5000 years of chance

Amidakuji (あみだくじ) traces its origins to medieval Japan during the Muromachi period (1336-1573). The earliest written records appear in documents from the Ashikaga shogun's court, where officials used diagrams with radiating lines to fairly distribute land parcels among peasants. The name "Amidakuji" comes from the Buddha Amida (Amitabha in Sanskrit), revered in Pure Land Buddhism (Jodo-shu, founded by Honen in 1175): the original drawing, with its lines radiating from a central point, evoked the luminous halo (kouhai) behind the golden statues of this Buddha at the Byodo-in temple in Uji, designated a national treasure in 1053. During the Edo period (1603-1868), the game evolved into its current form of parallel vertical lines connected by horizontal bridges. Merchants in Osaka adopted it to assign stalls at the Naniwa markets, and the Tenpo Suikoden (1829) mentions its use in the Yoshiwara pleasure quarters to determine the order of clients. Samurai used it during ceremonies to settle matters of etiquette without losing face, in accordance with the Confucian principle of wa (harmony). The mathematician Seki Takakazu (1642-1708), considered the "Japanese Newton," studied the combinatorial properties of similar configurations in his Hatsubi Sanpo (1674). In the 20th century, Amidakuji became widespread in the Japanese education system. The Ministry of Education (Monbukagakusho) recommended its use in elementary schools from the 1920s as a tool for teaching fairness and chance. Today, over 95% of Japanese schoolchildren know the game before the age of 10, according to a 2018 Benesse survey. Fourth-year elementary school mathematics textbooks use it to introduce the concepts of permutation and probability. In group theory, each Amidakuji diagram corresponds to a decomposition into adjacent transpositions of a permutation in the symmetric group S_n. Mathematician Takeuchi Yasuo demonstrated in 1994 that any permutation of n elements can be represented by an Amidakuji, and Matsui Tomomi proved in 1995 that the minimum number of bridges needed to achieve a given permutation corresponds exactly to its number of inversions. The connection with Coxeter diagrams and reduced words in the symmetric group was formalized by Eriksson and Linusson in 1996, making Amidakuji a subject of study in its own right in algebraic combinatorics. Social psychology sheds light on why Amidakuji is so effective as a consensus tool. The work of Thibaut and Walker (1975) on procedural justice shows that individuals more readily accept an unfavorable outcome when the process is perceived as fair. In Japan, where the concept of wa (group harmony) takes precedence over individual preferences according to anthropologist Nakane Chie (Japanese Society, 1967), Amidakuji offers a decision mechanism that preserves everyone's face. Yamagishi Toshio (Hokkaido University) showed in 2003 that Japanese people prefer visual and participatory drawing methods over anonymous digital draws, as process transparency strengthens mutual trust. Amidakuji is ubiquitous in contemporary Japanese culture. In manga, Gintama (Sorachi Hideaki, 2003) and Doraemon (Fujiko F. Fujio) dedicate entire episodes to it. Variety shows such as those featuring AKB48 use it live to assign roles and challenges before millions of viewers. In South Korea, the variant "sadari tagi" (사다리타기) is equally popular — the show Running Man (SBS, since 2010) has made it known across all of Asia. Mobile apps like Amidakuji Maker (over 500,000 downloads on Google Play in 2023) and built-in versions in LINE (230 million users) have digitized the practice for a new generation.

Despite its name, the fortune cookie traces its roots not to China but to Japan. Tsujiura senbei (fortune crackers) were sold near Shinto shrines as early as the 19th century, particularly in Kyoto's Fushimi district. These crackers, larger and darker than modern fortune cookies, contained predictions written on slips of paper called omikuji. Researcher Yasuko Nakamachi of Kanagawa University found references to these biscuits in Japanese ukiyo-e woodblock prints dating back to 1878, proving the tradition was well established before any emigration to America. The Sohonke Hogyokudo bakery, founded in Kyoto in 1846, still claims to produce these handcrafted ancestors of the fortune cookie to this day. The arrival of the fortune cookie in the United States remains a heated debate among several families. Makoto Hagiwara, designer of the Japanese Tea Garden in San Francisco's Golden Gate Park, reportedly began serving fortune cookies around 1914, made by Suyeichi Okamura's Benkyodo bakery. Meanwhile, David Jung, founder of the Hong Kong Noodle Company in Los Angeles, claimed to have created them in 1918 to distribute uplifting messages to homeless people in the neighborhood. In 1983, the city of San Francisco officially ruled in Hagiwara's favor during a "Court of Historical Review," sparking outrage in Los Angeles. Federal Judge Daniel Collins delivered the symbolic ruling while biting into a fortune cookie right in the courtroom. World War II marked a decisive turning point. In 1942, President Roosevelt's Executive Order 9066 led to the internment of 120,000 Japanese Americans in detention camps. The Japanese bakeries that had been producing fortune cookies were abruptly shut down. Chinese-American restaurateurs, whose establishments were booming thanks to returning GIs' fascination with Asian cuisine, took over production. The cookie thus shifted from one culture to another without American customers ever noticing. Within less than a decade, the fortune cookie became an iconic fixture at the end of every meal in Chinese-American restaurants. The industrialization of the fortune cookie truly began in 1964, when Edward Louie of the Lotus Fortune Cookie Company in San Francisco developed the first automatic folding machine. Before that, each cookie was folded by hand using chopsticks. In 1973, Wonton Food Inc. was founded in Brooklyn by Tat Shing Wong, and quickly became the world's largest producer with 4.5 million cookies per day and nearly 200 employees. Former vice president Donald Lau wrote the majority of the fortune messages for over 30 years, crafting 4 to 5 new texts daily, before passing the torch in 2017, admitting he had "run out of inspiration." Today, over 3 billion fortune cookies are produced each year, nearly all of them in the United States. Fortune cookie messages exploit a well-documented cognitive bias: the Barnum effect, named after the famous showman P.T. Barnum. This phenomenon, studied by psychologist Bertram Forer in 1948 at the University of California, Los Angeles, describes our tendency to accept vague personality descriptions as perfectly tailored to us. Forer demonstrated that students rated an identical psychological profile — taken from a newspaper horoscope — at 4.26 out of 5 for accuracy. Fortune cookie messages work on exactly this principle: "An unexpected journey will bring you joy" always seems relevant. Psychologist Paul Meehl coined the term "P.T. Barnum acceptance" in 1956, and later studies showed that confirmation bias amplifies the effect — we remember the predictions that come true and forget the rest. The fortune cookie remains paradoxically unknown in mainland China. In 1992, Hong Kong-based Fancy Foods attempted to introduce them in Shanghai and Guangzhou under the slogan "a genuine American product," but the venture fizzled out. Writer Jennifer 8. Lee, in her book "The Fortune Cookie Chronicles" (2008), traveled to 40 Chinese cities without finding a single one. However, the cookie has gone global: it can be found in Brazil (biscoito da sorte), France, Japan (where it returned in its Americanized form), and even India. On March 30, 2005, a fortune cookie made history by "predicting" five of the six winning Powerball numbers: 110 people who had played those numbers each won between $100,000 and $500,000, triggering a lottery investigation that ultimately confirmed it was pure coincidence.

