1. Preface
   1. Probability is not the mere computation of odds. It is the acceptance of the lack of certainty in knowledge and the development of methods for deling with our ignorance.
   2. The main idea in this book: "it's more random than we think", rather then "it's all random"
      1. Chance favours the prepared
      2. Skills count, but count less in highly random environments
      3. our brain sometimes gets the arrow of causality backwards
      4. Luck is democratic, and it hits everyone equally, regardless of original skill
2. Prologue
   1. Lucky Fool: a person who benefited by a disproportionate share of luck but attributed his success to some other reason
   2. Confusion between noise and meaning: between randomly constructed arrangement and a precisely intended meaning
   3. Courage often comes from an underestimation of the share of randomness in things rather than a more noble ability to stick out one's neck for a given belief
   4. Risk taking is frequently randomness foolishness
   5. Our mind is not equipped to think in terms of probabilities
   6. Two polarizing visions of man
      1. The Utopian Vision
         1. belief in reason and rationality
         2. we can control out nature at will and transform it by mere edict in order to attain happiness and rationality
      2. The Tragic Vision
         1. belief in inherent limitations and flaws in the way we think and act
         2. acknowledgement of this fact as basis for any individual and collective action
      3. the ideas in this book fall squarely into the Tragic Vision: we are faulty and there is no need to bother trying to correct our flaws
   7. there are those who think that there are easy, clear-cut answers and those who think that simplification is not possible without severe distortion. The generator of Fooled by Randomness, the false belief in determinism, is also associated with such reduction of dimensionality of things. As much as you believe in "keep it simple, stupid", it's simplification that it's dangerous.
3. Part 1: Solon's Warning (Rare events)
   1. #1: If you're so rich, why aren't you so smart?
      1. Nero Tulip's story
         1. risk-conscious hard work and discipline can lead someone to achieve a comfortable life with a very high probability
         2. Beyond that, it's all randomness; either by taking enormous (and unconscious) risks, or by being extraordinarily lucky
         3. Mild success can be explainable by skills and labour. Wild success is attributable to variance
      2. Serotonin and Randomness
         1. Lucky fools do not bear the slightest suspicion that they may be lucky fools; they don't know they belong to such category
         2. an increase in personal performance (regardless of whether it's caused deterministically or by the agency of Lady Fortuna) induces a rise in serotonin in the subject, itself causing an increase in what is commonly called "leadership abilities"
         3. Randomness will be ruled out as possible factor in performance, until it rears its head once again and delivers the kick that will induce the downward spiral
      3. Expected success and resistance to randomness
         1. John the dentist, who has been drilling teeth for 35 years
            1. if he were to live his relive a few thousand times, the range of possible outcomes is rather narrow
         2. John the janitor who wins the lottery
            1. if he were to relive his live a million times, almost all of them would see him performing janitorial activities, and spending endless money buying fruitless lottery tickets.
         3. John the dentist, in expectation, is considerably richer than John the janitor
   2. #2: A bizarre accounting method
      1. One can't judge a performance in any given field by the results, but by the cost of the alternative (if history played out in a different way)
      2. Reality is far more vicious than Russian Roulette
         1. 1) it delivers the fatal bullet rather infrequently (the "black swan" problem)
         2. 2) one does not observe the barrel of reality
            1. very rarely is the generator visible to th naked eye
            2. ons is thus capable of unwittingly playing Russian roulette, and call it by some alternative "low risk" name
         3. 3) there's an ingratitude factor in warning people about something abstract (protection from things that never happened)
      3. Learn to look for the invisible risks of blowup hidden in any portfolio
      4. Just because something hasn't happened in th past, it doesn't mean a prediction of that event is incorrect (Robert Shiller's views on irrational markets and volatility)
      5. The risks that merit our attention are always something vivid rather than something more abstract (risk of dying vs risk of death by terrorist attack)
         1. risk detection and risk avoidance are not mediated in the "thinking" part of the brain, but in the emotional one
   3. #3: A mathematical meditation on history
      1. Mathematics is principally a tool to meditate, rather than to compute
      2. Monte Carlo methods consist on creating artificial history
      3. Several branches of research have been examining our inability to learn from our own reactions to past events
      4. Historical determinism: we think that we'd know when history is made
         1. Things are always obvious after the fact (hindsight bias)
         2. when you look at the past, the past will always be deterministic. Our mind will interpret events not with the preceding ones in mind, but with the following ones
      5. History cannot lend itself to experimentation. But somehow, overall, history is potent enough to deliver, on time, in the medium to long run, most of the possible scenarios
         1. Ergodicity: under certain conditions, very long sample paths will end up resembling each other
      6. noise to signal ratio
         1. the shorter the time scale, the more noise you get (because of volatility)
         2. over a short time interval, one observes the variability
         3. our emotions are not designed to understand this point. Perhaps it would be better to get information in a larger time scale
            1. I deal with this "emotional defect" by having no access to information, except in rare circumstances. I prefer to read poetry.
