fair.