Estimating and ranking items by value are skills as old as trade itself. In Sumerian Mesopotamia, around 3000 BC, clay tablets from Uruk already listed prices for barley, copper, and livestock, enabling merchants to compare relative values. In ancient Greece, Aristotle distinguished between "use value" and "exchange value" in the Nicomachean Ethics (c. 350 BC), laying the groundwork for thinking about price hierarchies. Roman merchants relied on Diocletian's Edict on Maximum Prices (AD 301), a decree setting price ceilings for over 1,200 products and services — the first known price catalog in history. During the Middle Ages, the Champagne fairs (12th–13th centuries) became the center of European commerce, where merchants from across Europe had to master the relative prices of hundreds of goods — Flemish cloth, Eastern spices, Italian silks — in dozens of different currencies. The mathematician Fibonacci, in his Liber Abaci (1202), taught precisely these conversions and price comparisons, providing Pisan merchants with arithmetic tools to rank trade values. The price ranking game entered popular culture through American television. On November 26, 1956, Bob Barker hosted The Price Is Right on NBC for the first time, created by Mark Goodson and Bill Todman. The show, which asked contestants to estimate and rank prices, became the longest-running game show in American television history, with over 9,000 episodes on CBS since 1972. In France, Le Juste Prix, adapted by TF1 in 1988 and hosted by Vincent Lagaf', attracted up to 7 million viewers and popularized price estimation games across the country. Ranking items is also a fundamental problem in computer science. John von Neumann designed merge sort in 1945 for the EDVAC program. Tony Hoare invented quicksort in 1960 at the age of 26 — an algorithm so elegant it remains one of the most widely used in the world. But when a human ranks objects by price, they use none of these formal algorithms. The brain proceeds through approximate comparisons and mental "insertion sort," placing each new element into an existing ordered list, a method formalized by John Mauchly in the 1940s. The work of Daniel Kahneman and Amos Tversky, awarded the Nobel Prize in Economics in 2002, revealed the cognitive biases that distort our price estimation. The anchoring bias, described in their landmark 1974 paper in Science, means the first price seen influences all subsequent ones. The endowment effect, identified by Richard Thaler (Nobel 2017), leads us to overvalue objects we own. Psychologist George Miller showed in 1956 in "The Magical Number Seven, Plus or Minus Two" that our working memory can only handle about seven items — which is why ranking 4 objects feels easy but moving to 6 dramatically increases the difficulty. In the digital age, price estimation games are experiencing a spectacular revival. The Higher Lower Game, created by British developer Jack Sheridan in 2016, surpassed 100 million games played. On TikTok, "guess the price" videos have accumulated billions of views. The global quiz and trivia game market, including estimation games, was worth 8.3 billion dollars in 2024. E-commerce apps like Amazon use price sorting algorithms billions of times daily, while researchers at MIT and Stanford develop "price cognition" models to understand how the human brain intuitively evaluates prices.

Random multiple choice selection has its roots in the divinatory practices of antiquity. The Greeks consulted the Oracle at Delphi to decide between options, while the Romans drew lots to select magistrates from lists of candidates. In the Middle Ages, drawing lots among multiple options was commonly used to allocate lands, divide inheritances, or appoint community leaders. Methods varied across cultures: sticks of different lengths, colored pebbles, or folded slips in a hat. The Age of Enlightenment saw mathematicians like Pascal and Fermat formalize probability theory, giving a scientific foundation to fair random selection. Their work demonstrated that each option had exactly the same chance of being selected in a well-designed draw. In the 19th century, national lotteries popularized the concept of random selection among many options. Sophisticated mechanical machines were invented to guarantee the impartiality of draws, a fundamental principle still respected today. The digital revolution transformed random multiple choice into an everyday tool. Pseudo-random number generators, based on algorithms like the Mersenne Twister, enable perfectly fair selections in a fraction of a second. Today, online multiple choice tools are used in countless contexts: team meetings, classrooms, games among friends, family decisions, and even in certain participatory democratic processes. The simplicity and impartiality of chance make it a universal arbiter.

The understanding of colour dates back to antiquity. Aristotle, in his treatise "De Sensu et Sensibilibus" (c. 350 BC), proposed that all colours derived from mixtures of white and black — a theory that dominated for nearly two millennia. The Egyptians already mastered six fundamental pigments, including Egyptian blue, the first synthetic pigment in history, created around 3100 BC from copper and calcium silicate. It was Isaac Newton who revolutionised this understanding in 1666, decomposing white light through a glass prism in his room at Trinity College, Cambridge. He identified seven colours — red, orange, yellow, green, blue, indigo, violet — a deliberate choice to create a parallel with the seven notes of the musical scale. His findings, published in "Opticks" in 1704, established that colour is an intrinsic property of light, not of objects. Colour theory flourished in the 18th and 19th centuries. Johann Wolfgang von Goethe, in his "Theory of Colours" ("Zur Farbenlehre") published in 1810, opposed Newton by emphasising the subjective experience of colour. Although his physics was flawed, his observations on simultaneous contrasts and complementary colours profoundly influenced the visual arts. Michel-Eugène Chevreul, a French chemist and director of dyeing at the Gobelins Manufactory, published in 1839 "On the Law of Simultaneous Contrast of Colours", a work demonstrating how adjacent colours mutually alter their perception. His research directly impacted the Impressionists — Monet, Pissarro — and especially Georges Seurat's pointillism, whose "A Sunday Afternoon on the Island of La Grande Jatte" (1886) literally applies Chevreul's principles. The modern understanding of colour rests on the trichromatic theory of Thomas Young (1802), refined by Hermann von Helmholtz in the 1850s. They demonstrated that the human eye perceives colours through three types of retinal cones sensitive to red, green and blue respectively. James Clerk Maxwell proved this theory in 1861 by producing the first colour photograph in history: a Scottish tartan ribbon, photographed through three red, green and blue filters, then superimposed by projection. The RGB (Red, Green, Blue) model of additive synthesis, used by all modern screens, stems directly from this work. Subtractive synthesis (CMYK — Cyan, Magenta, Yellow, Key/Black), meanwhile, was formalised for industrial printing in the early 20th century. The need to standardise colours spawned several major systems. Albert Munsell, an American painter and teacher, created the first systematic colour space in 1905, organising colours along three axes: hue, value and chroma. In 1931, the International Commission on Illumination (CIE) published the CIE XYZ colour space, the first mathematical model capable of describing all perceivable colours. Pantone revolutionised the graphic industry in 1963 with its Pantone Matching System (PMS), a colour guide now containing over 2,100 referenced shades. With the advent of the web, hexadecimal codes (#RRGGBB) were adopted from HTML 2.0 in 1995. The 216 "web-safe colors" were defined to guarantee identical rendering on the 8-bit screens of the era. The HSL (Hue, Saturation, Lightness) format was introduced in CSS3 in 2011 to offer designers a more intuitive model. Colour psychology has been an active field of research since the pioneering work of Faber Birren in the 1940s. In "Color Psychology and Color Therapy" (1950), he documented the influence of colours on emotions and behaviour. Neuromarketing studies show that website visitors form their first impression in under 50 milliseconds, and that the dominant colour influences up to 90% of this initial evaluation (Satyendra Singh's 2006 study, "Impact of Color on Marketing"). Blue inspires trust — hence its omnipresence at Facebook, LinkedIn, PayPal and IBM. Red creates urgency and stimulates appetite (Coca-Cola, McDonald's, Netflix). Green evokes nature and health (Spotify, WhatsApp, Starbucks). However, these associations vary considerably across cultures: in China, red symbolises prosperity; in Japan, white is the colour of mourning; in India, saffron represents the sacred. Today, random colour generators are essential tools for designers and developers. The WCAG 2.1 standard (Web Content Accessibility Guidelines) requires a minimum contrast ratio of 4.5:1 between text and its background to ensure readability. The generative art movement, popularised by artists such as Casey Reas (co-creator of Processing in 2001) and Tyler Hobbs (creator of Fidenza, 2021), uses random algorithms to produce digital artworks where colour plays a central role. Modern design systems — Google's Material Design, Apple's Human Interface Guidelines — all incorporate rigorously calculated palettes with CSS variables for light and dark themes. The Pantone Color of the Year, awarded since 2000, influences the global design industry: in 2023, "Viva Magenta" generated over 30 billion media impressions within two weeks of its announcement.

