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Chance

In probability and philosophy, chance refers to the objective probability associated with the occurrence of events in single cases, arising from intrinsic properties of the systems involved rather than from mere statistical frequencies or subjective beliefs, as exemplified by a having a 0.5 probability of landing heads. This article focuses on chance in these contexts; for other uses such as in , , or as a name, see the relevant sections below. In philosophical and scientific contexts, chance represents outcomes that are unpredictable yet governed by probabilistic laws, distinguishing it from strict where all events follow necessarily from prior states. The concept of chance has been central to since the 16th century, when mathematicians like and analyzed gambling problems, such as dice rolls, to quantify likelihoods numerically—for instance, assigning a 1/6 probability to each face of a fair die. This mathematical foundation evolved through contributions from and in the 17th century, who developed via the "" in games, laying groundwork for modern probability. By the , formalized probability as a measure on set-theoretic spaces, providing a rigorous axiomatic basis. Philosophically, chance intersects with debates on , pitting incompatibilists—who argue that nontrivial chances (between 0 and 1) cannot coexist with a fully deterministic , as laws would dictate certain outcomes—against compatibilists, who propose that chances can emerge from deterministic micro-dynamics through Humean best systems of laws balancing simplicity and strength. Interpretations of probability further diversify the understanding of chance: the frequentist view treats it as the long-run frequency in infinite repeatable trials, as in Jacob Bernoulli's 1713 where coin flips converge to 1/2 heads, while the Bayesian approach views it as a degree of belief updated via evidence, for example, shifting odds from 1:1 to 2:1 given a diagnostic test with 80% sensitivity and 60% specificity. These perspectives influence fields from , where chance underpins , to and statistics.

Concept and Etymology

Definition and Meanings

Chance refers to an or outcome that occurs without apparent cause or predictable , embodying the of or unpredictability in natural or human processes. In philosophical terms, chance is understood as an objective probability inherent in a physical process, distinct from mere ignorance of causes, where an outcome is chancy if, under repeated identical conditions, it would vary according to certain non-zero probabilities less than one. This aligns with everyday usage, where chance denotes something happening fortuitously, as in "the meeting was a matter of ," highlighting without intentional design. Beyond , chance often signifies or , either positive or negative, as an impersonal force influencing outcomes beyond control. Positive might involve fortunate coincidences, such as winning a , while negative could manifest as misfortune, like an unexpected ; both are attributed to chance rather than or effort. In this sense, chance acts as a of unaccountable happenings, evoking the idea of in existence that shapes personal or collective experiences. Additionally, chance encompasses , denoting a favorable situation or possibility for action, as in "giving someone a chance" to succeed, which implies a window of potential rather than guaranteed . Philosophically, a key distinction exists between objective chance, which represents the physical tendency or propensity of an event to occur independently of human beliefs—such as the 50% chance of a landing heads—and subjective chance, which reflects an individual's degree of belief or credence in that likelihood based on . Objective chance is a mind-independent feature of the world, often tied to scientific processes like quantum events, whereas subjective chance is epistemological, varying by personal assessment yet constrained by rational norms. Examples illustrate these usages: "by chance" describes coincidental encounters without causation, while "take a chance" involves risking amid , contrasting sharply with , where outcomes are inevitably determined. At its core, chance poses a philosophical with , the view that all events are fixed by prior causes, as nontrivial chances (probabilities between 0 and 1) seem incompatible with a fully determined . This tension arises because implies certain futures, while chance allows for alternative possibilities, enabling branching paths in reality rather than a singular, inevitable sequence. Though some compatibilist theories reconcile them through macro-level probabilities, the underscores chance's role in introducing genuine openness to outcomes.

Historical and Philosophical Development

In , rejected the notion of true chance as a purposeless force independent of natural order, instead viewing it as the of independent causal chains that lack a final cause. In his Physics, he argued that events attributed to chance () or spontaneity () occur incidentally, without inherent purpose, and thus cannot explain regular natural phenomena that happen "always or for the most part." emphasized teleological causation, where chance events still fit within a purposeful , as coincidences arise from the intersection of efficient causes rather than per se. Around 300 BCE, introduced genuine through the concept of the atomic swerve (), a random deviation in the motion of atoms that prevents a strictly deterministic and allows for . This swerve occurs at indeterminate times and places, enabling atomic collisions necessary for the formation of complex structures, including living beings capable of voluntary action. , in his Epicurean poem (c. 55 BCE), elaborated this doctrine, portraying the swerve as essential to breaking the chain of and introducing chance as a fundamental aspect of , free from divine intervention. During the medieval period, reconciled chance with by positing that apparent randomness falls under God's primary causation, which directs all events toward ultimate ends while preserving secondary causes, including human freedom. In the , Aquinas explained that moves creatures in accordance with their natures, so what seems chancy to humans—such as coincidental outcomes—is foreknown and ordained by divine wisdom, ensuring no conflict with . In the , the rise of practices, particularly dice and card games, prompted early scholarly reflections on probabilistic reasoning, as seen in Gerolamo Cardano's Liber de Ludo Aleae (c. 1564), which analyzed odds and outcomes to guide betting strategies, laying groundwork for quantifying uncertainty beyond theological contexts. In the , Pierre-Simon Laplace's deterministic worldview challenged chance by envisioning a —his famous ""—that, knowing all initial conditions and forces, could predict every event with certainty, rendering apparent merely epistemic ignorance. , through his empiricist lens in (1739–1740) and An Enquiry Concerning Human Understanding (1748), further undermined necessary causation by arguing it derives from habitual associations of constant conjunctions in experience, not objective necessity, thus framing chance as the absence of such reliable patterns rather than an active principle. In the late , advanced objective chance within through his doctrine of tychism, introduced in "The Doctrine of Chances" (1878), positing that spontaneity and are real features of the universe, evident in statistical variations that defy strict laws and drive evolutionary change. This contrasted with , emphasizing chance's role in scientific inquiry and fallible knowledge. In contemporary philosophy, Robert Kane's libertarian theory of incorporates as essential for ultimate , where "self-forming actions" arise from indeterminate efforts in moral dilemmas, akin to quantum-like , allowing agents to originate choices without prior causal determination. The advent of in the has bolstered philosophical debates on chance by suggesting inherent in , as probabilistic outcomes in phenomena like challenge classical and revive Epicurean-style notions of objective , though interpretations vary on whether this implies true chance or merely epistemic limits.

Mathematics of Chance

Probability Theory

Probability theory provides the mathematical foundation for quantifying and chance, formalizing the concept of as a rigorous measure on sets of possible outcomes. It emerged as a distinct branch of in the early , building on earlier probabilistic ideas to create a consistent framework applicable across sciences. Central to this theory is the treatment of as a that assigns non-negative values to events, ensuring they sum appropriately for the entire space of possibilities. The modern axiomatic approach to probability was established by in his 1933 monograph Grundbegriffe der Wahrscheinlichkeitsrechnung. Kolmogorov defined probability as a measure P on a sigma-algebra of events within a \Omega, satisfying three s: (1) P(E) \geq 0 for any event E; (2) P(\Omega) = 1; and (3) for countable collections of pairwise disjoint events E_i, P\left(\bigcup_i E_i\right) = \sum_i P(E_i). A key consequence is countable additivity for finite disjoint events, such as P(A \cup B) = P(A) + P(B) when A \cap B = \emptyset. These axioms ensure probability behaves like a normalized measure of likelihood, with P(\emptyset) = 0 following directly from the second axiom applied to the . Earlier, classical probability offered a simpler, combinatorial definition, attributed to in his 1812 work Théorie analytique des probabilités. Laplace defined the probability of an event E as P(E) = \frac{\text{number of favorable outcomes}}{\text{total number of equally likely outcomes}}, assuming a finite, sample space. For instance, in a flip, the sample space has two outcomes (heads or tails), so P(\text{heads}) = \frac{1}{2}. This approach works well for games of chance but requires the assumption of equiprobability, which limits its generality. The frequentist interpretation views probability as the long-run relative frequency of an in an infinite sequence of independent trials under identical conditions, formalized by in his 1928 book Wahrscheinlichkeit, Statistik und Wahrheit. In this framework, P(E) is the \lim_{n \to \infty} \frac{n_E}{n}, where n_E is the number of occurrences of E in n trials, provided the limit exists and the sequence is "random" in a sense (satisfying von Mises' criteria of ). This interpretation grounds probability in empirical , emphasizing repeatable experiments. Conditional probability extends these ideas to dependent events, with providing a method to update probabilities based on new evidence. The theorem states that P(A|B) = \frac{P(B|A) P(A)}{P(B)} for P(B) > 0, where P(A|B) is the probability of A given B. This result was first articulated posthumously in ' 1763 essay "An Essay Towards Solving a Problem in the Doctrine of Chances," published in the Philosophical Transactions of the Royal Society. Bayes derived it to address inverse inference, such as estimating causes from observed effects. Random variables model numerical outcomes of chance experiments, mapping elements to real numbers. Discrete random variables take countable values, with probabilities given by their ; a example is the random variable X counting successes in n independent trials each with success probability p, where P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} for k = 0, 1, \dots, n. This distribution, originating in Jacob Bernoulli's 1713 , describes scenarios like the number of heads in n coin flips. Continuous random variables, in contrast, take uncountable values over intervals, characterized by a (pdf) f(x) such that P(a < X \leq b) = \int_a^b f(x) \, dx. The normal distribution, with pdf f(x) = \frac{1}{\sigma \sqrt{2\pi}} \exp\left( -\frac{(x - \mu)^2}{2\sigma^2} \right), for parameters mean \mu and standard deviation \sigma > 0, exemplifies this, arising naturally in applications.

