Annotated list of contexts where we perceive chance

This is a draft list of contexts where we perceive uncertainty/unpredictability in the real world (as opposed to mathematics or philosophy) and think in terms of chance, with illustrative examples. The list is not supposed to be definitive in any sense -- a reader might well prefer to group several of my categories into the same category, or to split one of my categories into many. But I am attempting to be comprehensive, in the sense that any instance of chance that might naturally arise should roughly fit some context on the list. So let me know of any instances that don't fit any of my categories.

Let me emphasize that I would be much happier if someone else had made a list like this if only because it's much more fun and less work to criticize and edit someone else's list than to start from scratch. The only slightly comparable list that I know is a list by Dennis Lindley discussed here of 20 instances of uncertainty, interpreted more broadly. The same link gives some implicit short lists of what authors appear to view as representative examples. For further indication of what I'm trying to do, see analogous "representative lists" in other topics.

I have several overlapping motivations. In my opinion, individual writers who have attempted to describe the big picture of the operation of chance in the real world tend in fact to cover only a small part of the picture. This thesis is argued at (xxx not written), of course with reference to the "big picture" provided by this list. A more constructive project is to gather and present data on how people engaged in some activity perceive chance as being involved. Three such data-sets can be found via the introduction on this page, obtained using protocols intended to ensure that examples are presented without subjective selection by me. Such data serves two purposes: checking the comprehensiveness of our list of 100, and providing a concise summary ("categories 16, 88,89") of the aspects of chance perceived by this activity group. Finally, in the spirit of Everything Is Miscellaneous, I am suspicious of top-down taxonomies, instead envisaging some "unorganized" list of 100 small categories as a starting point for composing a bottom-up taxonomy of chance.

I write perceived because one way of thinking about the subject is via

In other words, going from everyday life as seen by the man on the Clapham omnibus to scientific analysis. Of course every aspect of human life is unpredictable on some time scale -- what could one predict about human society in 500 years time? -- so again the issue is perception: what unpredictable events do we consciously view in terms of chance? See my discussion here.

The list is presented below within a narrative based on many distinct "trains of thought" separated by ************************. But let me emphasize this ordering is not intended as a basis for taxonomy; rather, as instances that need to be fitted in to any scheme that you might devise.

The list, as a narrative

Consider human uses of chance, which perhaps started in the pre-scientific era not with gambling but with

(1) Chance in divination.

More familiar, being both ancient and modern, is

(2) Chance for fairness.

This is used in many contexts, from a coin-toss at the start of a sporting match, to a random military draft, to jury selection. The latter is motivated both by fairness and by the next topic, representativeness. It is one of the basic insights of textbook mathematical probability that, in opinion polls for instance, using randomness rather than some haphazard or some complicated deliberate scheme to choose a sample gives controllable accuracy. The scope of such

(3) Random sampling for representativeness

is much wider than opinion polls. For instance, much monthly economic data reported in the news is based on sampling. Or one can estimate the number of trees in a large forest by sampling some small map squares and just counting trees in the sampled squares.

Another textbook context for the deliberate introduction of chance is

(4) Randomized controlled trials

exemplified by studying whether a new medicinal drug works better than an old drug. Using random allocation of subjects to control (old drug) or experimental (new drug) groups eliminates the possibility that statistical differences in medical outcome could be due to factors other than the difference of drugs, even factors that you didn't think of in advance.

Other instances in science and engineering of "deliberate introduction of chance", for instance randomized algorithms, appear later.

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Textbooks on mathematical probability typically start with

(5) Explicit games of chance based on artifacts with physical symmetry

exemplified by dice, roulette, lotteries, playing cards, etc. Stewart Ethier's recent The Doctrine of Chances gives an encyclopedic cross-section of the less-elementary mathematics of games of chance. Note the point that "background probabilities", e.g. of being dealt a certain bridge or poker hand, are calculable, but the results of a subsequent game involving human choices are not. There is a spectrum from "games of chance" to "games of skill", but even in the latter the result of a match between roughly equally skillful players or teams is unpredictable. In the context of sports it seems worthwhile to distinguish between

(6) Outcome of a sports match between players or teams at comparable levels

(and similarly the outcome of a season's play) and

(7) Performance of an individual player;

for a given professional player in a team sport, one cannot predict their peformance over a career, or over a season, or in the next game. Such things are prominent in our perception of chance, in part because they are things that are commonly gambled upon, as are horse races etc.