Measuring time is one of humanity's oldest intellectual endeavors. As early as 2100 BC, the Sumerians of Mesopotamia used a luni-solar calendar of 12 months of 29 or 30 days, with intercalary months to realign with the seasons. Ancient Egypt developed around 3000 BC a solar calendar of 365 days — 12 months of 30 days plus 5 epagomenal days — calibrated to the annual flooding of the Nile and the heliacal rising of Sirius (Sothis). The Maya devised the Long Count, a system capable of dating events across millions of years, including the famous 5,125-year cycle that fueled "end of the world" prophecies in 2012. These three civilizations, with no contact between them, each felt the need to structure time into regular units — proof that dating is a fundamental human need. In 46 BC, Julius Caesar tasked the astronomer Sosigenes of Alexandria with reforming the Roman calendar, then chaotic and manipulated by pontiffs for political purposes. The result — the Julian calendar — fixed the year at an average of 365.25 days through a leap year every four years. To make up for the accumulated drift, the year 46 BC lasted an exceptional 445 days, earning it the nickname "year of confusion" (ultimus annus confusionis). This calendar was adopted throughout the Roman Empire and endured in the West for over 1,600 years. The Council of Nicaea in 325 AD anchored the calculation of Easter to the first Sunday following the full moon after the spring equinox, making calendar precision a religious matter as much as a civil one. But the Julian calendar overestimated the year by 11 minutes and 14 seconds. By 1582, the drift had reached a full 10 days: the spring equinox fell on March 11 instead of March 21. Pope Gregory XIII promulgated the bull Inter gravissimas on February 24, 1582, establishing the Gregorian calendar. Ten days were removed at once: October 4, 1582 was directly followed by October 15. The century-year rule was refined: only those divisible by 400 remain leap years (2000 yes, 1900 no). This correction brought the average year length to 365.2425 days, a residual error of just 26 seconds per year — it will take until the year 4909 to accumulate a single day of error. Adoption was gradual and sometimes turbulent: France and Spain switched in 1582, Great Britain waited until 1752 (provoking "calendar riots" with the cry "Give us our eleven days!"), Russia didn't adopt the new calendar until 1918, and Greece until 1923. The algorithmic calculation of dates has a rich history. In 1583, the philologist Joseph Justus Scaliger created the Julian Day (JD), a continuous day count from January 1, 4713 BC, still used by astronomers to avoid calendar ambiguities. Carl Friedrich Gauss published in 1800 an algorithm for calculating the date of Easter that remains the reference today. The mathematician Christian Zeller presented in 1882 his famous congruence (Zeller's congruence) for determining the day of the week of any date in the Gregorian calendar using a single arithmetic formula. In the computing era, the choice of January 1, 1970 as the "Unix epoch" by Ken Thompson and Dennis Ritchie became the temporal reference point for virtually all digital systems. The ISO 8601 standard, published in 1988 and revised in 2004, standardized the YYYY-MM-DD format to eliminate ambiguities between national conventions (American MM/DD/YYYY vs. European DD/MM/YYYY). Human perception of dates harbors fascinating biases. The "birthday problem," formulated by mathematician Richard von Mises in 1939, demonstrates that in a group of just 23 people, the probability that two of them share the same birthday exceeds 50% — a result that defies nearly everyone's intuition. Psychologists John Skowronski and Charles Thompson showed in 2004 that humans suffer from a "telescoping effect": we perceive recent events as more distant and past events as closer than they actually are. Moreover, births are not uniformly distributed throughout the year: in the United States, September 16 is the most common birthday (a peak of conceptions during the holiday season), while December 25 and January 1 are the rarest days, according to data from the National Center for Health Statistics covering 20 years of births. Today, random date generators are indispensable tools in many fields. In software development, libraries like Faker.js (created by Marak Squires in 2014) and Factory Bot (Ruby) generate realistic fictitious dates for automated testing — verifying edge cases of leap years, century changes, and time zones. In financial auditing, AICPA (American Institute of Certified Public Accountants) standards recommend random sampling of transaction dates to detect fraud. In education, teachers use random dates to create historical exploration exercises: students receive a date and must research what happened on that day. In creative writing and role-playing games, a random date anchors a character or story in a credible time period. Random date drawing is even used in certain contests and lotteries to determine event dates or prize validity periods.

Polyhedral dice are inseparable from the history of tabletop role-playing games. While six-sided cubic dice have existed since antiquity — the oldest specimens dating back to the Indus Valley civilization around 2600 BC — multi-sided dice have a more recent but equally fascinating history. The Platonic solids, those five perfect regular polyhedra (tetrahedron, cube, octahedron, dodecahedron, and icosahedron), were known to Greek mathematicians as early as the 4th century BC. Plato himself associated them with the fundamental elements of the universe in his Timaeus. However, their use as gaming dice remained marginal for millennia. It was in 1974, with the publication of Dungeons & Dragons by Gary Gygax and Dave Arneson, that polyhedral dice entered popular culture. The original game required a set of special dice: D4, D6, D8, D12, and D20. The D10 was added shortly after to enable percentage rolls. At the time, these dice were so rare that TSR (the publisher) included numbers to be colored in with crayon. The D&D game system fundamentally relies on the D20, hence its name "d20 system." Every action — attacking a monster, picking a lock, persuading a king — is resolved by rolling a D20 and adding modifiers. A natural 20 is a "critical hit," a moment of glory that thrills every player around the table. The introduction of advantage and disadvantage in D&D 5th Edition (2014) revolutionized the mechanics. Instead of stacking numerical bonuses and penalties, the player simply rolls two D20s and keeps the higher (advantage) or lower (disadvantage) result. This elegant simplification is considered one of the greatest innovations in modern role-playing games. Today, polyhedral dice have become a true cultural phenomenon. Manufacturers like Chessex, Q Workshop, and Die Hard Dice produce millions of sets in materials ranging from colored resin to metal to semi-precious stone. The global RPG accessories market exceeds one billion dollars, with dice representing a significant share.

