Gronbog gave a great clinical analogy with the coin flip example. Let me re-share my real life example from early in my career. Apologies to those who have heard it. I think it was my 3rd year of playing for a living, playing very low stakes still trying to build a very small bankroll. I spent my first 2 years playing $5 tables, so my minimum wager was naturally $5. My bankroll had grown just a little bit by this third year, so I was moving up. I was able to play a $10 minimum wager with a small spread.
(Que the Jefferson's "Moving on up" theme).
So I start the year very, very positive. Best possible scenario when moving up in stakes. After about 6 weeks, I was way ahead of expectation. This would be the equivalent of gronbog's first 60 heads out of 100 flips scenario....except in my case the start was so good it was probably 70-75 heads out of 100 flips.
So I was sure a "correction" must be coming. You know like a 30 heads out of the next 100 flips type thing. Had to be....right?
So I cut my minimum wager, spread and ramp, in half, back to what I had been playing for those first two years, figuring I would only lose half as much during this correction that
surely was due.
No such correction ever came. I continued winning for the remainder of the year. Not at the crazy rate I had those first 6 weeks. Much closer to expectation, but I continued winning, with no "correction". By the end of the year, all I had managed to do was win half as much over those final 10 months as I should have. This was basically a wasted year (except for the learning experience) for someone that was where I was trying to grow and build a bankroll.
So I am not a math guy, and I don't know all the formulas and math. But I do know that you are never due to win or lose based on past results. Don't go looking for a correction, but yet, somehow, given enough trials and a large enough sample size, the math will work out to just about where it should be (expectation). Math is magical like that.