            2. If an event is important enough, it will find its way to my ears.
   4. #4: Randomness, nonsense, and the scientific intellectual
      1. We don't need to be rational an scientific when it comes to the details of our daily lives -- only in those that can harm us or threaten our survival.
      2. Modern life seems to invite us to do the opposite: become extremely realistic and intellectual when it comes to such matters as religion and personal behaviour, yet as irrational as possible when it comes to matters ruled by randomness.
   5. #5: Survival of the less fit: can evolution be fooled by randomness?
      1. Many amateurs believe that plants and animals reproduce on a one-way route towards perfection. Things are not that simple
         1. Once randomness is injected, what seems to be evolution may be merely a diversion, and possibly regression (negative mutations, or "genetic noise")
         2. Negative mutations are traits that survive in spite of being worse, from a reproductive fitness standpoint, than those that replaced. However, they cannot be expected to last more than a few generations.
      2. Darwinian fitness applies to species developing over a very long time, not observed over a short term. Time aggregation eliminates much of the effects of randomness.
         1. Owing to the abrupt rate events, we do not live in a world where things "converge" continuously towards betterment. Nor do things in life move continuously at all.
         2. On average, animals will be fit, but not every single one of them, and not all the times.
         3. Someone with only a casual knowledge about randomness would believe that an animal is at the maximun fitness for the conditions of its time. This is not what evolution means.
      3. An animal with a deficiency might have survived just because of luck: because its sample path is free of evolutionary rare events
         1. One vicious attribute is that the longer these animals can go without encountering the rare event, the more vulnerable they will be to it
      4. By some viciousness of the structure of randomness, a profitable person who is a pure looser in the long run and correspondingly unfit for survival, presents a high degree of eligibility in the short run and has the propensity to multiply its genes.
   6. #6: Skewness and Asymmetry
      1. Asymmetry
         1. Asymmetric odds means that probabilities are not 50% for each event, but that the probability on one side is higher than the prability of the other
            1. "Since no more than 50% of individuals can be wealther than the average": mistaking mean and median
         2. Asymmetric outcomes mean that the payoffs are not equal
         3. It's not how likely an event is to happen that matters, it is how much is made when it happens that should be the consideration. How frequent the profit is irrelevant; it is the magnitude of the outcome that counts.
            1. where the commulative [effect] does not matter, only frequency matters
      2. Rare events
         1. Rare events are not fairly valued, and the rarer the event, the more undervalued it will be in price
         2. Outliers: ignoring the extreme, infrequent events, not noticing that the effect of a rare event can bankrupt a company
         3. People tend to be sensitive to the presence or absence of a given stimulus rather than its magnitude.
            1. This implies that a loss is perceived as just a loss, with further implications later. The same with profits.
            2. The agent would prefer the number of losses to be low and number of gains to be high, rather than optimizing the total performance
         4. the more information you have, the more you are confident about the outcome. Now the problem: by how much?
            1. Common statistical method is based on the steady augmentation of the confidence level, in non-linear proportion to the number of observations.
            2. for an "n" times increase of the sample size, we increase our knowledge by the squared root of "n"
            3. Statistics become complicated, and fails us, when we have distributions that are not symmetric (where bigger sample size increases knowledge very slowly)
      3. Using the past to predict the future
         1. I reject a sole time series of the pas as an indication of future performance. My main reason is the rare event.
            1. If we were in a world where randomness is chartered, we could use Time Series Analysis (Econometrics). But we are not sure the world we live in is well chartered
            2. History teaches us that things that never happened before do happen.
         2. Problem of stationarity
            1. when the composition of the "urn" is itself randomly distributed. We will never get to know the composition of the urn
            2. We take past history as a single homogeneous sample and believe that we have considerably increased our knowledge of the future from the observation of the sample of the past. But, what if things have changed?
