As above, a "simple" multiple-choice question. Did you press the red button? Or green?
This question is more interesting than expected. Let me try to answer:
1, according to the expected value theory, the value of the green button is 50 million;
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;
In other words, if a person can't bear "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. Think openly. If you have the option, you can sell an option worth 50 million yuan to someone who can afford it, such as 20 million yuan (or even higher).
5. Continue to optimize the last item. Considering the possibility of increasing "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 ask the buyer to share it with you with/kloc-0.00 billion yuan;
6. Further, you can make this option into a lottery ticket for public offering, chop it up and retail it for two yuan each, and print 200 million copies. The first prize is 100 million. Contrast 5, the risk is lower and the income is greater;
In view of the successful business model, we began to raise the next billion yuan as the first prize to make it a business.
8. According to the P/E ratio, the company raised 2 billion yuan to go public, with a market value of 654.38+00 billion yuan.
From 654.38+0 billion to 654.38+0 billion, let's study the mathematical principle 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 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 the1970s, 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 would like to discuss several interesting topics:
1, the 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);
Nowadays, the popular artificial intelligence relies on independent and cold-blooded calculation of the optimal probability in every step, thus defeating human beings. Such as alpha dogs;
However, irrationality and impulsiveness may become the last bastion of mankind. (I'll write this separately later)
Go through the basic concepts first.
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%= (possibly rising) $2.55?
-6×65438 USD +05% = (possible decrease) -0.9 USD.
So, 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, and the probability of rising is about 70%." However, 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: if there is a 70% probability of the market going up next week, there is a 30% probability of going down. 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 result in the future is: 70 %×1%+30 %× (-10%) =-2.3%, so if you want to bet down, 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.
Probability sometimes seems "counterintuitive".
Example c:
A taxi caused an accident on a rainy night. A witness at the scene said that he saw the car was blue. Known as: 1, the witness's identification accuracy 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.
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 because it is "satisfied" with 654.38+0 million. As far as its wealth is concerned, 65.438+0 billion has brought about an order of magnitude change, and it is unimaginable to have one more order of magnitude; 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 is intertwined with the comprehensive function of "expected utility theory" and "prospect theory"
Prospect theory
"Don't be an ordinary fool" is summed up by Kahneman, who won the Nobel Prize for his prospect theory:
A, people get the risk aversion;
B, when lost, rational people are risk-averse, and "normal fools are" are risk-averse;
C, rational decision makers' judgment of gains and losses is not affected by reference points, and "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)
D. Normal fools usually avoid losses.
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.
There are exceptions.
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.
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 selection at the beginning of this article. In comparison, Zuckerberg's green button (penalty for losing) is much more cruel.
A few years later, snapchat rejected Zuckerberg's $3 billion offer in a similar way.
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 youth make their success rate of pressing the green button far lower than 50%.
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, which has a high enough reference point, will not be swept away by small interests, and can take risks (in fact, it is low probability), thus capturing high returns;
2. Demonstration effect of a group of people around;
3. Intrinsic motivation that is ignited.
They are less likely to sell their probability rights "cheaply" than ordinary people.
Give up probability weight
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 insist on acting according to the probability of superiority, and even if it is frustrated repeatedly, it will not change the principle of life bet;
3. Buying lottery tickets is the most expensive self-abandonment 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 implemented idiot 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.
Why can't smart people win a bet?
If life is a game of probability, if our 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. Count cards like the movie Won 2 1;
4. Under the advantage probability, increase the bet;
No matter what the result is, the mood will not fluctuate if the above strategies are carried out persistently.
A wise man can do 1-4 well.
But "anti-humanity" 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.
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 running 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 maximum winning probability of "now".
For example, Rubin, Taleb and Buffett mentioned earlier in this article are almost all human alpha dogs, and insisting on acting according to probability often seems "counterintuitive, anti-human and anti-comfortable".
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.
How not to sell options cheaply?
Many life multiple-choice questions may have an "other" option besides abcd.
In order to deal with the German cipher machine, Turing decided to "attack the machine with the machine", but 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 way to cash in?
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.
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 all because of some "not counting" choices.
Andre Goz said: "I began to think about what is the secondary thing that should be given up. If I give up, I can concentrate on 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 about the choice of name, so he said, it's 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.