Dice are among the oldest known instruments of chance in human history. The first objects resembling dice were knucklebones — animal astragali — found in archaeological sites in Mesopotamia dating back more than 5,000 years. At Ur, in present-day Iraq, cubic clay dice were discovered in a royal tomb dated to around 2600 BC. In ancient Egypt, four-sided bone dice were found in tombs of the 18th Dynasty (around 1550–1292 BC). The oldest known cubic die was unearthed at Shahr-e Sukhteh, in Iran, and dates to approximately 2800–2500 BC. In the Indus Valley civilization, terracotta dice were found at the site of Mohenjo-daro, demonstrating that dice games were practiced independently on several continents. In the Middle Ages, dice were ubiquitous in Europe, to the point of alarming religious and civil authorities. King Louis IX (Saint Louis) banned dice games in France by an ordinance of 1254, viewing them as a source of blasphemy and ruin. In England, Richard the Lionheart imposed a law in 1190, during the Third Crusade, prohibiting soldiers below the rank of knight from playing dice to avoid desertion and brawls. Despite these bans, dice games flourished in taverns. Hazard, the ancestor of modern craps, appeared in England in the 13th century — its name derives from the Arabic "az-zahr" (the die), evidence of cultural exchanges between East and West. During the Renaissance, dicemakers formed specialized guilds in Paris. In the 17th and 18th centuries, dice played a crucial role in the birth of probability theory. In 1654, the Chevalier de Méré posed to mathematician Blaise Pascal the famous "problem of points" concerning the fair division of stakes in an interrupted dice game. The ensuing correspondence between Pascal and Pierre de Fermat laid the foundations of probability theory. Before them, Italian physician and mathematician Girolamo Cardano had written around 1564 the "Liber de Ludo Aleae" (The Book on Games of Chance), the first systematic treatise on probability applied to dice, though it was not published until 1663. In the 19th century, French emigration to New Orleans transformed Hazard into "craps," which became the iconic dice game of American casinos. From a mathematical perspective, the standard cubic die (D6) offers perfect symmetry: each face has exactly a 1/6 probability of appearing. The convention whereby opposite faces of a die always total 7 (1–6, 2–5, 3–4) dates back to antiquity and became standardized in Europe from the 14th century onward. Polyhedral dice — D4 (tetrahedron), D8 (octahedron), D10 (pentakis dodecahedron), D12 (dodecahedron), and D20 (icosahedron) — correspond to Platonic solids described in the "Timaeus" around 360 BC. In 2022, a study published by researchers from the University of California at Davis analyzed 110 ancient Roman dice and found that their shape gradually standardized over the centuries, moving from irregular forms to near-perfect cubes. The psychology of dice players is fascinating. The phenomenon of "the illusion of control," identified by psychologist Ellen Langer in 1975 at Harvard, shows that dice rollers unconsciously believe they can influence the outcome through their gesture. Craps players at the casino throw harder when they want a high number and more gently for a low number. Dice cheating has a long history: loaded dice (weighted or deformed) have been found in Roman and Viking archaeological excavations. In Pompeii, loaded bone dice from the 1st century were discovered in a tavern. Today, Las Vegas casinos use "precision" dice manufactured to a tolerance of 1/10,000th of an inch, transparent so that no weighting can be concealed. The contemporary use of dice was revolutionized by role-playing games. In 1974, Gary Gygax and Dave Arneson published Dungeons & Dragons, popularizing the use of polyhedral dice (D4, D8, D10, D12, D20) to resolve character actions. The D20 became so iconic that it symbolizes the entire role-playing game culture. The global dice market is estimated at several billion dollars, fueled by the revival of board and role-playing games. Virtual dice, which appeared with the digital age, use pseudo-random number generators (PRNG) that offer superior mathematical fairness to physical dice — a well-implemented algorithm produces a uniform distribution of 16.667% per face, without the micro-imperfections of a real die. Platforms like Roll20 process hundreds of millions of virtual dice rolls per year for online role-playing sessions.

Random group allocation dates back to ancient Greece. In Athens, as early as the 5th century BC, the kleroterion — a marble machine fitted with slots — was used to draw jurors for the Heliaea court by lot from among 6,000 volunteer citizens. Aristotle describes this device in the Constitution of the Athenians (c. 330 BC) as a tool guaranteeing the impartiality of courts. The Romans practiced "sortitio" to distribute magistrates among provinces, and the Roman legion used decimation — one soldier in ten drawn by lot — as collective punishment. In each case, chance served to form subgroups perceived as fair. In the Middle Ages, group formation by lot reappeared in chivalric tournaments. From the 12th century onward, "mêlées" pitted two sides formed by drawing lots the evening before combat. The chronicler William Marshal (1147–1219) describes how knights were divided into teams for the tournaments of Champagne, a practice that prevented pre-established regional alliances. In England, the Statute of Winchester (1285) provided for the formation of night watch groups (watch and ward) by random rotation among parish inhabitants. The modern era saw random team formation enter the world of sports. In 1863, the first codified football rules by the Football Association did not include a draft, but informal matches at English public schools (Eton, Harrow, Rugby) used "picking" — two captains alternately choosing players — as early as the 1840s. This system, criticized for humiliating those chosen last, led progressive educators like Thomas Arnold to promote drawing lots. In the United States, the NFL established its first draft in 1936, but pickup basketball games in New York City playgrounds still use random draws today when captains prefer not to choose. The mathematics of group allocation fall under combinatorics and sampling theory. The number of ways to divide n people into k equal-sized teams is given by the multinomial coefficient n! / ((n/k)!)^k / k!, a calculation formalized by Euler in the 18th century. In 1925, statistician Ronald Fisher introduced randomization as a fundamental principle of experimental design in his work "Statistical Methods for Research Workers," demonstrating that random assignment to treatment and control groups eliminates systematic biases. The Fisher-Yates algorithm (1938), modernized by Richard Durstenfeld in 1964, remains the standard method for randomly shuffling a list — exactly what a team generator does. Social psychology has extensively studied the impact of group formation. Muzafer Sherif's experiments at Robbers Cave (1954) showed that boys randomly assigned to two teams rapidly developed group identity and intergroup rivalry, even without preexisting differences. Henri Tajfel confirmed this phenomenon with the "minimal group paradigm" (1971): the mere act of being assigned to a group — even on an arbitrary criterion like preference for Klee or Kandinsky — is enough to trigger in-group favoritism. More recently, Scott Page's work at the University of Michigan (2007, "The Difference") demonstrates that diverse teams, such as those formed randomly, outperform homogeneous teams in solving complex problems. Today, random team formation is ubiquitous. In education, Elliot Aronson's "jigsaw classroom" method (1971) relies on randomly formed groups to reduce racial prejudice — a technique adopted in over 30 countries. In business, companies like Google and Spotify use "guilds" and hackathon teams formed by lottery to stimulate cross-functional innovation. In esports, the "random matchmaking" mode of games like League of Legends (150 million monthly active players in 2023) forms teams of 5 from millions of candidates in seconds, balancing skill levels using the Elo system adapted by Arpad Elo in 1960.

