Anyone want to guess the win rate of a coin toss? (AI is crazy lol)

The text below is based on an article I read.
The content seemed quite interesting, so
I asked Claude to write it up
so I could post it here. hehe
For those who can't sleep, have a look~
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Let's play a simple game.
We toss a coin: if it's heads, you win 1,000 won; if it's tails, you lose 1,000 won. It is a perfectly fair coin. No manipulation.
Before we start, we set these rules: Stop if you win 100,000 won, and stop if you lose 50,000 won.
Now, what is the probability that you will walk away smiling with a 100,000 won profit?
.
.
.
If you thought it was 50/50, you are wrong. The answer is **33%**.
The coin is fair, so why is it one-third? The calculation is as follows:
My tolerable loss ÷ (Loss + Target profit)
50,000 ÷ (50,000 + 100,000) = 1/3
That's it. That's all there is to it.
In other words, the ratio of how much you are willing to risk versus how much you are aiming to gain determines your win rate. It doesn't matter whether the coin is fair or not.
Here is the chilling part.
Apply this directly to the stock market. There are people who put in 10 million won in seed money and say, "I'll sell if I make 20% and cut my losses if it drops 10%." In this case, the probability of hitting your stop-loss first is two-thirds. No matter how well you analyze a stock, if the ratio is designed that way, you will hit your stop-loss six or seven times out of ten.
"I keep my stop-loss short and aim for big gains" might sound cool, but mathematically, it is a structure that leads to frequent failure.
Let's take it one step further.
Have you ever heard the saying, "If I lose, I'll just double my bet next time and eventually recover"? This actually has a name in mathematics. It is called the Martingale.
And there is a mathematical proof explaining why this doesn't work.
In a fair game, no matter how you decide when to stop, the expected value is 0.
Whether you double your bet, only bet during winning streaks, or enter after three consecutive losses—no matter how sophisticated your personal rules are—it's all the same. The average doesn't move. Only the shape of the distribution changes. You either win small amounts frequently and lose big occasionally, or vice versa.
Therefore, you cannot create an edge through "timing rules." An edge must exist within the game itself.
Furthermore, casinos aren't even fair games to begin with. The expected value is designed to be negative from the start. People are trying to win at a negative game when they can't even win at a fair one.
Stocks are a bit different. The decisive difference from gambling is that because companies actually earn money, the expected value of the entire market is positive. That is why long-term holding of an index works.
However, day trading has little to do with that positive expectation. It is closer to the coin toss mentioned above, but with transaction fees added.
To summarize:
The shorter your stop-loss, the higher the probability of hitting it.
No matter how much you refine your trading rules, you cannot create an edge that wasn't there.
The edge must be within the game. If it's not there, the answer is not to play.
It turns out that "luck" isn't just a lack of rules. It is simply a rule regarding probability distribution, not just the outcome.