            3. if people were rational then their rationality would cause them to detect predictable patterns from the past and adapt, so that past information would be completely useless for predicting the future
   7. #7: The problem of induction
      1. Deductive thinking: no emphasis on observing the real world
      2. Inductive thinking: going from plenty of prticulars to the general
      3. The "Black swan" problem: no amount of observations of white swans can allow the inference that all swans are white, but the observation of a single black swan is sufficient to refute that conclusion
      4. Extreme empiricism, competitiveness, and absence of logical structure to one's inference can be a quite explosive combination
         1. Naive empiricism
            1. "Any testable statement should be tested" (Niederhoffer) is rarely practiced.
            2. How many effects we take for granted might not be there?
            3. I can use data to disprove a proposition, never to prove one
            4. I can use history to refute a conjecture, never to affirm it
            5. you can't make the leap from "never happened" to "it will never happen"
            6. why do we consider the worst case that took place in our own past as the worst possible case?
         2. Without proper method, empirical observation can lead you astray
            1. Pure empiricism implies necessarily being fooled by randomness
         3. Life is not a win/loose situation, as the cost of loses can be markedly different from that of the wins
            1. Maximizing the probability of winning does not lead to maximizing the expectation of the game when one's strategy includes skewness.
            2. don't approach anything like a game to win, except when it's actually a game
      5. Karl Popper's answer to the problem of induction
         1. A theory is never right
            1. 2 types of theories
            2. theories that are known to be wrong (tested and rejected, or falsified)
            3. theories that have not yet known to be wrong, but are exposed to proven wrong
            4. A theory cannot be verified. It can be provisionally accepted.
            5. A theory that doesn't present a set of conditions under which it could be considered wrong would be charlatanism
            6. Example: astrology, because there's no way to falsify it
         2. some types of knowledge don't increase with information, but which type could not be ascertained
         3. Open society: one in which no permanent truth is held to exist. This would allow counter-ideas to emerge.
            1. any idea of Utopia is necessarily closed owning to the fact that it chokes its own refutation.
            2. The sinmple notion of a good model for society that cannot be left open to falsification is totalitarian
      6. Taleb's way of dealing with the problem of induction
         1. I speculate in all my activities on theories that represent some vision of the world, but with the following stipulation: no rare event should harm me. I would like all conceivable rare events to help me.
         2. there are situation in which using statistics can be useful, But I don't want my life to depend on that
            1. We need to accept the assymmetry in knowledge
            2. I will use statistics and inductive methods to make aggressive bets, but I will not use them to manage my risks and exposure
            3. [take action] based on some observation, but making sure the costs of being wrong are limited (their probability is not derived from past data)
            4. have "stop loss": a predetermined exit point, a protection from the black swan
4. Part 2: Monkeys on Typewritters (Probability Biases)
   1. Intro
      1. how much can past performance be relevant in forecasting future performance?
      2. it depends on 2 factors
         1. the randomness content of the profession
         2. the number of "monkeys" in operation
   2. #8: Too many millionaires next door
      1. Survivorship Bias: the highest performing realization will be the most visible. Why? because the loosers don't show up
      2. emotional impact: feeling a failure by comparison
         1. we choose to live between people who have been successful, in an area that excludes failure
         2. those who have failed don't show up in the sample, thus making us look like we haven't done well
         3. treadmill effect: you get rich, move to a rich neighbourhood and become poor again
      3. 2 compounding flaws
         1. sample comes from the lucky monkeys on typewriters
         2. the problem of induction (generalizing based on a small sample)
      4. Survivorship bias is chronic, because we've been trained to take advantage of the information that is lying on front of our eyes, and ignore the information we haven't seen
   3. #9: It is easier to buy and sell than fry an egg
      1. there are well-known counterintuitive properties of performance records and historical time series: situations where performance is exaggerated by the observer, owing to misrepresentation of he importance of randomness
      2. Technical definition of "survivorship bias": to mistake the distribution of the maximum of a variable with that of the variable itself
      3. Nobody has to be competent
         1. a population entirely composed of incompetent managers will produce a small amount of great track records [just by luck]
         2. assuming a manager shows up unsolicited at your door, it will be practically impossible whether they are good or bad
         3. the number of managers with great track records in a given market depends far more in the number of managers who started, rather than their ability to produce good results
      4. Regression to the mean
         1. A "lucky streak" in games is another mispreception of random sequences
         2. The deviation to the norm [in a random sequence like coin tosses] is entirely attributable to luck, not the skills of the player