The origins of darts can be traced back to 14th-century England, during the Hundred Years' War (1337-1453). English archers, between battles, reportedly took to throwing shortened arrows at cross-sections of tree trunks. The natural growth rings of the wood formed concentric circles that served as rudimentary scoring zones. The English word "dart" derives from the Old French "dard" (javelin), attested as early as the 13th century. Anne Boleyn is said to have given Henry VIII a richly decorated set of darts in 1530, and the Pilgrims of the Mayflower are believed to have played darts during their Atlantic crossing in 1620, according to William Bradford's journal. By the 17th century, the game moved from military camps into English taverns and inns. The earliest targets were made from elm wood (Ulmus), whose fibres allowed dart points to stick without splitting the board. The wood had to be soaked overnight to prevent it from drying out and cracking. In the 1930s, the manufacturer Nodor (a contraction of "no odour") revolutionised the game by introducing targets made from sisal (agave fibre), which were far more durable and no longer required daily soaking. This material is still used in all competition-grade boards today. In 1896, Brian Gamlin, a carpenter from Lancashire, devised the modern layout of the 20 numbered segments. His system is a masterpiece of design: the 20, the most coveted zone, is flanked by the 1 and the 5, so that a slightly wayward throw scores very few points. Mathematicians have since confirmed the effectiveness of this arrangement: David Percy of the University of Salford demonstrated in 2002 that there are more than 121 billion possible arrangements of the 20 numbers, and Gamlin's layout ranks in the top 3% for penalising inaccuracy. In 1924, the National Darts Association was founded in London, standardising the dimensions: 451 mm diameter, the centre (bull) placed at 1.73 m from the floor, and a throwing distance of 2.37 m (the "oche", a term probably derived from the Old French "ocher", meaning to notch). A pivotal moment came in 1908 at Leeds Magistrates' Court. Pub landlord Jim Garside, prosecuted for hosting an illegal game of chance, invited local champion William "Bigfoot" Anakin to throw three darts before the judge. Anakin planted all three in the 20, and the judge then tried and failed to do the same. The court concluded that darts was a game of skill, not chance, paving the way for its legal play in pubs. This landmark episode is still cited today in the official history of the British Darts Organisation (BDO), founded in 1973 by Olly Croft. The professionalisation of the sport accelerated in the 1970s and 1980s. In 1978, the first BDO World Championship final was broadcast by the BBC, attracting 8 million viewers in the United Kingdom. Leighton Rees, a Welshman from Pontypridd, won this inaugural world title. In 1994, a group of 16 players led by Phil Taylor left the BDO to found the Professional Darts Corporation (PDC), triggering a split that lasted until the two circuits merged in 2020. The PDC transformed darts into a spectacle: the World Championship at Alexandra Palace in London ("Ally Pally") now draws over 90,000 spectators across two weeks and 3.5 million TV viewers for the final on Sky Sports. Phil "The Power" Taylor dominated the sport in unprecedented fashion with 16 PDC world titles (1995-2013) and 214 major tournament wins. His record of two 9-darters (perfect legs in just 9 darts) in a single televised final in 2010 remains unmatched. The Dutchman Michael van Gerwen ("Mighty Mike"), a three-time world champion (2014, 2017, 2019), continues the pursuit of excellence with a treble-20 percentage regularly exceeding 50%. Today, electronic dartboards and mobile apps are democratising the game: over 17 million people play darts regularly in Europe according to the World Darts Federation, and the sport has been a candidate for the Olympic Games since the early 2000s.

The password is one of the oldest security devices in human history. In ancient Rome, sentinels demanded a "tessera" — a password engraved on a wooden tablet — to authorise the passage of soldiers at night. The Greek historian Polybius (2nd century BC) describes in his Histories how the "watchword" was distributed each evening by the military tribune, passed from guard to guard throughout the camp. The Bible mentions a similar use in the Book of Judges (12:5-6): the Gileadites identified Ephraimites by asking them to pronounce "Shibboleth" — those who said "Sibboleth" were unmasked. This "linguistic password" became a foundational concept in computer security. During the Middle Ages, fortified castles and walled cities used passwords to control access to their gates. Medieval guilds, notably the Freemasons, developed elaborate systems of words, signs and handshakes to recognise their members. The "Mason's Word", transmitted orally during initiation, served to prove membership of the brotherhood. During the Hundred Years' War (1337-1453), English and French armies used daily passwords to distinguish allies from enemies during night fighting. The chronicler Jean Froissart reports that confusion over passwords at the Battle of Crécy (1346) caused the death of many soldiers through friendly fire. The computer era of passwords began in 1961 at MIT, when Fernando Corbató implemented the first password authentication system for the Compatible Time-Sharing System (CTSS). This system allowed multiple users to share an IBM 7094 computer while protecting each user's files. As early as 1962, Allan Scherr, a doctoral student at MIT, carried out the first known "attack": he found the master file containing all passwords in plain text and printed them, thereby gaining extra computing time. This anecdote illustrates the fundamental vulnerability of plain-text storage. The science of passwords took a major turn in 1976 when Robert Morris Sr., a researcher at Bell Labs, invented password hashing under Unix with the crypt() function, based on the DES algorithm. For the first time, passwords were no longer stored in plain text but as an irreversible "hash". In 1979, Morris added the concept of "salt" — a random value added before hashing to prevent attacks using precomputed tables. Entropy, a concept borrowed from Claude Shannon's information theory (1948), became the standard measure: E = L × log₂(N), where L is the length and N the number of possible characters. A 12-character mixed password reaches approximately 79 bits of entropy, enough to withstand brute force for millennia. The psychology of passwords reveals fascinating paradoxes. In 2003, Bill Burr of the National Institute of Standards and Technology (NIST) published Appendix A of document SP 800-63, recommending complex passwords with uppercase letters, numbers and special characters. In 2017, in an interview with the Wall Street Journal, he admitted that this recommendation was "largely wrong": users circumvent complexity with predictable substitutions ("P@ssw0rd!") and frequent changes push people towards weak patterns. Psychologist Jeff Yan of the University of Cambridge demonstrated in 2004 that passwords based on mnemonic phrases are both stronger and more memorable than those based on pure complexity. The contemporary industry is undergoing a profound transformation. NIST revised its guidelines in 2017 (SP 800-63B), favouring length over complexity and abandoning mandatory periodic expiry. Microsoft followed in 2019 by removing password rotation from its security baselines. The RockYou data breach of 2009 — 32 million passwords exposed in plain text — revealed that "123456" topped the charts, followed by "12345" and "password". In 2023, the NordPass report confirms that "123456" remains the world's most used password, cracked in under a second. The Argon2 algorithm, winner of the Password Hashing Competition in 2015, represents the state of the art in hashing. Meanwhile, passkeys based on FIDO2/WebAuthn, promoted by Google, Apple and Microsoft since 2022, may herald the end of the traditional password era.

