Originally Posted by bluem3
I have flipped a coin before and out of 10 flips I could get 7 heads in a row however after a 100 flips its more like 45/55, after how many hands dealt we would see this even out? Let's say i haven't gotten aces in 600 hands or I have flopped a boat but the other guy flopped a higher boat. After how many hands we would see this line even out like the coin flip line evening out?
Neither of those is expected to ever even out, on average the gap will continue to get larger in both coins and cards. The proportion of the gap to the total flips is what gets smaller, not the gap size itself. Here's a simple example:
We flip 100 times. Our expectation is 50 heads with a standard deviation of 5. So when flipping 100 times repeatedly, the absolute mean deviation will be approximately 5 away from the expected number. *
Now we flip 10,000 times. Our expectation is 5,000 heads with a standard deviation of 50. So now on average we expect our result to be 50 away from the expected number. We flipped 100x more flips, yet now our average absolute deviation will be 50 away from even instead of 5 away from even. It get's bigger, see?
What does get smaller, is 50/10000 is smaller than 5/100. One is 5% off the mean, and the other is 1/2% off the mean. But that is not "evening out".
So again, not getting Aces in 600 hands has absolutely no effect on how soon you will get Aces again. How would the cards "know" that you were due? Look up Gambler's Fallacy for more detail.
* yes I know the SD is not always exactly the same as the mean deviation but it's very close