This article is very long, but it is worth your time to read it in depth. It tells many ways of thinking that will affect your life.
The author's old metaphor
Source: Lonely Brain (ID: Lonely Brain)
1
Eight solutions to an interesting problem
This question is more interesting than expected, and there are the following eight answers:
1) According to the expected value theory, the green button is worth 50 million yuan;
2) Many people are still willing to choose the confirmed 654.38+00,000, because they can't stand the 50% chance of getting nothing;
3) In other words, if a person can't afford "nothing", then the choice on the right is equivalent to "you have a 50% chance to get a billion dollars and a 50% chance to die". Of course you can't bear to die, not to mention a 50% chance;
4) Open your mind. If you have the option, you can sell an option worth 50 million to someone who can afford it, such as 20 million (or even higher).
5) Continue to optimize the last item. Considering the possibility of "finding someone who is willing to buy your option", you can sell this right with only 6.5438+0 million yuan (low down payment), but the buyer is required to share it with you with/kloc-0.0 billion yuan;
6) Further, you can make this option into a lottery ticket for public offering, chop it up and retail it, and print 200 million copies for two yuan each. The first prize is 100 million. Contrast 5, the risk is lower and the income is greater;
7) In view of the successful business model, we started to raise the next 1 billion as the first prize to make it a business.
8) According to the P/E ratio, 2 billion yuan was raised for listing, with a market value of 654.38+00 billion yuan.
2
Three Concepts of Risk Decision-making
From 65.438+billion to 65.438+billion, let's jump out of the game of brain teasers and study the serious mathematical principles behind it.
There are three concepts in risk decision-making in economics: expected value, expected utility and prospect theory.
Expected value: In probability theory and statistics, the expected value of a discrete random variable (or mathematical expectation, or mean, also called expectation for short, called expected value in physics) is the sum of the probability of each possible result multiplied by its results in the experiment.
In other words, the expected value is the average of the equivalent "expectations" calculated by repeating the results of random experiments under the same opportunity. (from Wikipedia)
For example, if you roll a six-sided dice, the expected number of points is 3.5, and the calculation method is as follows:
Expected utility: In microeconomics, game theory and decision-making theory, expected utility is a utility theory, which means that under the risk situation, the choice made by individuals is to pursue the maximization of a certain number of expected values. This assumption is used to explain the expected value in gambling and insurance. (This concept was born to solve the "St. Petersburg Paradox")
Prospect theory: In the 1970s, Kahneman and Tworsky systematically studied the prospect theory. For a long time, mainstream economics has assumed that everyone is "rational" when making decisions, but this is not the case in reality; The prospect theory adds people's asymmetric psychological utility to the conditions of income loss and occurrence probability, and successfully explains many seemingly unreasonable phenomena.
Based on the above theoretical basis, I want to throw out a few consciously interesting conclusions:
1) the principle of anti-humanity "every step is taken according to the overall optimal probability" is the first secret of successful people in the traditional sense;
2) The poor sell their "probability right" to the rich at a low price, and the probability right is a more hidden and greater exploitation of surplus value (which does not mean that I agree with the concept of surplus value);
3) At present, the popular artificial intelligence relies on each step to calculate the optimal probability independently and in cold blood, thus defeating human beings. Such as alpha dogs;
4) However, irrationality and impulsiveness may become the last bastion of mankind. (I'll write this separately later)
Go through the basic concepts first.
three
Expectation theory (the basic decision-making tool of the wise)
According to the expected value theory, 100% probability of getting 50 million is the same as 50% probability of getting 1 000 million.
Bayesian theorem is one of the most commonly used simple formulas for smart decision makers.
Note: "The probability of loss is multiplied by the amount of possible loss, then the probability of profit is multiplied by the amount of possible profit, and finally the former is subtracted from the latter. This is what we have been trying to do. This algorithm is not perfect, but it is as simple as that. " (Buffett)
Example a: (from the biography of Rubin, former CEO of Goldman Sachs)
After the merger of the two companies was announced, Unevis's share price was $30.5 ($24.5 before the merger was announced).
This means that if the merger reaches a settlement, the share price from the arbitrage transaction may rise by $3, because Unevis's shares will be worth $33.5 (0.6075×Brady's share price).
If the merger is not successful, Unevis's stock may fall back to around $24.50 per share. The stock we buy may fall by about $6.
We set the probability of successful merger at about 85% and the probability of failure at 15%. On the basis of the expected value, the possible rising range of the stock price is 3 times 85% USD, and the risk of falling is 6 times 15% USD.