A first name is much more than a simple word: it's the first gift parents give their child, an identity that will accompany them throughout life. The history of first names stretches back to the very origins of human language, when early communities felt the need to distinguish individuals from one another. In antiquity, first names almost always carried a concrete meaning. Among the Romans, the "tria nomina" system (praenomen, nomen, cognomen) structured social identity. The Greeks chose names embodying virtues: Alexander means "protector of mankind," Philip means "friend of horses." In ancient Egypt, a name held magical power — to know someone's true name was to have power over them. During the Middle Ages in Europe, the Catholic Church imposed the use of saints' names as a condition for baptism. This rule, formalized at the Council of Trent in 1563, considerably reduced the diversity of first names for centuries. John, Peter, Mary, and Anne dominated parish registers across the continent. The French Revolution briefly unleashed imagination: children were named Liberté (Liberty), Égalité (Equality), or even Brutus. But the Civil Code of 1803 quickly restricted choices to "names in use in various calendars" and "figures known from ancient history." It wasn't until 1993 that France fully liberalized the choice of first names. In Arab cultures, a first name is inseparable from its spiritual meaning. Mohammed, the most common name in the world, means "the praised one." Compound names like Abdullah ("servant of God") reflect a direct relationship with the divine. In India, the Namkaran ceremony, held on the 12th day after birth, is a sacred ritual where the family astrologer may influence the choice. In Japan, first names are composed of kanji characters whose combination creates a unique meaning. Parents often consult an onomastics expert to ensure the number of strokes in the characters is auspicious. Haruto (陽翔, "soaring sun") has been the most popular boys' name for several years running. Today, choosing a first name has become both an intimate and social act, influenced by cultural trends, celebrities, TV series, and globalization. Random name generators address a real need: exploring the richness of naming traditions from around the world and discovering names one might never have considered.

Ilm al-Raml (علم الرمل, "science of sand") has its roots in pre-Islamic Antiquity. The Bedouins of the Hejaz already practised "darb al-raml" (striking the sand) to question destiny before crossing the desert. Islamic tradition attributes the invention of this art to the prophet Idris (identified with Enoch in the Bible and Hermes Trismegistus in the Hermetic tradition), considered the "father of sciences". The geographer al-Masudi, in his Meadows of Gold (Muruj al-Dhahab, c. 947), mentions that geomancy was already widespread among the Arabs before Islam, with diviners tracing signs in the sand of the Rub al-Khali to predict rains and raids. Traces of similar geomantic practices have been found on Mesopotamian cuneiform tablets dating from the 2nd millennium BC. The golden age of Ilm al-Raml coincided with the Abbasid period (8th–13th centuries). Caliph al-Mamun (813–833), founder of the House of Wisdom (Bayt al-Hikma) in Baghdad, had Greek and Persian divination texts translated, enriching the Arab tradition. The foundational treatise of the discipline is the work of Muhammad ibn Muhammad al-Zanati, a Berber scholar from the Zanata tribe of North Africa (13th century), author of Al-Fasl fi usul ilm al-raml. This text systematised the 16 figures, their planetary and elemental correspondences, and the derivation methods (tahwil). Ibn Khaldun devoted an entire chapter of his Muqaddimah (1377) to geomancy, classifying it among the "occult sciences" while acknowledging its popularity throughout the Muslim world. Arab geomancy crossed the Mediterranean by two main routes. The first passed through al-Andalus: Hugo of Santalla translated the first Arab geomancy treatise into Latin at Tarazona, in Aragon, around 1140, under the title Ars Geomantiae. The second took the Crusade routes: Frankish knights brought the practice back from the Levant in the 12th century. In Europe, geomancy became one of the most respected divinatory arts of the Middle Ages. Cornelius Agrippa devoted a chapter to it in De Occulta Philosophia (1531), and Robert Fludd published a detailed treatise in 1687. An apocryphal work, "The Oracle of Napoleon", claimed that Bonaparte consulted geomancy before his campaigns. The geomantic system rests on a remarkably elegant binary code: 4 lines of 1 or 2 dots generate 2⁴ = 16 possible figures. The mathematician Leibniz, who formalised the binary system in 1703, drew inspiration from the Chinese I Ching, a structurally related system (6 lines for 2⁶ = 64 hexagrams). The kinship between Arab geomancy and the I Ching has fascinated researchers: the ethnologist Robert Jaulin, in La Géomancie (1966), proposed a structuralist analysis showing that the 16 figures form a complete algebraic group under the XOR operation — each pair of "mother" figures produces a unique "daughter" by binary addition. The mathematician Ron Eglash, in African Fractals (1999), demonstrated that African geomancy practitioners intuitively manipulated information theory concepts well before Shannon. Psychology and anthropology have examined the cognitive mechanisms at work in geomantic consultation. The anthropologist Philip Peek, in African Divination Systems (1991), showed that geomancy functions as a "hermeneutic frame": the randomness of figures generates a space of meaning that the consultant and diviner co-construct through interpretation. The Barnum effect (Forer, 1949) — the tendency to accept vague descriptions as personally relevant — plays a central role. However, the work of Victor Turner on the Ndembu and Evans-Pritchard on the Azande shows that divination cannot be reduced to a "cognitive bias": it fulfils a social function of conflict mediation, offering a neutral arbiter accepted by all parties. In the contemporary Maghreb, Ilm al-Raml remains vibrant despite modernisation. In Morocco, geomancers practise in the medinas of Fez, Marrakech and Meknes — the anthropologist Abdelhafid Chlyeh, in Les Gnaoua du Maroc (1999), documents their integration into the social fabric alongside Sufi brotherhoods. In Mauritania, the practice is so widespread that the term "khattat" (sand tracer) denotes a recognised profession. In West Africa, Arab geomancy merged with the Yoruba Ifá system: the 16 basic figures correspond exactly to the 16 major Odu, a kinship studied by historian Théodore Monod and ethnologist William Bascom (Sixteen Cowries, 1980). In Madagascar, Sikidy (from the Arabic "sidq", truth) perpetuates the tradition through the ombiasy (diviners). Today, mobile apps and online simulators like ours allow people to discover this millennial art, while UNESCO inscribed the related Ifá system on the Intangible Cultural Heritage list in 2005.