         3. The larger the deviation from the norm, the larger the probability of coming from luck rather than skill
         4. A large outlier tends to produce "reversion", explainable as regression to the mean.
      5. Ergodicity
         1. Time will eliminate the annoying effects of randomness
      6. Data Mining and coincidences
         1. when one throws a computer at data, looking for about any relationship, it is certain that a spurious connection will emerge
         2. we can also fit the rule to the data (data snooping): the more you try, the more you're likely by mere luck to find a rule that works on past data
      7. Real randomness doesn't look random
         1. A single random run is bound to exhibit some pattern, if one looks hard enough
         2. data that is perfectly patternless would be extremely suspicious and appear to be man-made
         3. A random series of runs needs not to exhibit a pattern that looks random.
      8. A finding of absence and absence of findings get mixed together
   4. #10: Looser takes all - on the nonlinearities of life
      1. nonlinear: a very small additional input causing a disproportionate result
      2. Life is unfair in a non-linear way
         1. a small advantage in life can translate into a highly disproportionate payoff
         2. no advantage at all, but a very, very small help from randomness can lead to bonanza
      3. Path dependent outcomes
         1. Those who win are seen as representative of their [activity] (survivorship bias)
         2. Those who win capture most of the market regardless of merit (example: Bill Gates, QUERTY keyboard)
         3. chance events coupled with positive feedback rather than [objective] superiority will determine economic superiority
         4. Polya processes: the probability of winning increases after past wins, and that of loosing increases after past loses
      4. Network effects: the more connected a network, the higher the probability of someone hitting it and the more connected it will be (ex: phenomena that :spreads like wildfire")
      5. Our brain is not cut for non-linearities
         1. Our emotional apparatus is designed for linear causality
         2. owning to non-linearities, people cannot comprehend the nature of rare events
         3. there are routes to success that are non-random, but very few people have the mental stamina to follow them. Most people give up before the rewards
      6. Buridan's Donkey : using randomness to help break a stalemate
   5. #11: Randomness and our mind: We are probability blind
      1. Our brain can handle one and only one state at once
         1. A bet has an expected value that is the linear combination of multiple states x their probability.
         2. We can imagine each state, but not the combined expectation
         3. we are likely to bet irrationally as one of the states will tend to dominate the imagined picture
      2. Explaining "irrational" behaviour
         1. Satisficing (Herbert Simon)
            1. if we were to optimize at every step in life, it would take infinite time and energy
            2. you stop when you find a a near-satisfaction solution
            3. we are rational, but in a limited way (bounded rationality)
         2. Kahneman & Tversky: we're flawed, not just imperfect
            1. we follow "quick & dirty" heuristic rules
            2. these shortcuts come with side-effects (biases)
            3. these biases don't disappear in the presence of incentives
            4. this is in open contradiction with the orthodox neoclassical economics (rational expectations, efficient markets)
            5. Conflicting and contradictory laws
            6. our minds operate by a series of disconnected rules that may not be consistent with each other
            7. they may make the job locally, but not necessarily globally
            8. the absence of a central processing system makes us engage in decisions that can be in conflict with each other
            9. We don't "think" when making choices, but use "heuristics"
            10. "I'm as good as my last trade" (Prospect Theory)
            11. you don't have everything you know in your mind at all times, so you retrieve knowledge that you require at any given time, in piecemeal fashion
            12. retrieved knowledge chunks are placed in local context
            13. you have an arbitrary reference point and react to differences from that point, forgetting that you are not looking at absolute differences
            14. life is incremental: you will only look at the changes
            15. because loses hurt more than gains, and differently, that makes your accumulated performance less relevant than the latest change
            16. when something is in relation to something else, that "something else" could be manipulated (anchoring)
            17. Availability Heuristic
            18. the practice of estimating the frequency of an event according to the ease with which instances of the event can be recalled
            19. Representative heuristic
            20. gauging the probability that a person belongs to a particular social group by assessing how similar the person's characteristics are to a "typical" member of the group (the Linda problem)
            21. Simulation Heuristic
            22. the ease of mentally undoing an event, playing alternative scenarios (counterfactual thinking)
            23. Affect Heuristic
            24. emotions elicited from an event determine their probability in your mind
         3. Other branches of research
            1. Evolutionary Psychology
            2. people have difficulties in probabilistic reasoning but for different reasons: we are optimized of a different environment than the one prevailing today.
