Regression to the Mean vs. Gambler's Fallacy

[12AX7]

How did you make this?

And why?

Seriously.

Hi 12AX7,

You may be interested in this too. There are more sites like that if you do a Google search.

[ThinkQuick]

[ QUOTE ]
How did you make this?

And why?

Seriously.

[/ QUOTE ]

Haha. Its not mine, I swear. I just found it on a quick search.
Why would I have a name like Bill Butler?

I'm just pointing out that there is a lot of monopoly literature as any google search can show you.

[Abbaddabba]

Regression to the mean just implies that the impact of the statistically improbable outcome will be dilluted by the true long run average over time, when repeated indefinitely.

It doesnt say that outcomes will occur at any particular time to compensate for the initial irregularity.

[OrangeKing]

[ QUOTE ]
Regression to the mean just implies that the impact of the statistically improbable outcome will be dilluted by the true long run average over time, when repeated indefinitely.

It doesnt say that outcomes will occur at any particular time to compensate for the initial irregularity.

[/ QUOTE ]

Or to show it numerically, here's the example I always use.

You flip a perfectly fair coin ten times, and it comes up heads all 10 times. So far, heads has come up 100% of the time. The rest of your flips come at a perfect 50% rate, and you will see regression to the mean - without the coin ever "making up" for the first 10 flips. For instance:

After 100 flips: 55 heads/45 tails (55%)
After 1000 flips: 505h/495t (50.5%)
After 10000 flips: 5005h/4995t (50.05%)

Thus, regression to the mean is not contradictory to the Gambler's Fallacy. It doesn't predict that anything will happen to balance out those early flips, just that over time, those early flips will have a negligable effect on the overall results.