We all know of the concept of independent events. Take dice rolls, for example, with the numbers 1 through 6. A roll doesn't mysteriously "influence" the next roll, obviously. That's why if you roll a hundred times without getting a 4, your chances of rolling a 4 on the 101st roll are still 1 in 6. But is it? Yes, they are independent events, but if you made, say, 10 million rolls, you would NOT roll 10 million times without a 4. You would get each number occurring about 1,666,666 times. You WOULD. This is what I think is called the "drift towards balance," and it is undeniable. Does this defy the law of independent events? Is that probability of that 101st roll being a 4 REALLY 1 in 6? You would think that the longer you went without rolling a 4, the more likely the next roll would be a 4, because of the principle of drift towards balance. I was thinking of roulette and that system we were recently discussing. Say the bet is on any number 1 through 7. The odds of getting one of those numbers is about 1 in 5 in a single-zero wheel. The probability of making 20 spins without hitting one of them is about 1 in 60, I believe. So if you look at the history board and see that none of the numbers 1 through 7 have been hit in the past 30 spins, are you more likely to bet on them? Most people, probably including me, would hold up our forefingers and say, "no, they're independent events, silly!" OK, but what about the principle of drift towards balance? Are we denying that?