            3. Our "natural environment" (the environment in which we evolved and spent the largest number of generations) was much simpler, with less information
            4. In such environment, life would be simpler, and the space of probabilities would be much more narrow
            5. We have evolved out of that environment, but our genes haven't changed at all
            6. People can make incoherent choices because the brain works in the form of partial small jobs
            7. The heuristic we follow are "fast and frugal"
            8. Neurobiologists
            9. We have "3 brains"
            10. Reptilian (autonomous, automatic functions, like heartbeat)
            11. Limbic (center of emotions)
            12. Neocortex (cognitive brain)
            13. One cannot make decisions without emotion
            14. if we were to make rational decisions, it would take a very long time
            15. emotions are the "lubricant of reason"
            16. We feel emotions (limbic brain) and then find explanations (neocortex)
      3. Our modern world is ruled by probability (because of the explosion in information) while important decisions are made without the smallest regard for its basic laws
         1. mixing conditional and unconditional probabilities (OJ Simpson trial)
         2. we're option blind
            1. people tend to undervalue options as they are usually unable to correctly mentally evaluate instruments that deliver an uncertain payoff
            2. confusing expected value with the most likely scenario
         3. confusing absence of evidence with evidence of absence
         4. Difficulty with causality and significance of variance
            1. Difficulty distinguishing noise from signal, and attempting to explain every change
         5. We don't understand confidence levels
            1. My activity in the market (and other random variables) depends far less on where I think the variable is going so much as it does in the degree of error I allow around such confidence level
5. Part 3: Wax in my Ears (Practical/Philosophical Aids)
   1. Intro
      1. Do not attempt to be Odysseus
         1. I understood that I was not intelligent or strong enough to fight my emotions
         2. we have a predisposition to be fooled by randomness
         3. I am just like every single character I ridicule in this book. The difference between me and those I ridicule is that I try to be aware of it
         4. My brain can tell the difference between noise and signal, but my heart cannot
         5. Such unintelligent behaviour does not just cover probabilities and randomness
         6. The good news is that there are tricks (wax in my ears)
         7. These small daily emotions are not rational. But we need them to function properly
      2. unless the source of a statement has extremely high qualifications, the statement will be more revealing of the author than the information intended by him (Wittgenstein's Ruler)
   2. #12: Gambler's ticks and pigeons in a box
      1. I noticed superstitions creeping into personal/professional life
         1. We are not made to see things as independent of each other
         2. Our bias is to immediately establish a causal link
      2. I don't see why we should resemble a rational man who acts perfectly under uncertainty as propounded by economic theory
      3. Brain and instinct are not acting in concert
      4. I am emotional and derive most of my energy from my emotions. The solution doesn't reside in taming my heart
      5. most of us know how we should behave. It is the execution that is the problem, not the absence of knowledge
      6. We need tricks to get us there, but before we need to accept the fact that we're mere animals in need of lower forms of tricks, not lectures
   3. #13: Carneades comes to Rome: on probability and skepticism
      1. Probablity, the child of Skepticism
         1. The skeptics' main teaching was that nothing could be accepted with certainty, that conclusions of various degrees of probability could be formed, and these supplied a guide to conduct
         2. Being guided by probability allows you to contradict yourself
         3. We demand the right to contradict ourselves (Paris, 1968 riots)
            1. no need to hew stubbornly to an opinion for the mere fact that it was voiced in the past
            2. in modern times, self-contradiction is made culturally to be shameful
            3. We're supposed to be faithful to our opinions. One becomes a traitor otherwise.
            4. Beliefs are said to be path dependent if the sequence of ideas is such that the first one dominates
      2. One would think that when scientists make a mistake they develop new science. Nothing of the sort.
         1. participants in the 1998 financial near collapse blamed the "rare event", rather than question their understanding or validity of the (Nobel winning) theories they were following
            1. induction problem: how did they know it was a rare event?