Sig (سيق in Arabic, ⵙⵉⴳ in Tifinagh) belongs to the family of stick-dice racing games, one of the oldest gaming lineages in the world. Its most famous ancestor, the Egyptian Senet, dates back to 3100 BCE — boards and sticks were found in the tomb of Merknera at Saqqara and in Tutankhamun's tomb (c. 1323 BCE). The binary principle of the stick — one flat face (marked) and one rounded face (blank) — is probably the oldest random-number generation system after sheep knucklebones (astragali), used since the 6th millennium BCE in Mesopotamia. The Royal Game of Ur (c. 2600 BCE), discovered by Leonard Woolley in 1926–1928 in the royal tombs, used a similar mechanism. Sig thus perpetuates an unbroken gaming tradition spanning more than five thousand years. The earliest written mention of Sig dates to 1248, when the Egyptian poet and playwright Ibn Daniyal al-Mawsili describes in his shadow plays (khayāl al-ẓill) a racing game using stick-dice on a board drawn on the ground. These plays, performed in the streets of Mamluk Cairo, provide invaluable testimony about medieval daily life. The game is known by different names across the Arab world: "Tâb" (طاب) in Egypt and the Levant, "Sig" (سيق) in the Maghreb, "Tâb wa-dukk" in Sudan. The historian al-Maqrīzī (1364–1442) also mentions dice games in his descriptions of Cairene social life. The trans-Saharan caravan routes played a major role in spreading the game between Egypt, Libya, Tunisia, Algeria, and Morocco, as nomads carried this pastime that required nothing more than four pieces of wood and a little sand. It was French colonial ethnographers who provided the first detailed scientific descriptions of Sig. General Eugène Daumas, in "Mœurs et coutumes de l'Algérie" (1853), was among the first to describe the game in the context of Saharan nomadic life. Edmond Destaing, in "Études sur le dialecte berbère des Beni-Snous" (1907), meticulously documented the rules and variants of Sig as played in the Oran region. Émile Laoust, in "Mots et choses berbères" (1920), catalogued the different regional names — "sig" in the High Atlas, "sik" among the Tuareg, "tâb" in Egypt. The American Stewart Culin, in "Games of the Orient" (1895), drew parallels with Indian racing games such as Pachisi. Later, game historian R.C. Bell, in "Board and Table Games from Many Civilizations" (1960), mapped the lineage of this entire family of stick-dice racing games, from ancient Senet to the contemporary variants of the Maghreb. The Sig scoring system relies on an elegant binary combinatorics. Each stick having two possible faces (flat or rounded), four sticks generate 2⁴ = 16 combinations. The distribution follows a binomial law: 0 flat faces (Sīd, "the Master") appears with a probability of 1/16 (6.25%) and earns 6 points plus the right to replay — the rarest but most powerful throw. One flat face (Sīg, which gives the game its name) has a probability of 4/16 (25%) and is worth 1 point with replay. Two flat faces (Zūj, 37.5%) give 2 points, three flat faces (Tlāta, 25%) earn 3 points — both of these end the turn. Four flat faces (Arba'a, 6.25%) are worth 4 points with replay. In total, the player has a 37.5% chance of replaying on each throw, creating spectacular moments of tension where a lucky player can chain multiple throws and completely turn the game around. Sig is deeply rooted in the nomadic culture of the Sahara and the Maghreb. Among the Tuareg, it is played during long evenings under the stars, at seasonal festivals like the Tafsit (spring festival) and inter-tribal gatherings. The board is traced directly in the sand — an ephemeral gesture, mirroring nomadic life itself. The pieces are pebbles, date pits, or twigs, and the dice are made from date palm, argan, or olive wood — symbolic trees of the Maghreb. Anthropologist Jeremy Keenan, in his work on the Tuareg of the Hoggar (2004), emphasized the social function of the game: it brings generations together, accompanies storytelling (tinfusin), and serves as mediation in rivalries between camps. Sig also has a quasi-ritual dimension: some players recite propitiatory formulas before throwing the sticks, invoking baraka (divine blessing) to obtain a Sīd. Like many traditional games, Sig has suffered from competition with modern entertainment and rural exodus in the Maghreb. In large cities, it is virtually never seen. However, preservation initiatives are emerging. Algeria has organized national traditional games championships where Sig features prominently, and the country won the first Maghreb championship in this discipline. In Morocco, cultural associations incorporate Sig into their workshops for transmitting intangible heritage, particularly in the regions of Figuig, Errachidia, and Zagora. In France, the "Jeux du Monde" association organizes discovery workshops, and the Musée du Quai Branly in Paris exhibits Sig boards and sticks in its collections. The digitization of the game — through online simulators and mobile applications — offers a new path to introduce this millennial tradition to a worldwide audience, while preserving the essence of a game that once required nothing more than four pieces of wood and a little sand.

Le mélange aléatoire de listes puise ses racines dans les mathématiques combinatoires, une discipline formalisée dès le XVIIe siècle par Blaise Pascal et Pierre de Fermat. L'idée de permuter des éléments de manière équiprobable — c'est-à-dire en donnant à chaque arrangement la même chance d'apparaître — est au cœur de la théorie des probabilités moderne. L'algorithme le plus célèbre pour mélanger une liste est le Fisher-Yates shuffle, publié en 1938 par Ronald Fisher et Frank Yates dans leur ouvrage "Statistical Tables for Biological, Agricultural and Medical Research". À l'origine, il était conçu pour être exécuté à la main avec un crayon et du papier, en tirant des numéros aléatoires dans un tableau. En 1964, Richard Durstenfeld a proposé une version optimisée de l'algorithme, adaptée aux ordinateurs, qui fonctionne en temps O(n). Cette variante, souvent appelée algorithme de Knuth-Fisher-Yates (car popularisée par Donald Knuth dans "The Art of Computer Programming"), est aujourd'hui la méthode standard utilisée dans la quasi-totalité des langages de programmation. Le mélange aléatoire a pris une importance considérable avec l'essor du numérique. Les lecteurs de musique (comme le mode "shuffle" d'iTunes lancé en 2001) ont été parmi les premières applications grand public à démocratiser le concept. Apple a d'ailleurs dû modifier son algorithme car les utilisateurs percevaient le pur aléatoire comme "pas assez aléatoire" — les chansons d'un même artiste tombant parfois consécutivement. Dans le domaine scientifique, le mélange de listes est fondamental pour les essais cliniques randomisés, les sondages statistiques et les protocoles de test A/B. La qualité du mélange — sa vraie équiprobabilité — peut avoir des conséquences majeures : un biais dans la randomisation d'un essai clinique peut invalider des années de recherche. Aujourd'hui, les mélangeurs de listes en ligne sont devenus des outils quotidiens pour les enseignants (ordre de passage des élèves), les organisateurs d'événements (tirage de lots), les développeurs (tests aléatoires) et même les créateurs de contenu (sélection aléatoire de sujets). Leur simplicité d'utilisation cache une rigueur mathématique qui garantit l'équité du résultat.