Randomness and Stochastic Processes

In mathematics, randomness is defined as the property of a sequence or process exhibiting no discernible pattern or predictability, often formalized through concepts like algorithmic incompressibility or statistical independence. A practical test for randomness in discrete data is the chi-squared goodness-of-fit test, which evaluates whether observed frequencies deviate significantly from expected uniform or specified distributions, with the test statistic given by \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}, where O_i are observed counts and E_i expected counts; large values indicate non-randomness. Stochastic processes provide a framework for modeling chance in evolving systems, defined as a collection of random variables \{X_t\} indexed by time t or another , where each X_t represents the state at that index and the joint distribution captures dependencies over the . These processes extend to sequences of events, enabling analysis of systems like queues, financial markets, or . A fundamental class of stochastic processes is Markov chains, discrete-time processes where the conditional distribution of the next depends solely on the current , not the history, formalized as P(X_{n+1} = j | X_n = i, X_{n-1}, \dots, X_0) = P(X_{n+1} = j | X_n = i). The evolution is governed by a P, where P_{ij} is the probability of moving from i to j. For a simple two-state model with states "" (S) and "rainy" (R), the might be P = \begin{pmatrix} 0.8 & 0.2 \\ 0.4 & 0.6 \end{pmatrix}, indicating, for example, an 80% chance of following a day and a 40% chance of following rainy; the distribution after n steps is obtained by multiplying the initial distribution vector by P^n. The Poisson process models point events occurring randomly in continuous time at a constant rate \lambda, defined as a counting process N(t) with stationary and independent increments, where N(t) - N(s) for t > s follows a Poisson distribution with mean \lambda(t-s). The probability of exactly k events in time t is P(N(t) = k) = \frac{(\lambda t)^k e^{-\lambda t}}{k!}, making it ideal for rare events like radioactive decays or customer arrivals. The underpins many stochastic approximations, stating that if X_1, X_2, \dots, X_n are independent and identically distributed random variables with finite mean \mu and variance \sigma^2 > 0, then the standardized sum \frac{\sum_{i=1}^n (X_i - \mu)}{\sigma \sqrt{n}} converges in to a standard normal N(0,1) as n \to \infty. This result explains why normal distributions arise ubiquitously in aggregations of random phenomena, regardless of the individual distributions. In applications, Monte Carlo methods leverage stochastic simulation to approximate deterministic quantities, such as integrals \int f(x) \, dx \approx \frac{1}{N} \sum_{i=1}^N f(U_i) where U_i are uniform random samples, providing unbiased estimates whose accuracy improves with sample size N via the law of large numbers. Brownian motion, or the Wiener process, models continuous randomness as a stochastic process \{W_t\} with W_0 = 0, continuous paths, and independent Gaussian increments W_t - W_s \sim N(0, t-s) for t > s, serving as the continuous analog of a random walk and foundational for diffusion models in physics and finance.

Chance in Science

Physics

In classical physics, Newtonian mechanics provides a deterministic framework where the state of a system at any future time is uniquely determined by its initial conditions and the governing laws of motion. This predictability arises from the differential equations describing particle trajectories under forces, implying no intrinsic role for chance in the evolution of isolated systems. However, apparent randomness emerges in chaotic systems governed by these same deterministic laws, due to sensitive dependence on initial conditions, where minuscule differences in starting states amplify exponentially over time. A seminal example is the Lorenz attractor, a model of atmospheric convection introduced in 1963, which exhibits unpredictable long-term behavior despite following nonlinear differential equations, illustrating how chaos can mimic probabilistic outcomes in practice. Quantum mechanics introduces fundamental indeterminacy, where chance is inherent rather than emergent, as the evolution of the wave function under the Schrödinger equation is deterministic, but measurement causes an irreversible collapse to one of multiple possible outcomes. The probabilities of these outcomes are given by the Born rule, formulated in 1926, which states that for a quantum state described by wave function \psi, the probability P of measuring a particular result is P = |\psi|^2. This probabilistic interpretation underpins the Heisenberg uncertainty principle, established in 1927, which quantifies the intrinsic limits on simultaneous knowledge of conjugate variables, such as position x and momentum p, via the inequality \Delta x \Delta p \geq \frac{\hbar}{2}, where \hbar is the reduced Planck's constant. These principles ensure that quantum predictions involve unavoidable chance, distinguishing them from classical determinism. A notable recent advancement demonstrating the extension of quantum chance to macroscopic scales came with the 2025 Nobel Prize in Physics, awarded to John Clarke, Michel H. Devoret, and John M. Martinis for their experimental demonstration of macroscopic quantum tunneling and energy quantization in superconducting electrical circuits. This work showed that tunneling—a quantum process where particles probabilistically pass through energy barriers—occurs in systems involving billions of electrons (Cooper pairs), with chance playing a key role in the unpredictable timing of events, measured statistically similar to radioactive half-lives. These findings bridge microscopic quantum indeterminacy to larger systems, with implications for and further underscoring chance's fundamental nature in physics. Radioactive decay exemplifies quantum chance in nuclear physics, where the decay of individual atoms is unpredictable but follows statistical patterns modeled as a Poisson process. The probability that a nucleus decays in a small time interval is constant and proportional to the decay constant \lambda, leading to an exponential survival probability e^{-\lambda t} and a half-life t_{1/2} = \frac{\ln 2}{\lambda}, the time for half the atoms to decay on average. In applications like Carbon-14 dating, the probabilistic nature manifests in the measurement of remaining ^{14}C (half-life approximately 5730 years) in organic samples, where the age t is inferred from the ratio N/N_0 = e^{-\lambda t}, but uncertainties arise from counting statistics and calibration curves, typically yielding error bars of decades to centuries for samples up to 50,000 years old. In , chance underlies the second law, which states that the S of an never decreases, reflecting a probabilistic tendency toward in microscopic configurations. Ludwig Boltzmann's H-theorem, derived in 1872 from the for dilute gases, demonstrates this by showing that the H-function, defined as H = \int f \ln f \, d^3v (where f is the particle ), decreases monotonically toward , mathematically equivalent to an increase in S = -k H (with k Boltzmann's constant). This links macroscopic irreversibility to the vast number of microstates, where fluctuations against the gradient become negligibly probable for large systems. In , quantum randomness finds practical use in quantum random number generators (QRNGs), which exploit indeterminacies like photon detection or fluctuations to produce truly unpredictable bit sequences, certified by violations or bounds. Unlike pseudo-random classical algorithms, QRNGs provide provable essential for and simulations. In cosmology, quantum fluctuations during the —rapid expansion around 10^{-36} seconds after the —generate primordial density perturbations via the acting on the field, seeding the observed large-scale structure and anisotropies with a nearly scale-invariant power spectrum. These fluctuations, amplified from quantum to cosmic scales, represent a key instance of chance shaping the universe's architecture.

Biology

In biological systems, chance manifests as a fundamental driver of variation at the molecular level, primarily through random mutations in DNA that introduce genetic diversity. Point mutations, which involve the substitution of a single nucleotide, occur at an average rate of approximately 10^{-8} per base pair per generation in humans, enabling evolutionary change by altering genetic sequences unpredictably. These mutations are inherently stochastic, arising from errors during DNA replication or damage from environmental factors, and their fixation in populations is further influenced by genetic drift, particularly in small populations where random fluctuations in allele frequencies can dominate over selection. Motoo Kimura's neutral theory of molecular evolution, proposed in 1968, posits that the majority of such molecular changes are selectively neutral and fixed by drift rather than adaptive advantage, explaining observed rates of genetic divergence across species. At the cellular level, chance contributes to variability through gene expression, where random fluctuations in transcription and translation lead to noise in protein levels despite identical genetic backgrounds. In the of , for instance, stochastic switching between induced and repressed states results in bimodal expression patterns, with individual cells exhibiting heterogeneous metabolism even under uniform conditions. This noise arises from probabilistic binding of regulatory proteins and low molecule numbers, amplifying variability that can influence cellular decision-making and . On evolutionary scales, operates on this random variation generated by chance, shaping adaptive traits from unpredictable genetic inputs. The Hardy-Weinberg equilibrium describes the expected frequencies in a large, randomly absent selection, migration, or drift, given by the equation p^2 + 2pq + q^2 = 1, where p and q are the frequencies of two alleles; deviations from this equilibrium highlight the role of chance events like drift in altering genotypic proportions. A recent empirical published in January 2025 further illustrates chance's influence, showing that in genetically identical mice, early-life contingencies or ""—such as access to resources—affect adult and , particularly under high , where random events amplify in male quality while females show more consistency; this underscores how factors can drive evolutionary outcomes beyond and selection. In ecological contexts, random dispersal and demographic drive , as seen in models of where species equivalence allows chance to govern community composition and species abundance distributions. Stephen Hubbell's unified theory, formalized in 2001, integrates these processes to explain patterns of in metacommunities through birth, death, and events. Chance is thus irreducible in biology, serving as an essential mechanism that enables adaptation and diversity without implying purposeful direction, as random variation provides the raw material upon which selection acts contingently. This stochastic foundation underpins the emergent complexity of life, from genetic novelty to ecosystem dynamics.

