Law of Large Numbers, and being "due".

[BeerMoney]

Our experiment will be that we flip a FAIR coin N times, and on one side it has -1 and on the other it has a 1. Let x be the sum of the N flips... Let Y be the average of those flips... Both E(x) = 0 , and E(Y) = 0.. That is, in the long run, we expect both to be zero..

Consider if we flip the coin 50 times and all 50 times it is a one! Now, X = 50, and Y = 1. Well, what if we flip the coin another 50 times.. Now, what is E(X) and E(Y)? For those next 50 flips, we still expect both the totaland the average to be zero.. So, When we finish those fifty flips, we still "expect" the total will be 50+0 =50, but we would expect the average to be (50+0)/100 = .5. Same logic, consider if we flipped 999,950 more times... We would expect the total to be x = 50 + 0= 50, and y = (50+0)/1,000,000= .00005.

Point: The average is going to zero AS A LIMIT. However, we don't expect to experience a -50 downswing at somepoint, just because we had a strang occurence of a +50 upswing.

I hope this made sense..