3 × 85% = $2.55 (may increase)
-6 USD × 15% = -0.9 USD (possibly falling)
Therefore, the expected value = 1.65 USD.
This $65,438+$0.65 is what we hope to get by putting aside the company's $30.50 capital for three months. This gives a possible rate of return of 5.5%, or an annual rate of return of 22%. A lower rate of return than this is our bottom line. We don't think it's worth paying our company's capital for an annual return of less than 20%.
Rubin specifically explained that this is what he does every day. It seems to be gambling. Indeed, he often loses. But what he wants to make sure is that he makes money most of the time.
Example B: (from the author of Black Swan)
Taleb said at the investment seminar: "I believe there is a high probability that the market will rise slightly next week, with a rising probability of about 70%. But he shorted the S&P 500 futures in large quantities, betting that the market would fall.
His view is that the market is more likely to go up (I am optimistic about the market outlook), but it is better to short (I think the result is not good), because if the market falls, it may fall badly.
The analysis is as follows:
Suppose the market has a 70% probability of going up and a 30% probability of going down next week.
But if it goes up, it will only go up by 1%, and if it goes down, it may go down by 10%.
The expected results in the future are:
70%× 1%+30%×(- 10%)= -2.3%。
Therefore, you should bet, and you have a better chance of making a profit by shorting stocks.
As Munger said, what Buffett does every day is to calculate this simple math problem. It is not so much a mathematical ability as a way of thinking. It is easy to know, but extremely difficult to do.
Example c:
Probability sometimes seems "counterintuitive".
A taxi caused an accident on a rainy night. A witness at the scene said that he saw the car was blue. Known:
1) The accuracy rate of witness identification of blue-green taxis is 80%;
2) Taxis in this area are 85% green and 15% blue.
Excuse me: What is the probability that the taxi is blue?
Answer: The probability that a car is green but regarded as blue is (0.85×0.2), and the probability that a car is blue and regarded as blue is (0. 15×0.8), so the probability that a car is true blue is (0. 15× 0.8)/(0.85× 0.2). )。 That is, the car is more likely to be green.
Is it a little different from your brain intuition? Although our brain works wonderfully, it is immature in some mathematical intuition.
However, the expected value theory cannot answer why the value of the red button is as low as 1 10,000, and many people still choose.
four
Expected utility theory (ambition or fear)
In the paper 1738, daniel bernoulli used the concept of utility and the expected value of the challenge amount as the decision-making standard. This paper mainly includes two principles:
A, the principle of diminishing marginal utility: the better one's possession of wealth, that is, the first derivative of utility function is greater than zero; With the increase of wealth, the growth rate of satisfaction is decreasing, and the second derivative of utility function is less than zero.
B maximum utility principle: under the conditions of risk and uncertainty, the personal decision-making behavior criterion is to obtain the maximum expected utility value instead of the maximum expected amount value.
Back to the case of Wentou. Select the red button, immediately realize 6.5438+0 million, and give up the option worth 50 million. On the one hand, it is "satisfied" with 654.38+0 million. As far as its wealth is concerned, 654.38+0 million has brought an order of magnitude change, which can solve the biggest problem at present and is enough to satisfy.
And there is an order of magnitude more, why is 50 million omnipotent? May be unimaginable;
On the other hand, I want to avoid the risk of 50% zeroing of the green button. The fear of zero is far greater than the expectation of 49 million more.
To be exact, choosing the red button interweaves the comprehensive functions of "expected utility theory" and "prospect theory".
five
Prospect theory
"Don't be an ordinary fool" quoted Kahneman's summary, which won the Nobel Prize for prospect theory:
1) people hate risk when they get it;
2) When losing money, rational people are risk-averse, while "normal fools are" are risk-averse;
3) Rational decision makers' judgment of gains and losses is not influenced by reference points, while "normal fools" often decide gains and losses according to reference points; (For example, rational decision makers don't have to wait until they get back to basics to throw away a stock that should be thrown away)
4) Normal fools usually hate loss.
As behavioral economics studies, social, cognitive and emotional factors will make people make less "rational" choices.
For example, the base of wealth, as a reference point, largely determines that people press red and green.
six
Probability right given up by fools
Stupid people don't know the basic knowledge of probability and can't calculate expectations (based on one of three theories).
Myth 1: I don't understand the law of large numbers.
In mathematics and statistics, the law of large numbers, also known as the law of large numbers, describes the results of repeated experiments.
According to this law, the more samples, the closer the average value is to the expected value. Stupid people always want to make money in casinos, and casinos are just the firm winners of the law of large numbers.