Linguistic Usage

Synonyms and Idioms

In English, synonyms for "chance" encompass words that capture its multifaceted nature as an unpredictable or opportune event. Luck often implies a fortuitous outcome without deliberate effort, while fortune suggests a broader, destiny-like influence on events. Hazard conveys the risky or perilous aspect of chance, and coincidence highlights an unexpected alignment of circumstances. Antonyms such as certainty, which denotes predictability, and design, implying intentional structure, stand in direct opposition to the randomness inherent in chance. Idioms featuring "chance" vividly illustrate its rhetorical role in everyday language, often blending literal and figurative meanings. The phrase "by chance" describes something occurring accidentally or haphazardly, without prior planning. "Chance upon" refers to stumbling upon something unexpectedly, such as an idea or object during routine activities. In contrast, "fat chance" employs sarcasm to dismiss the likelihood of an event, implying near impossibility, whereas "even chance" denotes balanced probabilities, typically evoking a 50/50 scenario in decisions or wagers. Collocations with "chance" further refine its nuances in probabilistic or opportunistic contexts. "Slim chance" underscores a minimal probability of , often used to temper expectations. "Fighting chance" portrays a precarious but attainable that requires effort to realize, and "stand a chance" evaluates whether something has any realistic of prevailing against . These pairings emphasize chance's evaluative role in assessing viability. Culturally, expressions involving "chance" reflect dual connotations in English-speaking societies, balancing optimism and caution. Positive associations appear in phrases like "second chance," which symbolizes or renewed possibility, fostering themes of and in narratives and . Negatively, "game of chance" links to and inherent risks, evoking and potential loss in recreational or financial pursuits.

Etymology and Word Origins

The word "chance" entered the English language in the 13th century as "cha(u)nce," borrowed from Old French "cheance" or "chance," which denoted the "falling" of dice in gambling contexts. This Old French term derives from Vulgar Latin *cadentia, meaning "that which falls out," ultimately tracing back to the Latin verb cadere, "to fall." The Proto-Indo-European root *kad-, meaning "to fall," underpins this lineage, reflecting a conceptual link to unexpected occurrences akin to a fall or drop. Semantically, "chance" evolved from its literal sense of a physical fall—particularly in throws during medieval —to signify "what falls out" as an outcome, extending to notions of , , or unforeseen events by around 1300. This shift was heavily influenced by the cultural prominence of games of chance in medieval , where the unpredictable fall of symbolized variability and absence of deterministic cause. By the , the term had broadened to encompass opportunity and , diverging from its original mechanical connotation. Related English words share this Latin root cadere, illustrating broader semantic fields of descent or occurrence. For instance, "" refers to rhythmic flow, evoking the measured falling of sounds or steps, entering English in the late via Old Italian . "Incident" stems from Latin incidere ("to fall into" or "upon"), denoting events that befall someone, while "" arises from de + cadere ("to fall down" or "apart"), implying gradual deterioration. These connections highlight how cadere extended metaphorically from physical motion to processes of happening or decline. Cross-linguistically, cognates of "chance" appear in , such as cadenza (a musical falling or close) and Spanish caída (a fall), both directly from cadere. In contrast, the related concept of "fortune" derives from Latin fortuna, rooted in fors ("" or "chance") and linked to ferre ("to bear"), emphasizing fate borne by external forces rather than a literal fall. In modern usage, "chance" rose as a in the , primarily in English-speaking contexts, where it evokes "" or "good " independently of its etymological origins, often as a of Chauncey. This development reflects a shift toward virtue-inspired naming, with popularity surging in the .

Geographical Places

In the United States

, is a (CDP) in County on the state's Lower Eastern Shore, serving as a small rural community along the . Established as a hub for watermen, its economy has historically centered on oystering, crabbing, and seafood harvesting, with residents navigating the bay's tidal waters for generations. According to the , the population stood at 377, reflecting a tight-knit, predominantly White demographic in a sparsely populated area of about 0.91 square miles. By 2010, the count had declined slightly to 353, and the 2020 census reported 330 residents. This ongoing decline underscores challenges like and shifting fisheries in the region. In , Chance refers to an unincorporated community in the northern part of the county, near the and U.S. Route 17. This rural locale is historically tied to colonial-era agriculture and plantation life, with limited modern development. A key landmark is Glencairn, an 18th-century brick-nogged frame manor house built around 1730, which served as a residence for prominent local families. The property, spanning open fields and featuring period outbuildings, was added to the on May 14, 1979, for its architectural and historical value in illustrating Tidewater Virginia's agrarian past. Chance, , is a small, unincorporated rural community in Hardin County in , near Beaumont. Locally known as Chance in honor of an early pioneer family that settled the area, it originated as a site and emerged amid oil exploration in the early . The community is closely associated with the oil field, where the first productive well was drilled in 1932, followed by two more that initiated modest extraction operations and supported local economies. This development exemplified the transformative impact of petroleum discovery on remote outposts, though Chance remains sparsely populated today with no formal municipal government. Beyond these, several minor U.S. locales bear the name Chance, contributing to a total of approximately eight such places nationwide, most of which are rural and unincorporated. Examples include Chance in , a small populated place with historical ties to the region's farming heritage; and Chance in , an obscure unincorporated community where a post office operated briefly from 1904 to 1918. These sites, often documented only in geographic surveys, underscore the name's occasional use for modest settlements without significant urban development.

Elsewhere

Geographical places named Chance outside the are exceedingly rare, with global databases identifying only about 9 exact matches worldwide (8 in the U.S. and 1 in ), though variants and related names appear sparingly. This scarcity reflects the name's primary association with English-speaking North American contexts, where it often denotes small, unincorporated communities or historical settlements tied to themes of or prospects. No major cities or urban centers bear the name internationally, underscoring its limited adoption beyond American borders. In , Chancé (a variant spelling) represents a singular European example, serving as a former commune in the department of until its merger into the larger commune of Piré-Chancé on January 1, 2019, as a delegated commune. Located in northwestern , the area features rural landscapes typical of the region, with a population historically under 1,000 residents prior to the administrative change. Canada hosts one of the few non-U.S. instances incorporating "Chance" as part of the name: the town of Come By Chance in , positioned on the isthmus of the at the head of Placentia Bay. Incorporated in with a 2021 population of 208, the town's name—first documented as "Comby Chance" in 1706—likely stems from the chance discovery of its sheltered harbor by early explorers, evolving from its original designation as Passage Harbour in 1612. The community gained economic significance in the 1970s with the establishment of an oil refinery, now operated by North Atlantic Refining Limited, transforming it from a quiet outpost into an industrial hub. In the , Chance Hall Farm in , , stands as a notable rural property related to the name, a 550-acre operation near known for its ProCROSS herd and sustainable practices, though it functions more as a working farmstead than a populated .

Notable People

Given Name

Chance the Rapper, born Chancelor Johnathan Bennett on April 16, 1993, in , Illinois, is a prominent Grammy-winning rapper known for his independent releases and socially conscious lyrics. His breakthrough mixtape was released in 2013, blending introspective storytelling with jazz and gospel influences, while his 2016 mixtape became the first streaming-only project to win a Grammy, earning Best Rap Album along with Best New Artist and Best Rap Performance for the track "" at the 2017 ceremony. In 2025, he released his second studio album, Star Line, on August 15.) Beyond music, Bennett has been a vocal advocate for 's education system, donating $1 million personally and securing another $1.2 million through partnerships, including with the , to support public schools facing budget shortfalls in 2017. Chance Sutton, born September 2, 1996, rose to fame as a star and through comedic sketches and viral challenges on and , amassing over 2.6 million subscribers on his collaborative channel Chance and Anthony by 2023, often featuring collaborations with the collective. His acting credits include roles in the 2016 film Mono and the 2018 short All Night, showcasing his transition from to on-screen performances. Chance Perez, born November 10, 1997, gained early recognition as a pop-R&B singer after competing on season three of in 2013, where his covers of songs like "" highlighted his vocal range. He later released his debut EP First Chance in 2020, featuring tracks that blend with personal themes of perseverance. He gained further recognition for his role as Javi Garcia, the Green Ranger, in the Power Rangers series Dino Fury (2021) and Cosmic Fury (2023). Other notable figures include Chance Hurstfield, born in 2001, a Canadian actor who portrayed in the Netflix series (2017–2019), earning acclaim for his role in the adaptation of Lemony Snicket's novels. As a given name, Chance functions as a modern evoking "" or "," derived from the English word ultimately tracing to Latin cadens ("falling"). Its popularity among U.S. boys has risen since the , peaking in the at #236 in with 1,820 annual uses, before stabilizing in the top 500, ranked #418 in 2024 with 757 uses, per data.

