Palestis,
I agree with you that one of the player's great advantages is that he can choose what and when to play. But it's a common misconception that statistical independence only applies between one spin and the next. An "event" could be a series of spins of any length. Say black has hit 70 times in the last 100 spins, that doesn't tell you anything about how many times it will hit in the next 100 spins. Most of the time it will hit less than 70 times in the next 100 spin sequence, but that would happen anyway because it's a relatively rare occurrence. A "trigger" of 70 blacks in the first 100 spins doesn't affect the probability of the number of blacks in the second 100 spins; that's what independence means.
Statistical independence in a series of single events ( like betting Black or Red), doesn't mean that each single event restarts its probability
,
if you, as a player, intend to execute that single event for a number of predetermined trials . Single event probability applies if you play black here, then odd there, then red elsewhere. Or the same table.
But once you decided that you will play black 5 times, until you hit it once, the probability of series kicks in automatically.
That's the definition of probability of series.
Because a silent clause is to stop the trials. if the desired result occurs. And the series ends earlier than planned if the desired result happens.
That's what "at least once" means.
And in that case the probability of the desired result happening at least one, is
1- (.5x.5x.5x.5x.5).
Or 96.875%. Not 50% considered individually each time.
Your example that if in 100 spins black has hit 70 times is not applicable in this argument.
For once it has already happened, and secondly these are not spins that the player has decided to play in a continuous series of bets. That's a series of events the roulette itself produced. NOT THE PLAYER.
What you wrongly assume to support your argument is that after 70 blacks in 100 spins, there are many more reds due to happen.
This logic is not the foundation of a system. A good system at least.
The logic is that after an overwhelming majority of blacks, ONE RED in a series of future spins, should appear at least once fairly soon. That's where the system ends. There is no need to go any further to see that an equal number of blacks is matched against an equal number of reds.
Most likely this is not what is going to happen.
But I surely expect one red to appear, and that's good enough for me.
This logic also applies after a long streak of one EC, ( like 4,5 or 6), and we see it all the time.
Pick any daily results from a casino and you will see that an opposite EC will appear within a few spins after a long streak of the opposite EC most of the time.
Where to witness 5 more blacks after 5 or more already happened, you have to search thru hundreds or even thousands of pages of daily results. Y is that?
Let's not forget that the objective to playing roulette is profit. One step at a time. And stop.
The intention is not to defeat probability.
