That coin flipping analogy is not comparable to active trading. I'm going to paste a comment I made on this topic less than a month ago: https://news.ycombinator.com/item?id=13303395

In addition to the comment pasted below, others in this thread have shown that the actual odds of someone consistently beating the market for decades becomes 1 in billions or even trillions. Yes, there are very few traders and funds that consistently beat the market, but there are enough that it seems implausible to be due to chance when you do any reasonable math. You would need nearly the entire human population trying and failing at beating the market in order to justify the number of demonstrable winners we can observe as mere chance. It's much simpler to assume that 1) market inefficiencies exist and 2) some individuals have the technical skill, domain knowledge and/or business acumen to repeatedly capitalize on them.

I don't understand why this coin flipping analogy from efficient market hypothesis keeps popping up. We can clearly see that funds like RenTec exist, and average 70% returns year over year for literally decades. It's an attractive idea, but I've never seen anyone who puts it forward do any empirical calculation. The claim is essentially, "Get enough monkeys slinging poop in a room full of typewriters and you'll eventually get Hamlet." If you want to cast doubt on the fundamental possibility of people beating the market, at least least try to claim that these successful funds/traders illegally trade on insider information. Don't use the same analogy that is basically indefensible under real scrutiny.

Comment below:

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Yes, that's the classical coin flipping example from the strong position on Fama's Efficient Market Hypothesis. There are several problems with the coin-flipping analogy:

1. As stated, it's not falsifiable. So you start with a conception of the market as entirely random, and you observe that participants are consistently beating this market. Each time you observe someone beating the market, you chalk it up to the probability distribution. "Well, that's just a two-sigma event." Then you see it happen again. "Well, that's just a three-sigma event." Then again, and again, and again. How many sigmas from the average market performance are you willing to accept before you agree that someone is legitimately and purposely beating the market with a skill-based mechanism, not a chance-based mechanism?
Furthermore, do you have the numbers to turn this into a falsifiable claim? What is your time interval? Daily, weekly, monthly or annually? How many correct forecasts do they have to make ("how many sigmas from the average"), compared to the chance expectation of coin flipping over the same timescale? If you don't have these numbers handy, then it's purely a thought experiment. Subsequently, the observation that funds like Berkshire Hathaway, Bridgewater, Renaissance Technologies, Baupost Group, Citadel, DE Shaw, etc. consistently beat the market for at least 20% net of fees over 20-30 years suggests that, per Occam's Razor, people can beat the market due to skill.

2. The analogy is not comparable to active trading. You don't need to hit 20 heads in a row to beat the market consistently, you just need to hit a p-value number of x heads correct for y coin flips greater than chance would suggest. We don't assume that basketball is a game of chance if the players can't make all their shots in a row; nor do we assume that baseball players with a 0.3 batting average aren't clearly better than the average high school dugout. If your trading interval is weekly or monthly, and you're consistently up over the market (even net of fees!) for 240 months or 360 months, it doesn't matter if every single month was a winner.

3. Have you ever read Warren Buffet's response to the EMH assertion, as postulated by Fama?[1] He outlined an excellent rebuttal in his 1984 The Superinvestors of Graham and Doddsville. Essentially, if you assume that the coin flipping analogy does map to trading, then you should expect to see a normal distribution of the winners, given that the market is inherently random and no one is achieving superior coin flips through skill. However, if you observe that the winning coin-flippers consistently hail from a small village with standard coin-flipping training, then it is more reasonable to assume that there is something unique about those particular flippers. This is what we see in reality - yes, most amateur traders fail miserably, and yes, most hedge funds underperform the market over time. But there is a relatively small concentration of extremely successful funds and traders in an uneven distribution.

4. Even Fama has walked back on Efficient Market Hypothesis, and no longer espouses the view that the market is inherently random. It is deeply complex, yes, but it is not efficient, nor entirely random. Several studies have been conducted to empirically examine EMH, and the results in favor of the hypothesis are dubious.[2][3][4] A much more charitable retelling of EMH is the weak position, which essentially states that any obvious alpha will be quickly arb'd out of real utility, but that non-obvious alpha, or alpha which is technically public but not easily accessible will retain utility until it becomes obvious. This also maps more cleanly to reality, in which trading on e.g. news reports is mostly unprofitable (everyone can get a news report at around the same time, for the same level of skill) whereas mathematically modeling pricing relationships can be extremely profitable (doing so accurately requires public, but mostly unclean data and a great deal of skill).
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1. The Superinvestors of Graham and Doddsville - http://www8.gsb.columbia.edu/rtfiles/cbs/hermes/Buffett1984.....
2. Investment Performance of Common Stocks in Relation to Their Price-Earning Ratios: A Test of the Efficient Market Hypothesis - http://onlinelibrary.wiley.com/doi/10.1111/j.1540-6261.1977.....
3. The Cross-Section of Expected Stock Returns - http://onlinelibrary.wiley.com/doi/10.1111/j.1540-6261.1992.....
4. International Stock Market Efficiency and Integration: A Study of 18 Nations - http://onlinelibrary.wiley.com/doi/10.1111/1468-5957.00134/a....