Surname

The surname originates from "chea(u)nce," denoting fortune, luck, or mischance, derived from the Old French word "chance." In the United States, approximately 14,300 individuals bore the surname based on 2010 Census data, with estimates around 16,000 in recent years, and the highest concentrations in , , and . Frank Chance (1877–1924) was an American professional baseball player and manager, elected to the Baseball Hall of Fame in 1946. As a first baseman for the Chicago Cubs from 1903 to 1912, he formed the legendary "Tinker to Evers to Chance" double-play infield with Joe Tinker and second baseman Johnny Evers, immortalized in a 1910 poem by . Chance also managed the Cubs to four pennants (1906–1908, 1910) and two appearances (1906, 1907), compiling a career managerial record of 946–648. Dean Chance (1940–2015) was an American Major League Baseball pitcher renowned for his 1964 season with the Los Angeles Angels. He won the American League Cy Young Award that year with a 20–9 record, a 1.65 ERA, and 11 shutouts, leading the league in the latter category; he also pitched a no-hitter against the Boston Red Sox on August 21. Over his 11-year career with teams including the Angels, Minnesota Twins, and Detroit Tigers, Chance recorded 128 wins and a 2.92 ERA, earning three All-Star selections. Michael Chance (born March 7, 1955) is an English acclaimed for his interpretations of repertoire, particularly works by Handel and Purcell. He has performed with major ensembles such as the and the English Baroque Soloists, and recorded over 150 albums, including Handel's under conductors like and Sir Neville Marriner. Chance received a Grammy Award in 1993 for Best Opera Recording for his role in Handel's with the Symphony Orchestra under John Nelson. Members of the Chance family, notably through the industrial firm founded in 1821, were prominent British industrialists specializing in optics. James Timmins Chance (1814–1902), a key figure in the company, pioneered advancements in technology, including the integration of lamps within lens cages to amplify light output and the development of rotating optical systems for enhanced visibility; by the late , supplied lenses for over 400 s worldwide. Samuel Chance (c. 1790–after 1835) was an early settler and one of Stephen F. Austin's colonists. Born in , he received a land grant of one (approximately 4,428 acres) in what became Brazoria County on , , where he farmed and raised stock. Chance participated in early Texas colonization efforts, contributing to the Anglo-American settlement under Mexican rule before the .

Arts and Entertainment

Film and Television

In film, "Chance" (2002) is an independent dark comedy directed by and starring Amber Benson, who also wrote and produced the project. The story follows the titular character, a young woman grappling with personal relationships, family dynamics, and self-discovery through a series of romantic misadventures and introspective flashbacks. The film features a non-linear narrative and co-stars James Marsters as Chance's friend Simon, emphasizing themes of coincidence and emotional vulnerability in everyday life. A prominent example of a character named Chance in cinema is the 1979 satirical drama Being There, directed by Hal Ashby and based on Jerzy Kosiński's novel. Peter Sellers portrays Chauncey "Chance" Gardiner, a naive gardener isolated from the world who, after being thrust into high society, unwittingly becomes a media darling and advisor to political figures due to misinterpretations of his simple observations about gardening as metaphors for economics and society. The film critiques American media, politics, and celebrity culture, earning Sellers an Academy Award nomination for Best Actor and the picture a Palme d'Or at Cannes. On television, Chance (2016–2017) is a psychological thriller series created by Alexandra Cunningham and Kem Nunn, adapted from Nunn's novel Chance. Airing on Hulu for two seasons, it stars Hugh Laurie as Dr. Eldon Chance, a San Francisco forensic neuropsychiatrist whose routine life unravels when he encounters a patient claiming spousal abuse, pulling him into a web of trauma, mental illness, police corruption, and conspiracy. The series explores the blurred lines between perception and reality, with Laurie delivering a nuanced performance as a man confronting his own ethical dilemmas. Notable television episodes incorporate "chance" as a plot device or title element to drive narrative twists. In The Simpsons Season 4 episode "Last Exit to Springfield" (1993), written by Dan Greaney, Homer Simpson is unexpectedly elected president of the nuclear plant's union during a random nomination process, sparking a strike centered on dental plan benefits after Lisa reveals she needs braces for her malocclusion. This chance occurrence highlights themes of accidental leadership and family priorities amid labor disputes. Similarly, Breaking Bad frequently weaves chance encounters into its storytelling to underscore fate's role in moral descent; for instance, Walter White's serendipitous meetings with figures like Gus Fring propel his transformation from teacher to drug lord, as analyzed in discussions of the series' narrative reliance on unpredictable events to explore power and consequence. The of and the unpredictability of chance recurs across film and television as a lens for examining human agency versus randomness. A quintessential illustration appears in (1994), directed by , where the protagonist's mother, played by , imparts the line: "Life is like a box of chocolates. You never know what you're gonna get," symbolizing how unforeseen events shape destiny in the film's episodic journey through American history. This theme echoes in various works, portraying chance not merely as but as a catalyst for growth, , or .

Music

Chance the Rapper, born Chancelor Jonathan Bennett in 1993, is an American rapper, singer, and record producer known for his independent releases and integration of gospel, soul, and hip-hop elements. His breakthrough mixtape Acid Rap (2013) features introspective tracks exploring youth, addiction, and Chicago life, earning critical acclaim for its raw lyricism and jazz-infused production. Subsequent works include the Grammy-winning Coloring Book (2016), a streaming-only album blending positive messages with collaborations from artists like Kanye West and Kirk Franklin, highlighted by the hit single "No Problem," which critiques industry pressures and peaked at number 43 on the Billboard Hot 100. His discography also encompasses The Big Day (2019), a family-themed album, and STAR LINE (2025), reflecting personal growth and cultural commentary through eclectic tracks like "Buried Alive Interlude." SocialWorks, a Chicago-based nonprofit founded by in 2016 alongside Justin Cunningham and Kenya Butler, supports youth empowerment through , education, and community programs, including music initiatives like the New Chance Fund for school grants. The organization has distributed over $12 million in grants to the Chicagoland community since 2016, including over $5.1 million to via initiatives like the New Chance Fund, impacting over 50,000 students as of 2025. It has partnered with entities such as the NHL for youth and outreach. Other musical acts bearing the name "Chance" include , a pioneering band formed in 1977 in , blending , , and with chaotic energy on albums like Buy (1979), influencing the scene. In indie rock, the band Forever Young released the self-titled album The Chance in 2010 via I For Us Records, featuring upbeat tracks like "Keep It Posi" that draw on and influences. Notable songs titled or themed around "chance" span genres and eras. 's "" (1977), from the album ABBA: The Album, is a disco-pop written by and , reaching number one in several countries and emphasizing romantic opportunity with its infectious chorus and handclap rhythm. Earlier, Zion I's track "One Chance" from the album True & Livin' (2003) delivers conscious verses on seizing opportunities, produced by AmpLive with a laid-back vibe. Aleatory music, or chance music, incorporates randomness into composition or performance, pioneered by in works like Music of Changes (1951), where the determined note structures to eliminate composer bias and embrace unpredictability. This approach influenced subsequent pieces such as Earle Brown's December 1952 (1952), using graphic scores that allow performers interpretive freedom, highlighting "chance" as a core aesthetic in 20th-century .

Literature and Other Forms

In literature, the concept of chance often manifests as pivotal coincidences that drive plot and character development. Joseph Conrad's novel Chance, published in 1913, exemplifies this through its maritime narrative, where the protagonist Flora de Barral navigates the aftermath of her father's financial ruin, encountering opportunities and reversals shaped by unpredictable events at sea. The story, framed by multiple narrators including Marlow, explores chance as both a force enabling human agency and an indifferent arbiter of fate, marking a departure from Conrad's earlier tragic works toward themes of redemption. More contemporary examples include Karen Kingsbury's The Chance (2013), a centered on childhood sweethearts Ellie Tucker and Nolan Cook, whose lives diverge due to unforeseen circumstances but converge years later through a promised reunion, highlighting and second opportunities. The narrative uses a single serendipitous encounter to rekindle their bond, emphasizing emotional healing amid loss. In theater, Tom Stoppard's (first performed in 1966) reimagines Shakespeare's from the perspective of its minor characters, incorporating chance through recurring coin flips that always land heads, symbolizing over . The play delves into existential themes of versus , with the protagonists' futile attempts to assert control underscoring chance's illusory nature within a scripted world. Beyond prose and drama, chance influences visual arts and sequential storytelling. In Dada and Surrealism, artists employed chance operations to bypass conscious control and access the unconscious; Max Ernst pioneered frottage in the 1920s, rubbing graphite over textured surfaces to generate random patterns that informed paintings like those in Histoire Naturelle, evoking dreamlike imagery through serendipitous marks. This technique aligned with Surrealist automatism, where unintended results from physical processes mirrored objective chance, as theorized by André Breton. In comics, the 1990s series Leave It to Chance (1996–1999, Image Comics), written by James Robinson and illustrated by Paul Smith, follows teenage protagonist Chance Falconer as she tackles supernatural threats in a coastal town, often propelled by fortuitous discoveries and alliances. The story integrates chance as a narrative catalyst, with the heroine's impulsive decisions leading to pivotal, improbable resolutions in her paranormal adventures. Narratives across these forms frequently adhere to conventions limiting coincidences to maintain plausibility; a common rule in writing posits that only one major chance should anchor the plot, preventing contrived resolutions and preserving through elsewhere. This restraint, observed from classical to modern works, ensures coincidences serve thematic depth rather than expediency.

