Luck vs Skill vs Players?

[pokerpokerpoker]

[QUOTE=Eduardo]You might flip heads 10 times in a row or be 80% / 20% early on , but eventually the tails will balance out.Is it because the coin changes?Is it because the player starts flipping the coin differently?Or is it because of statistical tendencies and the wonder of mathematics, which is not the cause of the next flip, but a scientific analysis of past results as well as a reliable guide to future expectations?

The use of the words "balance out" is a bit misleading and helps to fuel notions like the gambler's fallacy. Actual results do not converge to the expected result over time because streaks in one direction are "balanced" by streaks in the other direction. Eduardo touched on the real reason when he said ...
Once you've flipped a thousand times, even 10 heads in a row won't affect the percentage very greatly from then on.The real reason that actual results converge to the expected results is that those early imbalances become insignificant over time. Those 10 heads in a row are 1% after a thousand flips and 0.1% after 10 thousand flips, etc.For those still counting on that magic "correction", consider this example:You flip a coin 100 times and get 70 heads (70%) and 30 tails (30%). The expected result is 50 / 50.You flip the coin 100 more times and get 60 heads and 40 tails. You now have a total of 130 / 200 = 65% heads and 70 / 200 = 35% tails. Even though you continued to see more heads than expected, your overall result is now closer to the expected result. No correction occurred. In fact, if you had been betting on tails, you would have lost even more during the second 100 flips.Now let's flip the coin 10 thousand times and let's say you got 5100 heads and 4900 tails. Your overall result is now 5230 / 10200 = 51.27% heads and 4970 / 10200 = 48.73% tails. Tails is now an even bigger loser, but the result is now even closer to expected. No correction ever came.These same principles apply to all games of chance, including VP.[/QUOTE]

Great explanation, thank you.

[billryan]

It's not that things balance out, it's that when you get into large numbers, small streaks are insignificant.

Let me illustrate using baseball.
Jos Smith goes 1-5 on opening day and is batting .200 as a result. The next game he goes 5-5 and is batting .600 for the year. He plays regularly after that.
Fast forward to August. He goes into a game again batting .200 and again goes four for four. Will his average go up four hundred points again?

Lets say you are flipping a coin and nine of the first ten come up Heads. Your results are 90 % heads. Your next thousand rolls are 50% heads, 50% tails- exactly what you expected. No rush of tails to even things out, right?
Your results are now Heads-510, Tails 500. Heads have gone from 90% to less than 51%. Tails didn't exceed 50% over the last thousand rolls but somehow closed the gap some 40%.