The phrase game theory refers to a very special setting, perhaps best described as

(8) Choosing strategy in a competitive setting without knowing competitors' choice of strategy [game theory].

The point is that the form of uncertainty is very specific: "competitors' choice of strategy". Aside from rock-paper-scissors, real-world instances of the precise game-theory setting are rare -- perhaps closest is the separately called plays by offense and defense in American football -- but game theory has been studied intensively as a "toy model" within competitive Economics.

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Let's turn to life as experienced by an individual, which will occupy several trains of thought. In everyday life, there are some occurrences that we recognize as chance.

(9) Coincidences in everyday life

such as receiving a phone call from someone you're about to call, or conversing with a stranger and finding they went to the same high school as you. Here is a nice collection of reader-submitted stories from the Understanding Uncertainty site.

(10) Minor good or bad luck in everyday life

such as getting stuck in a traffic jam, or finding a close parking space in a normally crowded zone. (Major good or bad luck is not "everyday" so is addressed elsewhere).

Having mentioned luck in the retrospective sense -- chance that worked out in one's favor -- let me mention

(11) Luck as superstition:

the belief, or acting on the belief, that certain activities or objects will create good or bad luck in the future without any rational causal mechanism. This relates to issues in the psychology of how we perceive chance, mentioned later.

Superstitious belief regarding luck is often aimed at health or money (which of course will appear later in this list) but also at romance. This reminds us of the role of chance in the human social world. Which of our acquaintances become friends or spouses should be our deliberate choice, but which particular people we come into contact with as new acquaintances in the first place is largely a matter of chance:

(12) Chance in making acquaintances.

The role that individuals have in affecting the character (personality, talents etc) of their children is a matter of eternal debate (one side represented by The Blank Slate), but few of us think we have much influence on our parents' character; so from one's individual viewpoint

(13) The character of our relatives

is largely outside one's control, in everyday language "largely a matter of luck". In the same vein one might say that the country and year of one's birth, the socioeconomic status of one's parents, etc, are a matter of chance, but here we enter philosophically contentious territory -- see item (*4) for where I draw the line. Next consider

(14) The course of our careers.

A few of us may decide as teenagers what career to pursue, and singlemindedly pursue it, but most of us in retrospect see a mixture of conscious choices and chance -- an inspiring teacher, a particular job opportunity, "being in the right place at the right time", etc.

At this point the reader may start thinking: "Look, no aspect of human life is perfectly predictable, so are you [the author] just going to list every aspect of human life?" And the author answers: "No. Imagine you overhear the single word lucky or unlucky in a conversation -- what sort of things might they be talking about?" Recall that I am (in part) trying to list the aspects where people perceive that chance plays a role.

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Let us turn to risks as perceived by an individual, and start with risks to health or life. See Risk for a nice account of 48 risks faced by individuals.

(15) Accidents

exemplified by automobile crashes, are an obvious item. Chance within the rest of health and sickness could be divided very finely, but I will present only 4 categories, motivated partly by our Bing query data.

(16) Possible future occurrence of diseases, for an individual

-- cancer or heart disease, arthritis or Alzheimer's.

(17) Uncertainty about prevention or causation of diseases

smoking, exercise, diet etc.

(18) Uncertain effectiveness of medical treatment or diagnosis on an individual.

See e.g. Tufte's Cancer survival rates: tables, graphics, and PP which is interesting for other reasons too. Also "false positives" as a textbook topic. Finally,

(19) Risks during pregnancy or of unwanted pregnancy

perhaps play a special role in that most of us go through pregnancy as mother or partner.

Even though statistically much less common, fiction and news media make us aware of

(20) Risks to health or wealth from crime.