Other Uses

Games and Gambling

In games and gambling, chance serves as a core mechanic that introduces unpredictability, distinguishing pure luck-based activities from those incorporating . Gambling games often exemplify this, with outcomes determined primarily by random events such as rolls or card draws, creating excitement through uncertainty. represents a quintessential game of pure chance, where players bet on a landing on a numbered of a . In the version, featuring 38 pockets including a double zero, the house edge stands at 5.26% across most bets, ensuring the casino's long-term advantage regardless of player strategy. Craps, by contrast, blends chance with elements of in bet selection, as players wager on the outcomes of rolls by a "shooter." The pass line bet, one of the most favorable, carries a house edge of approximately 1.41%, though taking "odds" bets can reduce the effective edge to near zero on certain points. Board games frequently incorporate chance to simulate real-world and drive narrative progression. In , the Chance cards—16 orange cards drawn when landing on designated spaces—trigger random events that can alter players' fortunes dramatically. For instance, the card "Bank error in your favor. Collect $200" provides an unexpected windfall, while others impose penalties like fines or property repairs, emphasizing luck's role in . Card games like poker highlight probabilistic chance within a framework, where players calculate based on hidden . In poker, the probability of being dealt —the highest hand, consisting of through ten of the same suit—is precisely 1 in 649,740, underscoring the rarity of such fortunate draws. Solitaire variants, such as , rely heavily on chance through the initial random deal of 52 cards into tableau, stock, and waste piles; approximately 80% of deals are theoretically winnable with perfect play, but the hidden cards introduce significant luck in uncovering sequences. Video games employ random number generators (RNGs) to manage chance in loot and progression systems, fostering replayability. In the Diablo series, RNG determines item drops from defeated enemies, with rare "legendary" gear having low drop probabilities—often below 1% per encounter—creating thrilling moments of serendipity amid grinding. This mechanic, powered by pseudorandom algorithms, simulates uncertainty akin to traditional gambling. The integration of chance in games traces back to ancient civilizations, where facilitated early forms of . In , tesserae (six-sided bone or ivory ) and tali (four-sided ) were used in popular games despite legal restrictions outside festivals like ; players bet on rolls, with tesserae enabling bets on specific numbers or sums. Modern lotteries extend this tradition on a massive scale, as seen in , where the odds are 1 in 292,201,338 due to selecting five numbers from 69 plus one from 26, amplifying chance's allure through enormous stakes.

Brands and Miscellaneous

The perfume line, launched in September 2002, is a series of floral fragrances for women created by , embodying themes of and joyful spontaneity through notes like pink pepper, , and white musk in its original variant. Subsequent iterations, such as Chance Eau Tendre (2010) with and , and Chance Eau Fraîche (2007) featuring and wood, expand the collection while maintaining its fresh, citrus-floral profile symbolizing serendipitous encounters. AB , a under Hubbell Systems founded in , specializes in lineman-grade tools and equipment for electrical and , including hot sticks, grounding clamps, and products designed for high-voltage . These tools, such as the C600-0197 ground clamp with a 5H for secure attachment, have become industry standards for and line work due to their durability and compliance with protocols. The Doctrine of Chances, published in 1718 by , is a foundational text in , expanding on his earlier 1711 paper "De mensura sortis" to detail methods for calculating odds in games of chance and annuities, spanning 175 pages in its first edition printed by W. Pearson. Later editions in 1738 and 1756 incorporated binomial expansions and approximations now known as the de Moivre-Laplace theorem, influencing and . In the arts, chance operations refer to compositional techniques using random processes to eliminate authorial intent, prominently employed by in his 1951 piano work , where the oracle determined structural elements like durations, densities, and sound parameters from pre-composed materials. This approach, first explored in Cage's Imaginary Landscape No. 4 earlier that year, extended to visual and performance arts, promoting indeterminacy as a means to experience unpredictability akin to natural phenomena. Medically, a Chance fracture denotes a flexion-distraction injury to the thoracolumbar spine, typically at L1-L2, involving transverse disruption of the vertebral body and posterior elements, often resulting from high-energy trauma like motor vehicle accidents with lap-belt restraint causing the "seatbelt sign." First described in 1948 by , this unstable fracture requires surgical stabilization in about 50% of cases to prevent neurological deficits, with associated intra-abdominal injuries in up to 50% of patients. In legal contexts, the doctrine of chances permits the admission of evidence showing a defendant's repeated involvement in similar improbable events—such as multiple deaths of spouses—to rebut claims of coincidence and support inferences of criminal intent without relying on propensity. Originating from English common law cases like R v. Smith (1915), it has been applied in U.S. jurisprudence under Federal Rule of Evidence 404(b) to objectively demonstrate low statistical probability of innocent recurrence, as analyzed in scholarly reviews emphasizing its distinction from character evidence. The , founded in 1917 by aeronautical engineer on [Long Island](/page/Long Island), , pioneered naval aircraft design, producing early biplanes like the VE-7 trainer and later icons such as the F4U fighter during . Evolving through mergers—including with in 1929 and Sikorsky in 1939—the firm contributed to over 90 years of aerospace innovation before integrating into in 1961 and eventually .

