Obligatory post on the GF.

http://www.roulettician.com/articles/article3.html

"But in truth, there is no "law of averages". As stated above when explaining bias, it's only "in the long run", or on average that outcomes even out, as shown by the law of large numbers. There is no "law of small numbers".


That is a quote from the article mentioned above.



So if that is true, then if you flip an umbiased penny 40,000,000 times, then heads should come up 20,000, 000 times and tails should come up 20,000,000 times.

I will bet everything that I own that won't happen.

Law of large numbers, law of small numbers and Regression Towards the mean all have to be read together and not in isolation of each other.

Law of small numbers says that in a small sample size any type of bias is likely and variance can be monstrous with or against the player or house. It is very true when we see 25 streaks of Red or no hit of Black for 28 times in a sequence due to reds and 0s occupying all the hits.
Similarly, it can be very bad scenarios like only 24 hits of Red in last 100 spins or 65 only in last 200 spins. Pretty unbeatable with any of the progressions one can use and even 1 million chips are not enough to cover all the cases possible to win just one unit of profit.

Law of Large numbers says that in enough trials, the count of two EC counterparts will be somewhat equal to their mathematical expectancies.

Regression towards Mean says that after an extreme sample of variance, the next sample of equal length is more likely to not be so much biased and more likely to revert towards mean.

            All the three laws or theories are correct if read cautiously and we do not derive our own conclusions from them.

Regarding law of average, it is a pure fallacy that says, after bias towards an EC, gradually they achieve corrective wins and counts of both EC counterparts will be equal in a fair wheel.

           There is nothing like corrections. It may occur, it may not. Expecting corrective wins covering prior losses leads to play in the most erratic manner causing very big losses.

Quote from: tdx on May 15, 2016, 03:04:33 PM
I will bet everything that I own that won't happen.

And you would be right to. I was hoping I'd made it clear that there's a big difference between the absolute numbers of head vs tails and the proportion of heads vs tails.

It's only the proportion which equalizes as you flip more times. The difference between H & T increases, contrary to popular belief.