Turning to uncertainty in financial matters from an individual's viewpoint, uncertainty about how much money you will earn, inherit or marry into is perhaps covered by (13,14). Finance and insurance are big businesses, so one could again divide into very fine categories. On the "investment" side, in lending money one typically knows the interest rate "reward" but one accepts

(21) Risks in lending money

primarily the risk of not being paid back (bankruptcy), secondarily the "interest rate risk" to capital of owning a long term bond. The other large part of "investment" is equity investment, which ranges from a conservative stock mutual fund to being a silent partner in your brother-in-law's plumbing business to home ownership, each representing

(22) Risk and reward in equity ownership.

On the "insurance" side

(23) Insurable financial aspects of non-investment risk

such as accidents, theft, liability, illness, disability, elder care, "life insurance". Finally, in The New Financial Order Shiller makes the interesting point that the majority of major financial risks to a typical American are in fact not currently insurable; one cannot insure against a slowdown in economic growth over next decade, or regional house price declines, or your skills becoming redundant; let's call these

(24) Non-insurable financial risks.

Moving from finance to material possessions:

(25) Reliability of manufactured items

Some manufactured items -- e.g. a sofa -- usually wear out slowly, so we perceive it as a matter of choice when to replace them; others -- a light bulb is the iconic example -- fail unpredictably and we perceive it as a random event.

Hard to fit into this list, but surely a main topic of conversation ever since humans invented speech:

(26) Weather

"30% chance of rain tomorrow" reminds us that weather provides a context where we do regularly hear or see numerical probabilities. This overlaps other categories; to most of us it's just good or bad luck (a game disrupted by rain, or a pleasant sunny day at the beach) whereas in agriculture it's an external risk to business.

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Now consider risks and chance from the viewpoint of an organization, for instance a commercial business or a non-profit or an educational or social institution. Let me rather arbitrarily give 4 categories. First, a new employee may turn out to be efficient or incompetent, key staff may die or leave, customers might not pay their bills, and so on. Call this

(30) Uncertainties in an organization's everyday operation.

Next, the organization is competing with related organizations; whether explicit competition in business, or implicit competition (one charity or religion implicitly competes with others for public attention). How well will the organization fare in such competitions? Here are three aspects of this uncertainty.

(31) Uncertain competence of organization management:

Competing organizations may just be "better managed".

(32) Explicit risks deliberately taken.

A high-tech start-up, or a family-run restaurant, are explicitly high-risk ventures; and in some industries (airplane manufacture; mining) established large corporations must occasionally make big bets with only an uncertain long-term payoff.

(33) Long-term external changes

which may reduce demand for your product; technological change, fashion change, regulatory change, international terms of competition changes, etc.

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Now turn to uncertainty at the level of a nation or society. Sometime over the last century it has become implicitly agreed that a major function of government is to facilitate short-medium term growth of the economy, which we know is unpredictable, so

(34) Uncertainty about economic performance (unemployment, inflation, GDP) in short-medium term future.

People in democracies are conscious of the uncertainty of the result of upcoming elections; on reflection, maybe what's important isn't the name of the winner but what they do after election, so let me classify this rather verbosely as

(35) Uncertainty about non-economic aspects of government policy over the next few years

in "peaceful transfer of power" states. And history makes us conscious of many possible medium-term events, which I will put in a portmanteau category

(36) Uncertainty about medium-term national and international changes: social upheaval, geopolitical competition and conflict, effects of technological change, etc.

A brief sampling of instances from (35-37) can be seen in Usage of the word "likelihood" in The Economist. Regarding the international arena, here is a list of 36 "global risks" for the next 10 years, from the 2011 World Economic Forum (more details here). The list is divided into 5 categories -- economic, geopolitical, environmental, societal, technological. One an also find analyses such as the 2010 U.K. Ministry of Defence's Global Strategic Trends -- Out to 2040 or the 2012 U.S. National Intelligence Council's Global Trends 2030.

In the long term cultures change in completely unpredictable ways -- 21st century British culture has scarcely any relation to that of the original Anglo-Saxons, so let's include

(37) Unpredictable long-term transformation of culture

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Most phenomena perceived as random are random "when viewed on some level of organization" and one can attempt reductionism -- how does this phenomenon emerge from some lower level phenomena? It may or may not be useful to try such reductionism; often the whole point of viewing a phenomenon as random is to avoid having to think of the details of such emergence. But it is often remarked that there are two instances of chance that seem irreducible. One is

(41) Quantum mechanics

for which the textbook "observable" aspect is Radioactive decay. The other is

(42) Free will

by which I mean not one's own free will (which of course seems not at all random) but the fact that other people's actions are intrinsically unpredictable.