References

  1. [1]
    [PDF] Chance and Determinism - PhilSci-Archive
    Determinism and chance seem to be irreconcilable opposites: either something is chancy or it is deterministic but not both. Yet there are processes which ...
  2. [2]
    Ten Great Ideas about Chance - American Mathematical Society
    Frequentist Philosophy takes a different approach, and gets a turn as the fourth great idea of chance. In the frequentist interpretation, probability does not ...
  3. [3]
    Chance versus Randomness - Stanford Encyclopedia of Philosophy
    Aug 18, 2010 · Randomness, as we ordinarily think of it, exists when some outcomes occur haphazardly, unpredictably, or by chance.
  4. [4]
    Definition of CHANCE
    ### Summary of Primary Definitions of 'Chance' from Merriam-Webster
  5. [5]
  6. [6]
    Interpretations of Probability - Stanford Encyclopedia of Philosophy
    Oct 21, 2002 · We are asking how much the evidence tells for or against the hypothesis. We are not asking what objective physical chance or frequency of truth ...
  7. [7]
    Aristotle - Stanford Encyclopedia of Philosophy
    Sep 25, 2008 · Because of its wide range and its remoteness in time, Aristotle's philosophy defies easy encapsulation. ... chance or spontaneity comes about ...
  8. [8]
    Aristotle on Causality - Stanford Encyclopedia of Philosophy
    Jan 11, 2006 · Aristotle developed a theory of causality which is commonly known as the doctrine of the four causes.
  9. [9]
    Ancient Theories of Freedom and Determinism
    Oct 30, 2020 · Aristotle thinks that effective deliberation and action presuppose the openness or contingency of the future—that what is going to happen is not ...
  10. [10]
    Lucretius - Stanford Encyclopedia of Philosophy
    Sep 22, 2023 · ... Epicurus argues for human agency over causal determinism, leaves it unclear how widely Epicurus relied on the swerve. Some think a swerve is ...
  11. [11]
  12. [12]
    Probability in Medieval and Renaissance Philosophy
    Dec 29, 2014 · The most prominent scholastic understanding of probability derived from Aristotle's notion of endoxon, which shaped the concept of “probable ...
  13. [13]
    David Hume - Stanford Encyclopedia of Philosophy
    Feb 26, 2001 · His empiricism is naturalistic in that it refuses to countenance any appeal to the supernatural in the explanation of human nature. As a ...Kant and Hume on Causality · Hume's Moral Philosophy · On Free Will · On Religion
  14. [14]
    Charles Sanders Peirce - Stanford Encyclopedia of Philosophy
    Jun 22, 2001 · Charles Sanders Peirce (1839–1914) was the founder of American pragmatism (after about 1905 called by Peirce “pragmaticism” in order to differentiate his views)Peirce's Deductive Logic · Peirce's View of the... · Benjamin Peirce
  15. [15]
    Incompatibilist (Nondeterministic) Theories of Free Will
    Aug 17, 2000 · If the choice is to be an SFW, then it is required that the strength of this effort be indeterminate; Kane likens its indeterminacy to that of ...Event-Causal Theories · Deliberative Indeterminism · Efforts of Will · Luck, Again
  16. [16]
    [PDF] The origins and legacy of Kolmogorov's Grundbegriffe - arXiv
    Feb 5, 2018 · In 1963, Kolmogorov complained that his axioms had been so successful on the purely mathematical side that many mathematicians had lost interest ...
  17. [17]
    Kolmogorov axioms of probability - The Book of Statistical Proofs
    Jul 30, 2021 · Definition: Kolmogorov axioms of probability. Index: The Book of ... Sources: A.N. Kolmogorov (1950): "Elementary Theory of Probability ...Missing: original | Show results with:original
  18. [18]
    Laplace's Essay on Probabilities - The Information Philosopher
    The probability of a future event is the sum of the products of the probability of each cause, drawn from the event observed, by the prob- ability that, this ...
  19. [19]
    (PDF) Von Mises' Frequentist Approach to Probability - ResearchGate
    Mar 31, 2016 · The definition of chance given by von Mises [4] is the inability to find a system that allows us to make a prediction about the place in a ...
  20. [20]
    LII. An essay towards solving a problem in the doctrine of chances ...
    LII. An essay towards solving a problem in the doctrine of chances. By the late Rev. Mr. Bayes, F. R. S. communicated by Mr. Price, in a ...
  21. [21]
    The Binomial Distribution: Historical Origin and Evolution of Its ...
    We present five historical links to the binomial phenomenon where problem situations of increasing complexity were addressed.
  22. [22]
    Normal Distribution | Gaussian | Normal random variables | PDF
    The CDF of the standard normal distribution is denoted by the Φ function: Φ(x)=P(Z≤x)=1√2π∫x−∞exp{−u22}du. As we will see in a moment, the CDF of any normal ...Missing: source | Show results with:source
  23. [23]
    [PDF] Randomness
    May 6, 2013 · Randomness. Morals: There are several precise mathematical notions of randomness. Several definitions are equivalent, and each captures some.
  24. [24]
    Testing for randomness - Steven M. LaValle
    Many sophisticated statistical tests of uniform randomness are used. One of the simplest, the chi-square test, is described here. This test measures how far ...
  25. [25]
    [PDF] Lecture 5 : Stochastic Processes I - MIT OpenCourseWare
    A stochastic process is a collection of random variables indexed by time. An alternate view is that it is a probability distribution over a space.
  26. [26]
    [PDF] MARKOV CHAINS: BASIC THEORY 1.1. Definition and First ...
    Definition 1.​​ A (discrete-time) Markov chain with (finite or countable) state space X is a se- quence X0,X1,... of X −valued random variables such that for all ...
  27. [27]
    Markov Chains — Stats366 / Stats 166 Course Notes
    We can model the weather with a two state Markov chain ... weather example: > P%*%P [,1] [,2] [1,] 0.44 0.56 ... Hidden Markov Model for CpG islands ...
  28. [28]
    [PDF] Chapter 2 - POISSON PROCESSES - MIT OpenCourseWare
    A Poisson process is a simple and widely used stochastic process for modeling the times at which arrivals enter a system.
  29. [29]
    [PDF] Central Limit Theorem and the Law of Large Numbers Class 6 ...
    The central limit theorem says that the sum or average of many independent copies of a random variable is approximately a normal random variable. The CLT goes ...
  30. [30]
    [PDF] Monte Carlo Methods - UMD MATH
    Monte Carlo methods are those where one evaluates something nonrandom using pseu- dorandom numbers. More precisely, one evaluates a nonrandom quantity as the ...
  31. [31]
    [PDF] BROWNIAN MOTION 1.1. Wiener Process
    A standard (one-dimensional) Wiener process (also called Brownian motion) is a stochastic process {Wt}t≥0+ indexed by nonnegative real numbers t with the ...
  32. [32]
    What is Chaos?: Determinism
    Newton's laws are completely deterministic because they imply that anything that happens at any future time is completed determined by what happens now, and ...
  33. [33]
    2 Newtonian mechanics and the deterministic world - Oxford Academic
    Sep 28, 2023 · Newtonian laws painted a deterministic picture of the universe—if the location of all the objects in the universe and the forces acting upon ...
  34. [34]
    Chaos at fifty - Physics Today
    May 1, 2013 · What Lorenz had observed with his model came to be known as sensitive dependence on initial conditions—a defining property of chaos. In ...
  35. [35]
    [PDF] The Born rule and its interpretation - Mathematics
    The Born rule provides a link between the mathematical formalism of quantum theory and experiment, and as such is almost single-handedly responsible for ...
  36. [36]
    Fig. 2. Poisson distribution for various values of µ.
    To take a concrete example, consider a typical radioactive source such as 137Cs which has a half-life of 27 years. The probability per unit time for a ...
  37. [37]
    [PDF] Radioactivity I: Counting and Poisson Statistics
    The time Tl/2 for half of the nuclei to decay is called the half life. It can easily be shown that: T1. 2 = ln(2) /𝜆 = 0.693/𝜆 . (3). Each unstable ...
  38. [38]
    Radiometric Dating - Tulane University
    Apr 18, 2012 · Because of the short half-life of 14C, it is only used to date materials younger than about 70,000 years.
  39. [39]
  40. [40]
    A Comprehensive Review of Quantum Random Number Generators
    Mar 1, 2022 · This paper reviews quantum random number generators (QRNGs), their features, the origin of randomness, and current and futuristic QRNGs.
  41. [41]
    A comprehensive review of quantum random number generators
    Dec 13, 2023 · This article provides a review of the existing QRNGs with a focus on their various possible features (eg, device independence, semi-device independence)
  42. [42]
    How Does Inflation Produce All the Structure in the Universe?
    In our Universe quantum fluctuations have been expanded into the largest structures we observe and clouds of hydrogen have collapsed to form kangaroos.
  43. [43]
    The cosmic microwave background and inflation - ESA
    It is thought that the fluctuations seen in the CMB are a result of the brief period of inflation. The exact details are hidden in the CMB, which Planck will be ...
  44. [44]
    What is the mutation rate during genome replication?
    In humans, a mutation rate of about 10-8 mutations/bp/generation (BNID 105813) was inferred from projects where both parents and their children were sequenced ...
  45. [45]
    Rate, molecular spectrum, and consequences of human mutation
    The per-generation base-substitutional mutation rate for humans is approximately double the average rate in Drosophila melanogaster (approximately 4.65 × 10−9) ...
  46. [46]
    The Effect of Stochasticity on the Lac Operon: An Evolutionary ...
    Jun 22, 2007 · Gene expression in the lac operon has been experimentally shown [2,7] to be stochastic. The lac operon is regulated via a positive feedback ...
  47. [47]
    Contingency and chance erase necessity in the experimental ... - eLife
    Jun 1, 2021 · For chance to strongly influence the outcomes of adaptive evolution, multiple paths to a selected phenotype must be accessible with similar ...
