I will put this discussion from the
other thread here, hope you don't mind @deisik
I think many people misunderstand how the house edge works(or it is I who misunderstands it, but, anyways, I think differently). The house edge is not working against you in particular, because you simply can't, you physically can't, not only play a quadrillion times in a row, like in your example, but you can't play a billion times during your lifetime. And, as you rightly put it, only with the enormous amounts of bets, we can predict with high probability what is going to happen.
In short, one particular player can either win because of good luck, or lose because of bad luck, but the house edge, especially as small as just 1%, has little to do with it.
I can't argue against that. There might be players, that only played dice very few times and they could be overall winning dice players. There are also people, that won millions in a lottery having played only once. But I am just looking at the theory/statistics/math behind it. The majority of people don't poker, play dice or do sportsbets only once, but they always come back and they are probably victims of the math then.
Change your point of view and think of the gambling site operator as a (single) player. They are easily able to play dice gazillion of times. And they will win 1% (if that is the house edge) with every play
on average.
Again, it is not that simple. The "longterm" can mean a thousand years. Within a year or two anything can happen with the best poker player, or sports bettor. Look at the Tom Dwan's performance during the year 2009, for example:
Yes, there are lots of graphs like this to be found from a lot of very good poker players. Quite a few of them were broke at least once during their career. Variance can hit very bad in poker - and for a long time. But Tom Dwan is a multi-millionaire nowadays. Is he a poker millionaire just because he was lucky ? No, he is a poker millionaire, because he mastered the game and played the odds/probabilities (while having the same starting hands - again on average - as everyone else). He surely played millions of hands in his career and the luck factor is negligible for him.