This juxtaposition has led to much speculation. For example Roger Penrose speculates that human consciousness is linked to quantum effects. And Conway and Kochen interpret their strong free will theorem as saying ``if indeed we humans have free will, then elementary particles already have their own small share of this valuable commodity. More precisely, if the experimenter can freely choose the directions in which to orient his apparatus in a certain measurement, then the particle's response ...... is not determined by the entire previous history of the universe."

Turning from free will toward a more concrete philosophical issue,

(43) Probability and ethics

cover questions such as: is it ethical to conceive a child with chance p of having a certain fatal genetic disease? Only a small further digression takes us to

(44) Probability and the law

illustrated by the the famous "beyond reasonable doubt" criterion for criminal conviction, deliberately never quantified as a numerical probability. Is it true in fact (and should it be true in principle) that "reasoning under uncertainty" is done differently in legal contexts than in other contexts? Technical material can be found in the journal Law, Probability & Risk. Recall that DNA profiling is one setting where numerical probabilities are brought into court.

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To what extent uncertainty about knowledge should be perceived in terms of chance is one of those contentious philosophical questions. Let me use the commonsense rule: does it feel natural to use the word "likely" in a given context? Via this rule we should include

(45) Uncertain validity of scientific theories

exemplified by
Most of the observed increase in global average temperatures since the mid-20th century is very likely due to the observed increase in anthropogenic GHG concentrations.
Similarly we should include

(46) Uncertainty about historical events

such as
It is likely that [during 1909-1913] Hitler experienced and possible that he shared the general antisemitism common among middle-class German nationalists.
And there is a very broad category

(47) Uncertainty about judgement in everyday life or occupation

Is that politician telling the truth? Would A or B be a better employee?

Another category, which looks strange at first sight, is

(48) Uncertainty about easily-checkable facts

If you want to call a friend and think you probably remember the correct number, then you have to decide whether to call that number or to look up the correct number. So this is a context where there is a direct link between probability assessments and actual actions.

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The distinction between probability and statistics is somewhat arbitrary. Some previous examples feature explicitly in statistics textbooks, and in many "everyday life" examples the only way to guess future probabilities is from implicitly "statistical" knowledge of the past. Here are some more explicitly statistical examples.

(51) (Mis)use of population statistics as probabilities for an individual.

When conceiving a child one can use the population statistics (about 50% of children are girls) to say that the chance your child will be a girl is about 50%. But this is a rather uncommon instance. Consider instead death by lightning; the U.S. population statistics are about 1 per 5 million people per year. However, pointing to a given individual and saying "your chance of death by lightning in the next year is about 1 in 5 million" is just wrong; the chance varies enormously between different individuals, according to their propensity to be outdoors during thunderstorms. Perhaps most instance are intermediate between these extremes. U.S. '"life expectancy" tables put the chance of a 21-year old living past 70 at about 77%. How this applies to a typical individual is a matter of judgement; someone with no visible health problems presumably has a slightly higher survival probability.

(52) Statistical estimates of probabilities for an individual, based on data for that individual and population statistics concerning relationships between factors

This is a huge topic, exemplified by credit scores which seek to predict your likelihood of defaulting on a loan using data about you and the past record of similar people; or the algorithms by which offers you suggestions based on your past purchases and browsing; cf. the Netflix Prize . Originally based on classical statistical techniques like multiple regression, it is nowadays often regarded more as part of the theory of algorithms under names such as machine learning .

(53) Repeatable chance experiments.

Here I am cheating by stating a conceptual category rather than specific real-world setting. "Dropping a thumbtack, and seeing if it ends point-up or point-down" is the iconic classroom example of a repeatable chance experiment, generalizing (yyy - games of chance based on artifacts with physical symmetry) because we do not have an a priori knowledge of the probabilities. Items (yyy - Random sampling for representativeness) and (yyy - Randomized controlled trials) fit the category, as does the classical topic of measurement error. The category is conceptually prominent for two reasons. Dogmatic frequentists assert this is the only context in which numerical probabilities make sense. Second, much classic mathematical probability concerns conclusions (law of large numbers, central limit theorem) of the hypothesis that observations are independent identically distributed random variables, the mathematical formalization of "repeatable chance experiment".