  48. [48]
    CHANCE Definition & Meaning | Dictionary.com
    a possibility or probability of anything happening. a fifty-percent chance of success. Synonyms: contingency. an opportune or favorable time; opportunity.By chance · Fat chance · Fighting chance · Sporting chance
  49. [49]
    CHANCE definition and meaning | Collins English Dictionary
    ### Summary of "Chance" from Collins Dictionary
  50. [50]
    CHANCE - 99 Synonyms and Antonyms - Cambridge English
    Synonyms: accident, happenstance, fortune, luck, destiny, fate, providence. Antonyms: plan, design, intent, intention, premeditation.
  51. [51]
    Chance - Idioms by The Free Dictionary
    a chance to spread (one's) wings · a dog's chance · a fighting chance · a one in a million chance · a one-in-a-million chance · a snowball's chance in ...
  52. [52]
    30 English collocations with CHANCE
    We're going to learn 30 collocations with the word CHANCE. Chance can mean a possibility (which could be good or bad) or an opportunity (which has a more ...
  53. [53]
    Collocations with CHANCE | Collins English Dictionary
    chance encounter His academic career had been undistinguished, and he was playing for a local club when a chance encounter changed his life.
  54. [54]
    Chance - Etymology, Origin & Meaning
    Originating from Old French "cheance" (12th c.) and Latin "cadentia," chance means an unexpected event, occurrence, or fortune, often unforeseen and beyond ...
  55. [55]
  56. [56]
    The History of Chance - The Information Philosopher
    Chance is often defined as the opposite of Necessity. The English word derives from the Latin cadere - to fall, especially cadens a fall, falling.
  57. [57]
    Cadence - Etymology, Origin & Meaning
    Originating in the late 14th century from French and Old Italian "cadenza," cadence means the rhythmic flow in music or prose, derived from Latin "cadere" ...Cadence(n.) · Cadence(v.) · Entries Linking To Cadence
  58. [58]
    *kad- - Etymology and Meaning of the Root
    Proto-Indo-European root meaning "to fall." It might form all or part of: accident; cadaver; cadence; caducous; cascade; case (n.1); casual; casualty; casuist ...
  59. [59]
    Decay - Etymology, Origin & Meaning
    Late 15c. origin from Anglo-French and Vulgar Latin *decadere* ("to fall off"). Meaning: to decline, deteriorate, or lose strength and value gradually.Decay(v.) · Decay(n.) · Entries Linking To Decay
  60. [60]
    Fortune - Etymology, Origin & Meaning
    Originating c.1300 from Old French and Latin fortuna, meaning chance or luck, this word derives from PIE root *bher- implying "to carry," linking to fate or ...
  61. [61]
    Meaning, origin and history of the name Chance
    Originally a diminutive of Chauncey. It is now usually given in reference to the English word chance meaning "luck, fortune" (ultimately derived from Latin ...
  62. [62]
    Chance : Meaning and Origin of First Name - Ancestry
    The name Chance, originated from English etymology, holds the meaning of Fortune or luck. It is believed to have emerged during the medieval era, ...
  63. [63]
    [PDF] Chesapeake Quarterly
    Horseman, who has lived his whole life in the small commu- nity of Chance on Maryland's lower Eastern Shore, will fish for ... Chesapeake Bay History and Culture,.
  64. [64]
    [PDF] Maryland: 2000 - Census.gov
    ... 2000 and histori- cal comparisons of the 100-percent population and housing unit counts. It provides land and water area measurements, and population density.
  65. [65]
    [PDF] Maryland: 2010 - Census.gov
    ... Somerset County................................................ 26,470. 36.5 ... Chance CDP.............................................. 353. 51.1. 15. 37.
  66. [66]
    [PDF] NAME. . % - Virginia Department of Historic Resources
    Glencairn, a long, story-and-a-half, brick-nogged frame building erected in the. 18th century, is set in a flat, open field adjacent to Route 17 in northern ...Missing: 1979 | Show results with:1979
  67. [67]
    Glencairn – DHR - Virginia Department of Historic Resources
    May 14, 1979 · The informal old manor house of Glencairn, a landmark to passing motorists on nearby U.S. Highway 17 in the Occupacia-Rappahannock Rural ...Missing: Chance plantation
  68. [68]
    Ariola, TX - Texas State Historical Association
    Nov 1, 1994 · In 1932 the first of three oil wells in the Ariola field was brought in. ... Local residents call the community Chance, in honor of a pioneer ...Missing: Jeff Davis
  69. [69]
    Chance Populated Place Profile / Clarke County, Alabama Data
    Chance is a populated place located in Clarke County at latitude 31.749 and longitude -87.532. Chance appears on the Chance US Geological Survey Map.
  70. [70]
    Chance, Kentucky
    Chance was an Adair county community about 10 miles south of Columbia. The origin of the name is obscure. The Chance post office opened in 1904 and closed in ...
  71. [71]
    Chance the Rapper | Artist - GRAMMY.com
    Born Chancelor Johnathan Bennett on April 16, 1993, in Chicago, Illinois. Following the release of two mixtapes, Chance The Rapper's third mixtape, ...Missing: birthdate | Show results with:birthdate
  72. [72]
    Chance The Rapper: 'Coloring Book' & Adulting Journey - Billboard
    May 13, 2016 · From his little-known 2012 mixtape 10 Day to the beloved 2013 'tape Acid Rap to the release of last night's (May 13) long-awaited 14-track ...
  73. [73]
    Chance The Rapper Releases New Mixtape 'Coloring Book'
    May 13, 2016 · Chance the Rapper released his new mixtape, Coloring Book, on Thursday. It includes the “No Problem” track he released earlier on the day he ...
  74. [74]
    GRAMMY Rewind: Chance The Rapper Highlights Faith And ...
    Chance the Rapper holds his GRAMMY Award after winning Best New Artist in 2017. Photo: The Recording Academy.New Music Friday: Listen To... · Chance The Rapper's Road To... · Gratitude Playlist: 20 Songs...Missing: birthdate | Show results with:birthdate
  75. [75]
    Chance the Rapper Donates $1 Million to Chicago's Public Schools
    Mar 7, 2017 · Chance the Rapper has donated $1 million to Chicago's public school system, stoking a long-running debate about the city's education system ...
  76. [76]
    Chance the Rapper announces $1 million donation from Chicago ...
    Mar 31, 2017 · Chance the Rapper and Chicago Bulls President Michael Reinsdorf announced Friday that the basketball team has donated $1 million to the city's financially ...
  77. [77]
    Chance Sutton - IMDb
    Chance Sutton. Actor: All Night. Chance Sutton is known for All Night (2018), Mono (2016) and Jake Paul: Team 10 Tour Minnesota (2018).
  78. [78]
    Chance Perez - Age, Family, Bio | Famous Birthdays
    Born on November 10 #26 · First Name Chance #3 Born in Seal Beach, CA #1 · 27 Year Old Scorpio #33 Last Name Perez #12. Chance Perez Is A Member Of. Boy ...
  79. [79]
    Chance - Baby Names 1000
    Chance: Statistics About The Baby Name Chance ; 1981, 619, 189, 0.0102%, * ; 1980, 606, 206, 0.0111%, * ; 1979, 510, 269, 0.0150%, * ...
  80. [80]
    Popular Baby Names | SSA - Social Security
    Name rankings may include: Percent of total births. Number of births. Popularity of a Name. See How the Popularity of a Name has Changed Over Time! Name: Years ...Popular Names by State · Decade · Change in Popularity · Top 5 namesMissing: 1980s | Show results with:1980s
  81. [81]
    Chance Name Meaning and Chance Family History at FamilySearch
    Chance Name Meaning. English (West Midlands): from Middle English chea(u)nce 'fortune, luck; accident, mischance ...
  82. [82]
    Chance Surname Origin, Meaning & Last Name History - Forebears
    The last name Chance is the 13,002nd most widespread family name world-wide, borne by around 1 in 168,908 people. It occurs mostly in The Americas, where 50 ...
  83. [83]
    Frank Chance – Society for American Baseball Research - SABR.org
    Jan 4, 2012 · Frank Chance made his mark as the Cubs' player-manager from 1905 through 1912 as part of the “Tinker-to-Evers-to-Chance” double play infield.
  84. [84]
    Dean Chance Stats, Age, Position, Height, Weight, Fantasy & News
    MLB Cy Young. Year, Team, League. 1964, Los Angeles Angels, AL. Twins Joseph W. Haynes Pitcher of the Year Award. Year, Team, League. 1967, Minnesota Twins, AL.
  85. [85]
    Dean Chance Stats, Height, Weight, Position, Rookie Status & More
    Dean Chance. Position: Pitcher. Bats: Right • Throws: Right. 6-3, 200lb (190cm, 90kg). Born: June 1, 1941 in Wooster, OH us.
  86. [86]
    Angels hall of famer Dean Chance dies - ESPN
    Oct 11, 2015 · In 1964, Chance went 20-9 with a 1.65 ERA for the Angels and won the Cy Young; from 1956 to 1966, only one pitcher in the majors won the award ...
  87. [87]
    Biography | Michael Chance Countertenor
    He received a Grammy award for his participation in Handel's Semele for Deutsche Grammophon with John Nelson and Kathleen Battle. He has recorded frequently ...
  88. [88]
    Recordings | Handel: Messiah - Michael Chance Countertenor
    Handel: Messiah ; CD (1988). ARCHIV Produktion ; Tags: Baroque ; Composer: George Frideric Handel ; Conductor: Trevor Pinnock ; Performers: Arleen Auger Anne Sofie ...Missing: singer Grammy 1992
  89. [89]
    Chance Brothers and Co - Graces Guide
    Jul 29, 2025 · Chance Brothers and Co became a major lighthouse engineering company, producing optical components, machinery, and other equipment for ...
  90. [90]
    Chance, Samuel - Texas State Historical Association
    Sep 18, 2019 · Samuel Chance, born in Georgia around 1790, was a pioneer of Texas colonization, one of Stephen F. Austin's Old Three Hundred, and a farmer and ...
  91. [91]
    Chance (2002) - IMDb
    Rating 6.8/10 (1,291) Chance is a dark comedy about a chapter in the life of a young woman searching to find herself. It stars Amber Benson and James Marsters as Chance and Simon ...Missing: Canadian addiction
  92. [92]
    Chance | Rotten Tomatoes
    Rating 77% (52) Chance (2002) is a comedy about a young woman dealing with life and family problems. It has a 77% Tomatometer score. Some audience reviews praise the ...
