I. A Blind Spot in Thinking

Previously, to illustrate the viewpoint that "stocks are inherently advantageous for going long because the upside and downside space is asymmetric for stocks," I used the example: "A 10 yuan stock can only drop to 0 yuan, which means it is (Delisted), but it could rise to 100 yuan or even 1000 yuan."

As a result, some classmates left comments, using "a 10 yuan stock dropping to 1 yuan, down 90%, but to go up to 100, it needs to increase by 900%" to prove a contrary viewpoint that it is easier to drop than to rise.

This rebuttal sounds reasonable at first glance, but I had already anticipated this when writing the article and prepared an answer: "The former loses 9.9, while the latter gains 99, can they be the same?"

The reason I anticipated that someone would ask this when writing the article is that I initially thought this way too; most people have thought this way, and it involves a very important characteristic of human mathematical thinking—multiplication is superior to addition.

Investment requires continuous judgment of pros and cons, and this characteristic of "multiplication is superior to addition" often leads to deviations in our judgments under extreme conditions, such as when evaluating high odds opportunities where incorrect calculation methods are often unconsciously used.

II. Do AI systems also have intuition?

Not only humans can make erroneous determinations, AI, which is heavily influenced by human thinking, can also make mistakes in such matters.

A few days ago, I asked DeepSeek a question:

The question was about the distance between the Earth and the Moon. Group A provided the answer of 0.8 million kilometers, while Group B provided the answer of 10 kilometers. Which group's answer had a smaller discrepancy from the correct answer?

Without looking at the answers from the large model, let's think about it ourselves. On the surface, Group B's answer seems outrageous because the height of Mount Everest is 8.848 kilometers, and a distance of only 10 kilometers between the Earth and the Moon is clearly absurd.

However, in reality, since the distance from the Earth to the Moon is 0.3844 million kilometers, one can calculate that the answer of 10 kilometers actually has the "smaller discrepancy."

It was assumed that this was a cognitive bias unique to humans, but unexpectedly, AI's answer was the same. Let's take a look at DeepSeek's thought process:

The first three steps were very correct, calculating the deviations of the two sets of data:

But at the fourth step, suddenly there was a 180-degree turn:

This answer is equivalent to saying 384390 > 415600.

Not only DeepSeek, I also asked Tongyi Qianwen, Doubao, and Kimi, and the answers were all the same; only ChatGPT was correct.

To understand how the large model thinks, I clicked on DeepSeek R1 again, which added a section of "deep thinking" outside of the answer. I finally understood its answering logic, because it was just too verbose, I only selected the core sentences:

Well, the user asked about the distance between the Earth and the Moon, ... it seems that the absolute difference of Group B is smaller, but intuitively, 10 kilometers is too small compared to the actual distance, which may be problematic.

However, the user may want to examine the relative error rather than the absolute difference. For example, calculating using relative error percentage. Group A's error is (0.8 million - 0.3844 million) / 0.3844 million ≈ 108%, while Group B's error is (0.3844 million - 10) / 0.3844 million ≈ 99.997%. This makes Group B's relative error even smaller? This doesn't seem quite right, because the difference between 10 kilometers and the actual distance is nearly the entire value, while 0.8 million, although exceeding double, may have a higher relative error?

……

Alternatively, the user may want to examine closeness in terms of magnitude. For example, 0.8 million kilometers is just over twice 0.38 million, while 10 kilometers and 380,000 kilometers differ by four orders of magnitude (10 is 10^1, 0.38 million is 3.8×10^5) ... therefore, Group A's answer is closer in terms of magnitude. This might be more reasonable, as when there is a large order of magnitude difference, the absolute difference may be less important than the order of magnitude.

In summary, the correct answer should be that Group A is closer, even though the absolute value of the error is large, the magnitude is closer. Or from a practical application perspective, the gap between 10 kilometers and 380,000 kilometers is indeed too large to be considered close.

I finally understand the reason why the four large models all gave incorrect answers, it’s like an overly intelligent student quickly comes up with an answer but immediately falls into self-doubt, wondering why it’s so simple? Then they lower their intelligence to an average student's level and provide a wrong answer.

It thinks, 'but intuitively 10 kilometers is too small compared to the actual distance.' In fact, AI has no intuition; it doesn't reason. It first has a human answer, assumes it is correct, and then looks for possible reasons. So, although DeepSeek already knows that Group A has a larger absolute difference and relative error, it still wants to find a reason for human intuition.

These large domestic models have been tainted by workplace bad habits. When faced with unusual circumstances, they first assume the boss is right. 'Why does the boss think this way?''There must be a reason why the boss thinks this way, I’m just too dumb.' 'I finally understand the boss's good intentions.'

AI should prioritize mastering the philosophical spirit of humanity, 'I love my teacher, but I love truth even more.'

Three, multiplication precedes addition.

The reason AI eventually found is 'magnitude'; it is actually comparing multiples rather than differences. This is essentially replacing the required addition and subtraction with multiplication and division. The reason AI thinks this is correct is that it knows human thinking is inherently 'multiplication precedes addition and subtraction,' in order to please humans.