(54) Residuals (errors) in estimation.

Abstractly, if we are trying to estimate some near-future numerical quantity, and then observe its actual value, then the "error" in estimation becomes a known quantity, the residual. If our estimation procedure were the best possible then the residuals would be (in a certain sense that can be made precise) ``purely random", because any systematic non-randomness could be used to improve estimation. This context covers many phenomena, from errors in forecasting tomorrow's temperature to deviations from the "spread" in Football.

(55) Probability as methodology within mathematical statistics

I am deliberately trying to exclude mathematical methodology from this list, so I will not elaborate on the topic above.

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Several instances of probability in science have already appeared in this list, but let me now try a more systematic list of instances. In biology we are all familiar (children may be boys or girls!) with

(61) Random inheritance of genes by offspring from parents

and the associated discipline of mathematical population genetics . Continuing, the two opposite ends of a spectrum from microevolution to macroevolution are

(62) Random mutation as the bottom-level mechanism on which evolution by natural selection operates

(63) Unpredictability (over millions of years) of origin and extinction of species

In the physics there are two opposite paradigm contexts for randomness.

(64) Kinetic theory of gases.

The academic discipline statistical physics seeks more broadly to study the behavior of large populations of "entities" in terms of macroscopic probability descriptions rather than detailed microscopic interactions. See e.g. this brief list of topics. Let's include Brownian motion here.

(65) Deterministic chaos

refers to a system governed by deterministic rules but so sensitive to initial conditions that its long-run behavior is effectively random. As mathematics, it's fascinating that various rules (either completely artificial, or over-simplified models of real phenomena) do indeed have this property. Alas, popular accounts vastly over-sell the usefulness of thinking in terms of chaos rather than general unpredictability. Earthquakes, for instance, are in principle deterministic but at present we can only make probabilistic predictions of their occurrence.

Loosely connected to the "science" theme is

(66) Lucky discoveries (serendipity).

The word serendipity is sometimes used merely as a colorful variant of luck, but let me use it in the narrow context of a discovery in which luck played a noticeable role, an iconic example being the discovery of penicillin, with other scientific examples retold in Serendipity: Accidental Discoveries in Science. See also the taxonomy on this page.

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Let's move on to the engineered world. The idea that it might be useful to view e.g. writing as if it were somehow random is at first sight bizarre -- my deliberate choice of words to write here seems the opposite of "monkeys on typewriters" randomness. But there is some statistical regularity in e.g. how often writers use the word "the", forming the basis of what is rather misleadingly called Information theory but more concretely

(71) Data compression.

English language is "inefficient" in the sense that most letter strings like JQTOMXDW KKYSC have no meaning. But one can "code" (in this context a public, not secret, code) English text so that the coded text is shorter than the uncoded text. The theory of how well this can be done is based on modeling text as having a certain kind of randomness (stationarity: not as restrictive as ``monkeys on typewriters") and it is philosophically interesting that algorithmic schemes designed to be optimal relative to this theory actually work well on real English.

(72) Signal noise

most familiarly radio "static", refers to some (generally small) undesirable errors or disturbance to a designed physical system. These are often modeled as random -- if they were predictably non-random one could try to engineer them away (cf. 54 above).

(73) Software using randomness.

It is sometimes technically useful to use randomized algorithms in settings without explicit randomness; also a possible criterion for choosing betwen algorithms is to imagine the input data will be random and choose the algorithm which will be better "on average" -- this is probabilistic analysis of algorithms. Monte Carlo methods are widely used in many sciences for numerical study of models. Such software typically uses (pseudo)random number generators (RNGs) to generate "synthetic" rather than "true" random numbers. Online poker gambling, for instance, obviously has to use RNGs rather than physical card shuffling, and indeed sites now boast about the quality of their RNGs. Less obvious, modern slot machines are controlled by RNGs without any "physical randomness" of revolving cylinders.