  93. [93]
    Being There (1979) - IMDb
    Rating 7.9/10 (81,746) The plot is quite simple with Sellers playing the main character, Chance (or "Chauncey") Gardener, who becomes homeless, when the master of the house he lived ...Plot · Full cast & crew · Peter Sellers as Chance · Trivia
  94. [94]
    Being There movie review & film summary (1979) | Roger Ebert
    Rating 4/4 · Review by Roger EbertSellers plays Chance as a man at peace with himself. When the old man dies, the household is broken up and Chance is evicted, there is a famous scene where he ...
  95. [95]
    Chance (TV Series 2016–2017) - IMDb
    Rating 7.5/10 (11,382) A forensic neuro-psychiatrist reluctantly enters a dangerous and violent world of mistaken identity, police corruption and mental illness.Full cast & crew · Episode list · User reviews · Chance
  96. [96]
    Chance | Rotten Tomatoes
    Rating 75% (32) This provocative thriller follows Dr. Eldon Chance ("House" star Hugh Laurie), a San Francisco-based forensic neuropsychiatrist who has some skeletons in his ...Season 1 · Season 2 · Cast and Crew
  97. [97]
    The Role of Chance and Fate in Breaking Bad's Narrative
    Feb 1, 2025 · Chance and fate play a crucial role in Breaking Bad's exploration of power dynamics and moral decay. The unpredictable nature of events in the ...
  98. [98]
    STAR LINE - Album by Chance the Rapper - Apple Music
    Aug 15, 2025 · Listen to STAR LINE by Chance the Rapper on Apple Music. 2025. 17 Songs. Duration: 1 hour 7 minutes.
  99. [99]
    About SocialWorks - Chicago's Youth Charity
    SocialWorks is the Chicago charity of Chance the Rapper, supporting youth and those experiencing homelessness. Learn More about our organization here.
  100. [100]
  101. [101]
    The Chance | Forever Young - I For Us Records - Bandcamp
    Free deliveryThe Chance by Forever Young, released 12 May 2010 1. Forever Young II 2. Keep It Posi 3. Bigger Than Hardcore 4. 090 5. Time Is Running Out 6.
  102. [102]
    ABBA – Take a Chance on Me Lyrics - Genius
    Take a chance on me, that's all I ask of you honey. Take a chance on me. [Verse 1: Agnetha & Frida, Benny & Björn] We can go dancing, we can go walking As long ...
  103. [103]
    Zion I - True & Livin' Lyrics and Tracklist - Genius
    True & Livin' Tracklist ; Luv · 664 ; I Need Mo · 308 ; Rockin' · 153 ; One Chance · 992.
  104. [104]
    Aleatory Composition, Chance Music, Improvisation | Britannica
    Oct 10, 2025 · Aleatory music, (aleatory from Latin alea, “dice”), 20th-century music in which chance or indeterminate elements are left for the performer to realize.
  105. [105]
    Chance – Modernism Lab - Joseph Conrad - Yale University
    “Chance” hovers between referring to an opportunity for human will and activity, and an indifferent force which can reverse the significance of human action.Missing: analysis | Show results with:analysis
  106. [106]
    The Chance - Karen Kingsbury
    The Chance is a heartwarming story about childhood friends, broken lives, and a long ago promise that just might offer the hope of love for today.
  107. [107]
    The Chance by Karen Kingsbury - Goodreads
    Rating 4.2 (15,907) Mar 5, 2013 · A heartwarming story about childhood friends, broken lives, and a long-ago promise that just might offer the hope of love for today.
  108. [108]
    Rosencrantz and Guildenstern Are Dead | play by Stoppard
    Oct 31, 2025 · Stoppard's play Rosencrantz and Guildenstern Are Dead (1964–65) was performed at the Edinburgh Festival in 1966. That same year his only novel, ...
  109. [109]
    Becoming Machine: Surrealist Automatism and Some Contemporary ...
    There is a direct connection between this work and Ernst's use of frottage and other automatic procedures in the 1920s. Between 1927 and 1928 Yves Tanguy ...
  110. [110]
    Leave It to Chance - League of Comic Geeks
    Browse issues from the comic book series, Leave It to Chance, from Image Comics. Fourteen-year-old Chance Falconer has the occult in her blood.
  111. [111]
    Coincidence or Contrivance? - Reactor
    Jan 16, 2009 · Most writers and editors of fiction will agree that, while a story can handle one coincidence, two is stretching matters, and three is “right out.”Missing: pivotal | Show results with:pivotal
  112. [112]
    A Poetics of Coincidence in Narrative Fiction - Duke University Press
    Sep 1, 2004 · In the major form of the traditional coincidence plot, estranged relatives meet in remarkable circumstances. In complex representations ...
  113. [113]
    How Casinos Ensure Profit: Understanding the House Edge
    The house edge when playing American roulette, which uses a roulette wheel with both a zero and a double zero.2 So for every $1 million bet at the roulette ...The Casino's House Edge · Impact of the House Edge
  114. [114]
    Roulette Basics – Rules, Bets, and Game Variations Explained
    Jul 1, 2025 · The house edge on all bets is 1/19, or 5.26%, except for the 0-00-1-2-3 combination, which carries a house edge of 7.89%. Double-Zero Roulette ...
  115. [115]
    How the House Edge for Each Bet is Derived - Wizard of Odds
    The player's edge is the expected return divided by the initial bet. For example when betting against the line on a sporting event you have to bet $11 to win $ ...How The House Edge For Each... · Introduction · Net Gain/loss Per Session<|control11|><|separator|>
  116. [116]
    Amazon.com: Hasbro Monopoly Card Pack (Deeds/Titles, Chance ...
    Includes All 28 Deed/Title Cards; Includes All 16 Community Chest Cards; Includes All 16 Chance Cards; New Monopoly M Currency Symbol; Cards are 3 and 1/4 ...
  117. [117]
    The Probability of Being Dealt a Royal Flush in Poker - ThoughtCo
    Jul 6, 2019 · A royal flush is the highest ranked hand in the card game of poker. ... 5 ) = 2,598,960 possible distinct hands. Royal Flush. A royal flush ...
  118. [118]
    We finally know the odds of winning a game of solitaire | New Scientist
    Nov 17, 2019 · Renowned mathematician Irving Kaplansky once played 2000 games and… won only 36.6 per cent. Later, computers won more than 80 per cent, but ...
  119. [119]
    Is Diablo 3 loot system really RNG? [closed] - Arqade
    Mar 13, 2019 · If the loot system is truly RNG, then it means that the "normal drop" will be getting better! Such as dropping Rare Items left and right!
  120. [120]
    The Ancient Origins of Dice - JSTOR Daily
    Feb 18, 2018 · To this end, some ancient Romans employed a device called a dice tower. About 7.5 inches tall, made of bone, and inscribed with elaborate ...
  121. [121]
    Powerball Prize Chart
    Powerball® Odds​​ The overall odds of winning a prize are 1 in 24.87. The odds presented here are based on a $2 play (rounded to two decimal places).
  122. [122]
    CHANCE EAU VIVE Eau De Toilette Spray (EDT) - 1.7 FL. OZ.
    In stock Rating 4.6 (40) Our Chance, Eau De Toilette Spray has notes of Pink Pepper, Jasmine and Amber Patchouli. Please know that this fragrance came out in 2002 which is when the ...
  123. [123]
    Chanel Chance, Chance Eau Tendre & Chance Eau Vive
    Aug 3, 2015 · Its notes include grapefruit, quince, hyacinth, jasmine, amber, cedar, iris and white musk. Eau Tendre is a soft, sheer fragrance that smells to ...
  124. [124]
    Chance Lineman Grade Tools | Hubbell Power Systems
    Chance Lineman Grade Tools offers over 10,000 products that help lineworkers build and maintain transmission and distribution lines and substations. Since 1937, ...
  125. [125]
    Chance | Hubbell Power Systems
    Delivering the highest quality pole line hardware, switches, cutouts, and fuse links, anchors, foundations, hot line tools, fiberglass, and rubber products.
  126. [126]
    The doctrine of chances: or, a method of calculating the probability ...
    Oct 1, 2023 · The doctrine of chances: or, a method of calculating the probability of events in play. By A. de Moivre. F. R. S. 1718 ; Publication date: 1718.
  127. [127]
    The Doctrine of Chances - Cambridge University Press & Assessment
    Abraham de Moivre. Publisher: Cambridge University Press. Online publication date: October 2014. Print publication year: 2013. Online ISBN: 9781139833783. DOI ...
  128. [128]
    Music of Changes - John Cage Complete Works
    For this work, Cage employed I Ching-derived chance operations to create charts for the various parameters, i.e. tempi, dynamics, sounds and silences, durations ...
  129. [129]
    John Cage's Music Inspired by the I Ching (Book of Changes)
    Jun 2, 2023 · One of the first works that he used the I Ching for was Imaginary Landscape No. 4 (March No. 2) in 1951. This work, for 24 performers at 12 ...
  130. [130]
    Chance Fracture (Flexion-Distraction Injury) - Spine - Orthobullets
    Oct 12, 2025 · Chance fractures are traumatic fractures of the thoracic and lumbar spine that occur via a flexion-distraction injury mechanism and are ...
  131. [131]
    Chance fracture | Radiology Reference Article | Radiopaedia.org
    Oct 29, 2025 · Chance fractures also referred to as seatbelt fractures, are flexion-distraction type injuries of the spine that extend to involve all three spinal columns.Chance fracture · Burst fracture · Ct · Three column concept
  132. [132]
    [PDF] Comment: The Doctrine of Chances, Brides of the Bath and a Reply ...
    Aug 24, 2014 · The 'doctrine of chances' claims to reconcile the apparent contradiction by demonstrating that admission of evidence of defendant's similar acts ...
  133. [133]
    Demystifying the Doctrine of Chances by Sean Sullivan :: SSRN
    Feb 4, 2014 · Proponents of the doctrine argue that evidence of multiple unlikely events of a similar nature supports an objective, statistical inference of ...Missing: repeated | Show results with:repeated
  134. [134]
    Chance Vought Survivor Club - History
    The Company traces its origin in 1917 to a small Long Island, N.Y., aircraft firm established by Chance Milton Vought, a young aeronautical engineer and ...
  135. [135]
    Vought Aircraft Industries, Inc. - Company-Histories.com
    1929: Vought joins Pratt & Whitney-led United Aircraft and Transport Corporation. 1935: Chance Vought becomes part of new United Aircraft Manufacturing Company.