The question is why, why a number hits twice in a row while another doesn't hit for 600 spins??

Also the same number which one day missed for long time the next day could be one from the hottest numbers, it's quite paradox if you consider that, theoreticaly at least, all numbers have the same probability to hit.-Blue Angel

It's because of variance. Variance is basically your "luck". Probability and Variance = What may happen. Think of variance as being the square root of the number of trials. In order to account for what variance may do 99% of the time use (3 x the square root of the number of spins).

Shouldn't this probability theory being reflected on the results?-Blue Angel

It is, you just don't comprehend it. If you did, then you wouldn't be toiling around with systems based on the layout.

What is the underlying reason which causes great deviations and instability on the results?-Blue Angel

Again, variance. It's described above.

If your answer is variance, then my new question is what causes variance??-Blue Angel

The degrees of freedom/the number of possible outcomes.

If your answer is randomness then what's the origin and causation of randomness??

Again, the degrees of freedom/the number of possible outcomes. By the way, the only limit to variance is really the size of the sample. For example, you can't get four reds in a row if there are only three spins.

No one would ever get certain answers regarding this matter because it's not like asking what's the sum of 1+1.

I believe in roulette like in almost every other aspect of life timing is essential...-Blue Angel

I've given you the answers above. Why haven't you read more on the history of the game? Why don't you trust what's written down by people like Dr. Thorp?

If any given number, for any reason, doesn't hit within a fixed number of spins why not to replace it with another?

In the random game, it doesn't matter. However in the live game, on a live wheel then you're looking in a better direction.

For example wouldn't be more reasonable to bet the hottest number of any given cycle of 37 spins?

By saying hottest I mean the number with the most hits within a fixed number of spins, the hottest is very difficult to turn into frozen because the cooling down effect happens gradually and not suddenly.

Why only 37 spins? You'd be better off chasing the hottest numbers after several thousand spins, but that would require some real effort. Real effort is something that you're not willing to try.

It's difficult for a number to disappear during the next cycle when on the previous has appeared more than any other, but it's not impossible.

No. It can go from being the hottest number to instantly being the coldest.

Most likely it will hit again at least once, that's what I call gradual cooling down effect, what is hot as fire cannot become ice immediately.

There is not always a gradual cooling. There's simply an increasing spin sample, variance, and changing playing conditions on the live wheel. Such conditions are where you should be looking for answers.

So let's say I select the hottest and doesn't hit within the next cycle of 37 spins, how many times do you think the hottest numbers could turn suddenly in cold??

They can stay cold for as long as they'd like to stay cold. In a pinch, don't chase them past 180 spins. Wait for them to begin hitting again.

Another important fact for numbers with 3+ hits within 37 spins is the gaps comparison from one hit to the next...

If for example the last gap is longer than the previous perhaps means that the particular number starts to fade away...on the contrary if the last gap is shorter than the previous probably is a positive indication.

You can't determine if a number is really "fading" or not. However, on the live wheel you can tell if the current "playing conditions" are possibly changing too much. For example the wheel speed, or the ball.

Just remember, given the time roulette can and it will produce any result, that said the very next spin could never provide certainty for a win, even if you bet too many numbers.

All too often people foolishly try to hedge the negative expectation game. The fewer numbers on which you bet, the greater chance you have of still being a winner after a large sample of spins.

But the degree of certainty increases as the time expands, the more the time you wait for a certain outcome, the better it's probability.

Not sure what you're trying to say here, but numbers don't ever become "due to hit". The probability of winning never changes based on what's hit in the past because the same number of pockets remain on the wheel from one spin to the next.