Lior, your opening post shows a profound lack of understanding regarding statistics
“Isn’t it amazing? If you flipped a coin ten thousand times the odds are unlikely that there would be within a small margin roughly the same number of heads as tails.”
If it is an even coin the odds are extremly likely that the spread will be close (not exact) 50/50
As PAA points out over a short period you will get a wider distribution, and this is in fact the case (OF course short period is relative given an infinite number of coin flips 10,000 is a VERY short period)Though short period isnt the best term, few number of “flips” is better and this is the case. Consider a couple that has 2 children over the course of a year (or so) it obviously is not unusual if both are boys or girls, we see that often. But as the number of flips grows the closer to 50% you’d expect as in fact occurs. Even every year the number of “flips” isnt small in the U.S. alone it is around 4,000,000. And as expected it is near 50/50. But if you break down that statistic by State/County/City/Neighborhood/Block etc… You will find a wider spread in some areas (like the couple that had 2 children both boys) that “even out” over the long run.