There are everyday occurrences that we don't usually recognize as chance. There are many services that we want to use at whatever time we choose -- making a phone call, driving, going to a grocery store -- and the associated "system" is designed to handle typical demand, but would be overloaded if too many people happened to want the service at the same time; smooth functioning relies on the fact that over short time periods the unpredictable demand is spread roughly uniformly, as it would be under simple random models. Let me call this

(74) Customer service system regularity.

Another type of everyday phenomenon is exemplified by elevators or buses tending to bunch up; and by stop-go motion in traffic jams or in long waiting lines. Such phenomena occur in systems that (as a side-effect to their main purpose) act to amplify underlying minor randomness into qualitatively predictable larger-scale behavior; call this

(75) Everyday incidental amplification of randomness.

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We have already mentioned some "economics" examples from the individual's viewpoint. The most intensively studied quantitative aspect of real-world randomness is perhaps

(81) Short-term fluctuations of equity prices, exchange rates etc.

The random walk/ Brownian motion model works reasonably well though not perfectly. The best known aspect of this theory is the famous Black-Scholes formula for option pricing. Conceptually, such models are based on the idea that prices respond rationally to new information. An opposite notion, under the phrase

(82) Animal spirits

is that much investment/speculation activity is fundamentally irrational. It is a short segue to the study within Psychology of how people think about chance and risk, a topic associated with Daniel Kahneman and colleagues, and surveyed in his book Thinking, Fast and Slow. I will split this into two categories.

(83) Intuitive inferences involving probability that are incorrect (according to uncontroversial theory).

Typical instances: believing small samples are representative, assigning causes to observations explicable as chance (regression fallacy, coincidences), mis-estimating probabilities by ignoring base rates, or by the availability heuristic.

(84) Psychological aspects of making decisions under uncertainty.

Whether people should act in accordance with utility theory is debatable; the many ways in which they do not have been extensively studied. Prospect theory predicts when people will be risk averse and when risk-seeking; decisions are influenced by framing effects, endowment effect, regret or responsibility, etc ; weights attached to outcomes are not linear in probabilities.

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There is a rather broad category of academic work I will call

(87) Applied probability toy models

Very few interesting phenomena are "purely random". So, making a mathematical model of a non-deterministic phenomenon involves specifying some combination of deterministic rules and randomness. In the categories above I have attempted to mention a cross-section of the major academic disciplines where such probability models have been studied and are (at least somewhat) realistic and useful. One can find models for an incredible range of other topics, but the realism of such models varies hugely. Consider a setting where we seek "general understanding" of a phenomenon for which we don't have a well-understood science/engineering background, and we don't want to be tied to some particular case in which we have empirical data. In such a setting one can just invent some rules and study the mathematical behavior of hypothetical processes obeying those rules. A typical instance, often found in recent popular science accounts, concerns small-world networks and the six degrees of separation assertion. Studying such "toy models" is fine as pure mathematics, but regarding them as providing instances of chance operating in the real world is more problematical.

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The next line of thought, "life, the universe, and everything", doesn't really fit our seting of ``small categories of contexts where chance plays a role" (so may be cut in a later version of this list) but is interesting to say somewhere. Standard theory says that atoms formed about 379,000 years after the Big Bang, at which time the mass density of the Universe was roughly homogeneous but with random small fluctuations. So to a hypothetical observer instantaneously after the Big Bang, the evolution of the Universe up to this time might be predictable in outline, except for these

(91) Spatial fluctuations in mass density of the early Universe.

These fluctuations were necessary for subsequent emergence of structure, though theory implicitly suggests that a different realization would have made no qualitative difference. Consider next a hypothetical observer at 379,000 years. According to standard theory, the subsequent qualitative evolution of the Universe -- formation of galaxies and stars and solar systems -- would be predictable in outline. Perhaps less predictable, and hence an instance of chance, is

(92) Formation of an Earth that was physically hospitable to life.

There is a standard theory of formation of the solar system starting with an interstellar molecular cloud undergoing gravitational collapse, and ending with a recently formed Earth at around 4 billion years ago. The point is that this formation of Earth gave a planet that was physically hospitable to life; we don't know how common is the formation of such "physically hospitable to life" planets, or indeed what is actually required to be "physically hospitable to life".