Myth 2: Gambler fallacy
Tworsky and Kahneman concluded:
In real life, people mistakenly associate the independent probability between each randomized trial. Take a coin toss as an example. We know that the probability of getting the pros and cons every time is 1/2, but some people think that if you get the pros and cons several times in a row, the probability of getting the cons next time will be even greater.
People often think that the expected probability distribution as a whole will encounter the same probability locally. This phenomenon of applying the law error obtained from a large sample to a small sample is called the "law of decimals".
Looking back at the stock market crash of 20 15, it was the bargain-hunting that brought fatal blows to investors. After falling so hard, there should be a decent rebound. This is also a gambler fallacy.
Myth 3: Survivor prejudice
It means that the statistical analysis based on the survivors of the incident is biased, because the losers (or "victims") are not selected into the sample (silent evidence in Black Swan), so the whole represented by the survivors is biased (even wrong).
Myth 4: Vividness effect
People attach too much importance to more vivid and easily extracted evidence from memory.
Who should say "bon voyage" to whom? Friend B drives 20 kilometers to the airport, from where A will fly to a city 750 kilometers away.
When leaving, friend B will say to A, "Have a safe trip". Ironically, the 20-kilometer drive home by B is more than three times as likely to die in a traffic accident as that by A.
But influenced by the "vivid effect", it is still B who wishes A..
seven
Probability right given up by the poor
The poor are eager to cash in, unable to meet the delay, and have low expectations for effectiveness.
Harvard professor Cederhill wrote in Scarcity:
We are in a dilemma of scarcity. Once everyone is faced with scarcity, whether it is the scarcity of time or money, we will enter a state of "wait and see", which leads to our scarcity mentality and easily leads to short-sightedness and borrowing for the future. In the end, we are getting poorer and busier.
I once chatted with a buddy, and he said that what we lack most is actually that a father tells himself that you are awesome.
In addition to genes and resources, there may be the following reasons for the emergence of talented people from scholarly families or wealthy families:
1) has a high enough reference point, will not be led by small interests, and can take risks (in fact, it is low probability) to capture high returns;
2) the demonstration effect of a group of people around;
3) Intrinsic power that is ignited.
Compared with the poor, they are less likely to sell their probability rights "cheaply".
So:
1) At the key decision point of the gap between the rich and the poor, the poor gave up their probabilistic rights and interests;
2) The secret of the so-called winner is to stick to the advantage probability and not change the principle of life bet even if you are frustrated repeatedly;
3) Buying lottery tickets is the most expensive self-destruction about probability options, so it is called IQ tax.
If you have more money, you will invest in value, and if you have less money, you will gamble. This is probably the most widely practiced stupidity in the investment field.
Things with small probability are difficult to achieve, but they look easy; Things with high probability are far away, but in fact, the possibility of reaching the destination is much greater.
Giving up one's own probability right and choosing a comfortable small probability is actually subsidizing the "winner" with one's meager resources.
eight
The probability right given up by smart people
In other words: Why do smart people do stupid things?
Smart people can not only calculate the expected value accurately, but also be ambitious. Why do they lose the right of probability and can't live a good life in the real world?
1) Smart people can't escape the "stupid" behavior ridiculed by behavioral economists;
2) Most smart people suffer from "cognitive impairment", and what they want to understand intellectually is emotionally unacceptable.
3) preconceived and smart;
4) The correct way of thinking is not internalized into behavioral habits.
If life is a game of probability, if a series of choices and decisions determine the final outcome, then it seems that smart people should have "innate advantages." But this is not the case.
Probability comes from gambling. Pascal and Fermat's interest in the strange results of gambling led them to put forward some principles of probability theory, thus creating probability theory.
Take casino player 2 1 with the highest probability of "losing" as an example. The secret of making money is:
1) Choose a "friendly" casino (equivalent to choosing the right industry);
2) Familiar with the basic skills of playing;
3) Counting cards like the movie Win 2 1;
4) under the advantage probability, increase the bet;
5) No matter what the result is, the mood will not fluctuate if the above strategies are implemented persistently.
A wise man can do 1-4 well. But the "anti-humanity" of 5 is the weakness of many smart people.
In the casino, you have to face all kinds of interference, such as: the best time to bet but no place, the gambler next door smoking, the dazzling beauty with big breasts, and fear.
nine
Each winner is a human alpha dog.
Google's technical team and professional chess players have jointly studied the chess score of Alpha Dog against Li Shishi, from which we can see how "artificial intelligence" thinks when playing this most difficult intellectual game.