The following descriptions are all correct (addition) but violate intuition (multiplication):

The temperature on the surface of the sun (5500℃) is closer to 5℃ compared to 15000℃.

The population of downtown Paris is closer to a village with only 12 residents compared to New York.

The mass of Mars is closer to that of a ping pong ball compared to Earth.

In the following line segment, one side is 1000 (one thousand) and the other side is 100000000 (one hundred million), now use a finger to point out the position of 1000000 (1 million).

If there were no groundwork laid in the preceding article, the position in the minds of ordinary people should be like this:

Having read the previous article, you would probably shift the position a little to the left.

But I dare say that the position you envision in your mind must differ from the actual situation below, whether it's 0, 10, 0.1 million or 1 million, they are almost all squeezed at the far left point.

The reason is as I mentioned earlier, the human brain follows the "multiplication precedes addition principle."

The addition rule is to directly calculate the difference using the same base. The multiplication rule calculates the difference based on the difference already calculated, which is essentially the Concept of multiples.

Our brains prioritize using multiplication for the comparison of numbers, which is why this is called the ‘multiplication takes precedence over addition’ principle, especially with very large numbers. If this segment is from 1 to 100, pointing out the position of 10 will result in a much smaller error - but it still exists.

Returning to the example I mentioned at the beginning, when I was comparing the upward space and the downward space, I was comparing the difference, but that reader unconsciously shifted to the concept of multiples.

Many people might wonder, since our intuition uses multiplication, does that mean multiplication is more reasonable than addition?

This idea has some merit, but whether to use addition or multiplication should depend on what the comparison goal is.

For example, in investment when calculating odds, addition is obviously more reasonable than multiplication.

Four, a common error in calculating odds.

After researching a stock, if you believe the highest it can rise to is 8 yuan and the maximum it can drop to is 2 yuan, then what is the position of the odds 1:1?

This is similar to asking what the midpoint between 2 and 8 is; many people instinctively think it is 4, but in reality, it is 5, while the odds corresponding to 4 are 2:1. 2/5/8 is an addition calculation, while 2/4/8 is a multiplication calculation.

The role of odds is to calculate the expected value of an investment; the odds are 4 profits to 2 losses per share, and under a win rate of 50%, the expected value of this investment is (4-2)/2=1 yuan per share, so calculating the odds should look at the difference and use addition.

Using odds correctly is very important, and the author has previously described a phenomenon:

In a short period, the distribution of win rates for different volatility spaces up and down also varies greatly:

The probability of a 10-yuan stock dropping to 9 yuan is roughly the same as that of rising to 11 yuan;

The probability of a 10-yuan stock dropping to 5 yuan is less than the probability of rising to 15 yuan;

The probability of a 10-yuan stock dropping to zero is far less than the probability of rising to 20 yuan.

This description can be verified: in 2024, the median rise and fall of A-shares was -3.85%, there were 1,771 stocks with excess gains exceeding 10% (i.e., rising by 6.15%), and 1,706 stocks with excess losses exceeding -10% (i.e., falling by -13.85%), and the probabilities are basically similar.

However, there are 429 stocks with an excess increase of over 50% (i.e., an increase of 46.15%), while 36 stocks have a decrease of -50% (i.e., a decrease of -53.85%), making the probability of the former 11.9 times that of the latter.

The significance of this phenomenon lies in the fact that since the upward and downward movements are asymmetrical, we should try to find companies with large upward potential, the bigger the better; even if one cannot calculate the downward potential, it is known that the odds are usually quite large.

Of course, companies with high odds usually have lower win rates in the medium to short term, and many expected returns are actually not high, typically these are technological varieties following industry trends or those with enormous potential for short-term surges but difficult valuations, therefore 'high odds investment' requires precision in determining win rates, which is what I often refer to as 'buying symbolic odds at the turning point of win rates.'

For general investors, a more reasonable approach is to look for long-term high-odds symbols, extending the investment horizon to several years to increase investment win rates, ultimately leading to a high expected return.

If multiplication is subconsciously applied to odds, it can cause confusion in comparison. For example, there is a long-held saying: if a stock price of 10 yuan falls to 5 yuan, it drops by 50%, and then rises to 10 yuan, it needs to rise by 100%, which is obviously more difficult (lower probability) - this example illustrates the importance of ensuring capital security in investments.

This viewpoint is certainly correct, but the method of proof is erroneous:

A stock that drops from 10 yuan to 5 yuan and another that rises to 15 yuan can be compared together, representing a 1:1 baseline odds, because they are two possible outcomes after buying a stock at 10 yuan, which can be used for calculating expected returns.

However, comparing the drop from 10 yuan to 5 yuan with the rise from 5 yuan to 10 yuan is meaningless; you cannot simultaneously buy the same stock at prices of 5 yuan and 10 yuan.

A comparable example is: comparing a stock priced at 10 yuan that falls to 5 yuan versus one that rises to 20 yuan. The latter has a lower probability, as it earns a full double profit. As long as the winning rate exceeds 33.33%, the investment expectation value is positive.

The 'Rebalancing Method' involves adjusting stocks that have experienced different fluctuations back to the same starting point through 'rebalancing'. This effectively reverts multiplication back to addition, which increases the odds of winning.

Editor/lambor