If we stick to the theory that life on Earth originated on Earth, fairly quickly after its formation, then such origination (on a planet "physically hospitable to life") is presumably not an unlikely event. Acceptance of the theory of evolution often means people take for granted the notion that simple life is likely, or at least not very unlikely, to become complex. But this is not self-evident, and the Rare Earth Hypothesis asserts that the way complex life actually developed on Earth required an "improbable combination of astrophysical and geological events and circumstances"; if so, then we can regard

(93) Evolution of complex life on Earth

as an instance of chance.

Granted complex life, to a hypothetical observer at any given time between (say) the Cambrian explosion and (say) 10 million years ago, what would be the chance of future emergence of some species that we would recognize as ``human-style intelligent"? This is a matter of debate; though it seems to me that, at least from the Cambrian viewpoint, the emergence of any species similar to humans was not predictable. Asking about "evolution of some intelligent species" invites distraction from those who insist that dolphins or poodles are intelligent. Perhaps more helpful is to take some list of Human Universals that all existing human cultures share; then regard the instance of ``the chance event that actually happened" as

(94) Evolution of a primitive human society with the given list of universals.

(Precisely, it is not logically necessary that there was an ancestral society with the same universals, but the most recent common ancestral society must have had a least a predisposition thereto). Next consider a hypothetical observer of such a primitive human society, The fact that preliterate human societies in different parts of the world of underwent many roughly parallel cultural and technological developments suggests that the very broad outline of such developments was predictable; what is the "instance of chance" are the particular forms of languages, technology development, political entities, social customs and so on, throughout recorded history and today.

(95) Development of the particular forms of contemporary technological civilization and culture.

Looking to the future, there is a very diverse set of

(96) Global catastrophic risks

to contemporary civilization, from asteroid impact to global warming to intelligent machines to worldwide totalitarian government.

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(100) Chance in fiction.

This is a strange item for a "real world" list. But as discussed further here, fiction often exploits chance for dramatic effect, so part of our perception of how chance operates must derive, if only unconsciously, from fiction.

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The list has deliberately been very broad in what is considered an instance of chance, but where should one draw the line? Of course this depends on one's philosophical stance. Here are some things that (I assert) are not instances of chance. The reason I disqualify these instances is that there is no implicit observer (xxx link not written).

(*1) Fictional settings.

I assert that it doesn't make sense to talk about probabilities within fictional settings. Talking about "the chance Bart Simpson gets injured in the next new episode of The Simpsons" makes sense as a statement about the scriptwriters' intentions, which are unknown to you, but doesn't make sense "within the fictional world of The Simpsons". Analyzing fictional characters as if they were real soon becomes silly. What is a fair bet, to Bugs Bunny? What premiums should a life insurance company ask for a Jedi knight?

(*2) Mathematical conjectures.

If you specify some well-known unsolved mathematical problem, it certainly makes sense to talk about "the chance that a (generally accepted) solution is published before 2020" -- after all, this is the kind of thing one can bet on. On the other hand -- imagining a "yes or no" problem -- I assert it does not make strict sense to talk about "the chance the answer is "yes"".

(*3) The chance of a Universe favorable to life coming into being.

To me, this only makes sense to a hypothetical observer outside the Universe -- and where exactly do you imagine this observer to be? (More comments here).

(*4) The chance you were born.

Saying "you and I are lucky to have been born in the 20th century, rather than some earlier century in which conditions of life were generally worse" conveys some meaning. But what? It is estimated that about 6% of the humans ever born are alive today. I assert it is not correct to interpret that data as implying ``you being alive today is the occurence of a random event that had an a priori chance of 6%". For this requires there to be a notion of "you" before you are conceived, for an observer to make a chance statement about. Which presupposes some unconventional theology -- God first creates all human souls and later randomly assigns them to biological humans.

This instance leads into philosophically contentious teritory. By the same argument, it is incorrect to say that the country and year of our birth, the socioeconomic status of our parents, etc, are matters of chance. There is a fuzzy line, which I don't intend to examine, between this and the "character of our relatives" item.