Alpha dog will calculate his winning probability in almost every game of chess. That is to say, for him, every decision point is independent, and Alpha Dog will calmly look for the biggest winning probability at present.
For example, Rubin, Taleb and Buffett mentioned earlier in this article are almost all alpha dogs with human flesh, and they always seem to be "counterintuitive, anti-human and anti-comfortable" by insisting on acting according to probability.
Most smart people don't have this wisdom and great way of doing things.
Fools who are taxed by lottery IQ, and smart people who know the probability but can't firmly implement it, can't escape a trap: desire.
Faced with strong desires, smart people think that their luck will improve their chances of winning. Stupid people think that diligence can make up for it.
The so-called winners are really diligent, but this is not a sufficient condition. Winners are the result of choice, and the secret of their success is attribution afterwards.
Therefore, there is another tax that is more hidden than IQ tax: issuing fiscal and taxation.
This can explain two common "economic phenomena":
1) Why are the commercial streets in China always being renovated and changed businesses? (In contrast, foreign companies rarely change. )
2) Why are a large number of Taobao shopkeepers willing to work hard for 24 hours for an income below wages?
The high rent of shops that change hands frequently on the street and the hard work of online entrepreneurs without paying back are precisely paying a premium for the dream of getting rich.
10
How do you define your own "casino"
Zuckerberg comes from a middle-class family. He can also refuse Yahoo's acquisition of $654.38+0 billion in the difficult stage of the company's establishment for two years.
This is a difficult decision. A few years later, Zuckerberg told reporters that within a year of refusing to buy, almost all the executives left.
Will you get 1000 billion right away, or will you get 1000 billion in a few years? Zuckerberg's previous choice is very similar to the button choice at the beginning of this article. In comparison, Zuckerberg's green button (penalty for losing) is much more cruel.
The secret is that Zuckerberg is not faced with the choice of 65.438+0 billion and 65.438+0 billion, but the choice of sticking to or giving up his dream.
A few years later, snapchat rejected Zuckerberg's $3 billion offer in a similar way.
No matter how it ends, this is one of the spirits of Silicon Valley. It's hard to drive a big career just by dreaming of making a fortune.
Wealth, ambition and vigor surpass the greed of economic animals, and the probability of success for them to press the green button is far below 50%.
1 1
How not to sell options cheaply?
Many life multiple-choice questions may have an "other" option besides abcd.
Turing decided to "attack the machine with the machine" when dealing with the German cipher machine. However, the leader refused to approve the budget and ordered him to obey the orders of his superiors. Turing had a brainwave and asked, who is your superior? Then he wrote a letter to Churchill and settled100000.
I can press red or green, which means I have the right to choose. Can I have another cash channel?
The third way is to sell options to VC and PE, and share the value range between 654.38+00,000 and 50,000,000 by taking advantage of the risk preference and tolerance of capital.
Interestingly, the wealth world has left a secret door for poor young people. They don't have to miss 50 million because they are eager for 654.38+0 million. They just need a broader view.
This is one of the core driving forces for the creation and distribution of social wealth. It is also the beauty of capital.
The decision-making thought and action mode of "option" determine the final wealth food chain.
12
Probability common sense of success
If you are in the right area, there must be a gold mine below (this is also a false proposition, there is a gold mine below the earth, how accurate is the definition? Then you repeat trial and error, and try and error wisely. These trial and error can accumulate and snowball, and constantly improve your chances of success.
Quote a chicken soup joke: If the success rate of one thing is 1%, what is the probability of success at least 1 after repeated attempts of 100 times?
Answer: If the success rate is 1%, the failure rate is 99%. According to 100 repeated attempts, the failure rate is 99% to the power of 100, which is about 37%. Finally, our success rate should be 100% minus 37%, which is 63%. If something is tried repeatedly, its success rate will miraculously rise from 1% to an incredible 63%.
As I said before, don't bet repeatedly when the winning percentage is not dominant. If you do this, according to the law of large numbers, you will lose everything.
But why can the above success formula be reversed?
The reason is that you lost money in the casino.
In the inversion formula of success science, it is assumed that your time cost, energy cost, opportunity cost and money cost are all ignored.
You need to admit failure, your physical strength is very important, and you are willing to invest time. These are your expenses.
Some people will not lose energy because of repeated setbacks. Every time he comes back, he is as passionate as the first time. Every time he is ready.
As can be seen from the above, the mistakes in life are either errors in the calculation of mathematical probability, or insufficient repetitions, or they can't stand the toss.
