Well they would mean something if you tested a system that's supposed to produce a winning probability of say 98 - 99%. Perhaps HFT in some niche areas can reach that.
Either way I'm still wrapping my head around the gambler's fallacy and the Monte-Carlo casino situation:
https://en.wikipedia.org/wiki/Gambler's_fallacy#Monte_Carlo_Casino
"Perhaps the most famous example of the gambler's fallacy occurred in a game of roulette at the Monte Carlo Casino on August 18, 1913, when the ball fell in black 26 times in a row."
Now even under the reasonable assumption of a fair toss (50% probability), getting one side 26 times in a row is not falling under "probability laws" any more, it's a freakin' black swan event.
What you can learn from such events:
- Never bet your castle, even on high probability events (>90%), let alone in the 50% range
- Apply a reasonable limit for "bad luck", say 1 in 10,000 events. For a fair coin (50% probability), that's some 17 tosses. Think if it as "not that unusual" not to get a win in 17 rounds, if the winning probability is 50%. So if you really are sure on that 50% probability, you gotta have at least capital for betting 20 times. But as the Monte Carlo Casino event shows, that's only a rough guideline, in practice you need to have a lot more - I'm taking a risk and saying that having runway for 100 bets ought to be enough.
- The problem with low probability bets is that it takes a long streak of loses to figure out you're wrong. So if you believe the win probability is 50%, you can still lose 20 times in a row and can't disprove that the win probability still is 50%. If you lose 50 times in a row though, then surely it's not 50%. Therefore, go as high as possible in the probability of your bets.