            2. Wittgenstein's Ruler: their explanation of a "ten sigma event" would suggest it happens once every several times the history of the universe
         2. attribution bias: attribute success to skills and failure to randomness
            1. it's a human heuristic that makes us believe so in order not to kill our self-esteem and keep us going against adversity
            2. it gives people the illusion of being better at what they do
         3. Science is great, but scientists are dangerous (because they are human)
   4. #14: Bacchus abandons Antony
      1. The stoic's prescription was to elect what one can do to control one's destiny in front of a random outcome. We always have an option against uncertainty
      2. Odds, randomness will have the last word. We are left only with dignity as the solution
         1. dignity defined as the execution of a protocol of behaviour hat does not depend on the immediate circumstance.
            1. Grace under pressure
         2. there's nothing wrong and undignified with emotions. What's wrong is not following the heroic or, at least, dignified path
         3. the stoic is the person who combines the qualities of wisdom, upright dealing, and courage
      3. Randomness and personal elegance
         1. ideas don't truly sink in in when emotions come into play
         2. Start stressing personal elegance in your next misfortune
            1. dress at your best on your execution day
            2. stand erect in front of the death squad
            3. don't play victim when told bad news
            4. don't blame others for your fate, even if they deserve blame
            5. never exhibit self-pity
            6. do not complain
         3. The only article Lady Fortuna has no control over is your behaviour
   5. Postscript: 3 afterthoughts in the shower
      1. 1) The inverse skills problem
         1. the inverse rule: the higher up the corporate ladder, the lower the evidence of contribution
         2. the degree of randomness in an activity and our ability to isolate the contribution of the individual determine the visibility of the skills content
         3. Repetitiveness is key for the revelation of skill (ergodicity)
         4. consider the difference between judging on process and judging on results
            1. lower ranking people in the organization are judged on both
            2. top management is ranked on results, no matter the process
            3. there is no such thing as a foolish decision if it results in profits
         5. The link between the skill of the CEO and the results of the company are tenuous
            1. CEOs take a small number of decisions , like a person walking into a casino with a single million dollar bet.
            2. External factors, such as the environment, will play a considerably larger role than with lower ranking contributors
            3. the CEO may be subjected to the monkey-on-the-typewriter problem
            4. With the acceleration of winner-takes-all effects in our environment, such differences in outcomes are more accentuated, more visible, and more offensive to people's sense of fairness
            5. CEOs making thousand times what the janitor makes
         6. CEOs are not entrepreneurs
            1. Entrepreneurs are those who stuck up their necks out for some idea, and risked belonged to the vast cemetery of those who did not make it
            2. CEOs have skill in getting promoted within the company rather than in making optimal decisions
            3. there's assymmetry, as these executives have almost nothing to loose
            4. the shareholdes bore the risk, the executives got the reward
            5. We continue to worship those who won the battles, and despise those who lost, no matter the reasons
      2. 2) on some additional benefits of randomness
         1. Some degree of unpredictability (or lack if knowlege, which has the same effect) can be beneficial to our defective species
         2. it can force you to be a satisfier rather than a maximizer
            1. research on happiness shows that those who live under self-imposed pressure to be optimal in their enjoyment of things suffer a measure of distress
            2. people of happy disposition tend to be of the satisfier kind. Their goals and desires don't move along with their experiences
            3. causality is not clear: the question remains whether optimizers are unhappy because they are constantly seeking a better deal, or if unhappy people tend to optimize out of their misery
         3. A mild degree of unpredictability in your behaviour can help you protect yourself in situations of conflict
            1. if you randomize your trigger points, people will not know how far they can push you
      3. 3) standing on one leg
         1. we favour the visible, the embedded, the personal, the narrated, and the tangible; we scorn the abstract