Therefore, suffering is probably the most calculated and repeated chip, especially suitable for young life gamblers.
Robert Thornton, an engineering professor at Stanford University in the United States, said: In the creative process, talent is not necessarily more important than productivity. To find a useful good idea, you have to try a lot of useless ones first. This is a pure numbers game.
There is a book devoted to this question: if innovators make unreliable judgments about their own ideas, how to improve the probability of creating masterpieces?
The answer is: they came up with many ideas.
Simonton found that, generally speaking, creative geniuses' works in their field are not better than those of their peers, they just have a lot of ideas. This gives them more changes and a higher chance of getting originality.
"The probability that a person can come up with influential and successful ideas," Simon said, "is directly proportional to the total number of ideas he has put forward. 」
For example, Shakespeare: We are familiar with a small number of his classic works, but forget that in 20 years, he wrote 37 plays, 154 sonnets.
How to be a successful CEO? Here, the author Holovitz shared an important experience:
The CEO of a startup should not calculate the probability of success. When starting a company, you must firmly believe that there is a solution to any problem. Your task is to find a solution. Whether the probability is nine out of ten or one in a thousand, your task remains the same.
He also believes that there is no secret to being a successful CEO. If there is such a skill, it is to see its ability to concentrate on choosing the best route when there is no way out. Compared with ordinary people, those moments that make you want to hide or tear it up the most are the things that you have to experience as a CEO.
"As long as you are willing to do it, you will be able to get ahead. Dare to be the first in the world "These are the popular outlook on life in China at present. Combined with the above calculation of success probability, should we put all our eggs in one basket for the future?
Still depends on the chips in your hand.
In our life, in the face of uncertainty, most of our time to roll dice is limited and consumes resources. Never give up refers to your fighting spirit, not the last dollar in your wallet.
Should I gamble if I have less money?
From this, we can discuss two topics that are often misunderstood:
Should investors with less money buy risky stocks?
When your chips are "limited" money, the difference between people with less money and people with more money is just a number. Bets should be distinguished by proportion, not by amount.
Some people feel that they have less money, so they have to take risks. It's as stupid as trying to withdraw money from a casino (unless you have a doctorate in mathematics). Can you not follow the law of probability if you have less money? Do you have to pay less to go to casinos and push yourself into the meat grinder of the law of large numbers?
This is why "poor people" often give up on themselves and quickly gamble away their last chips.
2. Entrepreneurs are selling their lives.
Then the last topic, "I only have two thousand dollars in my hand. Even according to Buffett's rate of return, I can't afford a house in my life. " 」
Answer:
1) If you use money as a bargaining chip, you must follow the probability principle of money;
2) You can also have another chip and gamble your life in another way.
That is: sell your fate, but use your brains and work hard.
Entrepreneurship or a small probability event. Even if your wisdom, energy and time are zero-cost, even if you keep trying and exploring, your success rate will be higher and higher, and there will not be many in the end.
The innovation of big companies is often not higher than the success rate of entrepreneurs. So they will buy successful startups. In a sense, they just bought the entrepreneur's "A Good Life with Little Lotus" to avoid paying the high trial and error costs of big companies.
13
Limited choices in life
There are many choices in life, and we can't always be driven by "probability" and "optimality".
Just like in Captain and Commander, Captain Jack temporarily gave up chasing enemy ships and chose to dock on an island to meet the Darwinian scientific exploration that the ship doctor dreamed of.
Thinking of a friend, the husband and wife chose to postpone starting a business to buy a house and leave time for their growing children.
Many beautiful things and moments are due to some "not counting" choices.
Andre Goz said, "I began to think about what is the secondary thing that should be given up. Only by giving it up can I concentrate on the pursuit of the most important thing. In the final analysis, there is only one thing that matters most to me: being with you. 」
Of course, we'd better have enough chips won by the alpha dog probability calculation method for ourselves to squander or help those who have no right to live in casinos. For example, Gates' charity fund.
Perhaps choice itself is more important than wealth. If time is the most precious wealth, what about life choices that are more limited than time?
I remember 1995 I went to Guangzhou alone after graduation and met a teacher. He saw that I had some self-taught spirituality and boasted "this is a talented boy" in front of others. Time always likes old people too much and young people too much. So far, no one has called me a middle-aged genius. )
When he registered his own company, he had a headache to choose a name, so he said, it is better to call it "choice"
So this company became the first company I joined, and its name contains a wide range of life metaphors:
Limited choice company.
The article is taken from (Socket College)