Rock paper scissors originated in China during the Han Dynasty (206 BC – 220 AD), where it was known as "shǒushìlìng" (手势令), literally "hand gesture commands." The book Wuzazu by Xie Zhaozhi, written during the Ming Dynasty (around 1600), mentions that this game already existed in the Han era and was used to settle bets at banquets. The three original signs were the frog, the snake, and the slug — a cycle in which the frog eats the slug, the slug dissolves the snake, and the snake devours the frog. The game spread to Japan during the Edo period (1603–1868) under the name "sansukumi-ken" (三竦みけん), a term designating any game with three gestures forming a cycle. The most popular variant, "jan-ken" (じゃんけん), adopted the signs we know today: rock (gū), scissors (choki), and paper (pā). Jan-ken became a fundamental element of Japanese culture, used not only as a children's game but also to settle everyday decisions. The cry "jan-ken-pon!" accompanying the throw is still recognized worldwide today. The game arrived in Europe in the late 19th century, introduced through trade with Japan after the Meiji era (1868). The first written mention in English dates to 1924, in an article in The Times of London describing the rules under the name "zhot." In France, the game became popular in schoolyards after World War II, with the rhyme "pierre-papier-ciseaux, un-deux-trois!" North America adopted it under the name "Roshambo" — a term whose etymology remains debated, with some attributing it to the Count de Rochambeau, a hero of the American War of Independence. Far from being a purely random game, rock paper scissors has been the subject of serious scientific study. In 2014, a team from Zhejiang University led by Zhijian Wang analyzed 360 games played by 72 participants and discovered a recurring behavioral pattern: winning players tend to repeat their gesture, while losers switch following the cyclical order rock → paper → scissors. This unconscious strategy, dubbed "win-stay, lose-shift," contradicts the notion of a purely random game and opens the door to exploitation strategies. In game theory, rock paper scissors is a classic example of a zero-sum game with no Nash equilibrium in pure strategies. The only Nash equilibrium is the mixed strategy: playing each sign with a probability of 1/3. John Nash himself, Nobel laureate in economics in 1994, used this type of game to illustrate his work. Artificial intelligence researchers have also seized upon it: in 2011, a team from the University of Tokyo created a robot capable of winning 100% of the time by using a high-speed camera that detects the shape of the opponent's hand in 1 millisecond — before the human gesture is fully formed. Rock paper scissors became spectacularly institutionalized in the 21st century. The World RPS Society, founded in Toronto in 2002, organized annual world championships with prizes of up to $50,000. In 2005, Florida federal judge Gregory Presnell ordered the lawyers of both parties in a case to settle a procedural dispute by a game of rock paper scissors, ruling that both sides were behaving "like kindergartners." The auction house Christie's used the game in 2005 to decide who would sell an Impressionist collection worth $20 million — Sotheby's president played paper, while Christie's representative, advised by the 11-year-old daughter of one of his clients, chose scissors and won the contract.

The idea of guessing the value of an object dates back to antiquity. The Greeks played "artia e peritta" (odds or evens), a game mentioned by Plato in Lysis around 380 BC, where one player hid pebbles and the other guessed their number. In the bazaars of Persia and the Levant, "dast-forushi" (hand selling) required the buyer to propose a price without seeing the item, then negotiate through successive iterations — a direct ancestor of the "higher or lower" mechanic. In Rome, public auctions organized by praecones (town criers) were already a collective exercise in price estimation, described by Cicero in his Verrine Orations (70 BC). Price estimation became a spectacle with the birth of television. On November 26, 1956, Mark Goodson and Bill Todman launched The Price Is Right on NBC in the United States, hosted by Bill Cullen. The concept was simple: contestants had to guess the price of everyday items without exceeding the actual price. The show won over the American public and aired continuously for eight years. In 1972, Bob Barker took over on CBS in a revamped version that would last 35 years (1972–2007), an absolute record for a game show host. Drew Carey succeeded him in 2007 and the show is still on the air, totaling over 9,000 episodes. In France, the concept arrived on January 4, 1988 on TF1 under the name Le Juste Prix, hosted by Vincent Lagaf'. The show became a cultural phenomenon of the 1990s, attracting up to 7 million daily viewers. The cry "Le Juste Priiiiix!" entered French popular culture. In the UK, The Price Is Right aired from 1984 on ITV, hosted by Leslie Crowther then Bruce Forsyth. The format has been adapted in over 40 countries, from Australia to Brazil to India (Sahi Daam Batao). The "higher or lower" principle relies on a fundamental mechanism in computer science: binary search, formalized by John Mauchly in 1946. This algorithm halves the search space at each step: with just 10 comparisons, you can identify one element among 1,024 possibilities. Charles Antony Richard Hoare drew inspiration from it to invent quicksort in 1960, a sorting algorithm based on successive comparisons. The human brain uses a similar but imperfect process: a study by Daniel Kahneman and Amos Tversky published in 1974 in Science showed that our price estimates are systematically biased by the anchoring effect — the first price seen disproportionately influences the next estimate, even if it is random. The psychology of price estimation has been widely studied in behavioral economics. Richard Thaler, winner of the 2017 Nobel Prize in Economics, described the "endowment effect" as early as 1980: we overvalue objects we own by approximately 2 to 3 times their market price. Baruch Fischhoff documented the overconfidence bias in the 1970s: after a streak of correct answers, players become too bold and make more mistakes. Sarah Lichtenstein and Paul Slovic showed in 1971 that preference between two options depends on the measurement method used (preference reversal), a phenomenon directly observable in price estimation games. More recently, Dan Ariely demonstrated in Predictably Irrational (2008) that "free" prices completely distort our mental calibration. In the digital age, the "higher or lower" concept has experienced a spectacular revival. In 2016, Briton Nick Sheridan launched The Higher Lower Game website, which asks players to compare Google search volumes between two topics. The game went viral, reaching millions of players within months and spawning a mobile app. On Twitch and YouTube, streamers popularized variants comparing product prices, salaries, or sports statistics. The format has also taken over social media: "more expensive or cheaper?" quizzes on TikTok have accumulated billions of views. In 2024, the global online quiz game market was estimated at 8.3 billion dollars, with price guessing games among the most shared formats.

La roue des lettres trouve ses origines dans les jeux de société éducatifs du XVIIIe siècle, quand les pédagogues européens cherchaient des moyens ludiques d'enseigner l'alphabet aux enfants. Les premières roues alphabétiques étaient des disques en bois peints à la main, utilisés dans les salons bourgeois pour animer des jeux de vocabulaire. Ces ancêtres modestes allaient donner naissance à l'un des concepts de jeu télévisé les plus populaires au monde. C'est en 1975 que le concept explose avec la création de "Wheel of Fortune" par Merv Griffin aux États-Unis. L'émission, qui utilise une grande roue mécanique pour sélectionner des montants et des lettres, devient rapidement le jeu télévisé le plus regardé d'Amérique. Le principe est simple mais addictif : les candidats tournent la roue, proposent une lettre, et tentent de deviner un mot ou une expression cachée. Le succès est tel que le format est adapté dans plus de 60 pays. En France, l'adaptation "La Roue de la Fortune" fait son apparition sur TF1 en 1987, présentée par Michel Royer puis Christian Morin. L'émission connaît un immense succès populaire et reste à l'antenne pendant plus de 25 ans. Le concept de la roue des lettres devient un élément culturel incontournable, associé aux après-midis télévisés de millions de Français. Les expressions "je voudrais un A" ou "je tourne la roue" entrent dans le langage courant. Au-delà de la télévision, la roue des lettres s'est imposée comme un outil pédagogique de premier plan. Les enseignants du monde entier l'utilisent pour rendre l'apprentissage de l'alphabet interactif et amusant. Des études en sciences cognitives montrent que l'aspect aléatoire et visuel de la roue stimule l'engagement des élèves et améliore la rétention des lettres, particulièrement chez les jeunes enfants de 4 à 7 ans. Le jeu du "petit bac" (aussi appelé "baccalauréat" ou "jeu des catégories") est probablement l'usage le plus répandu de la sélection aléatoire de lettres. Joué dans les cours de récréation et les soirées entre amis depuis des générations, il consiste à trouver des mots commençant par une lettre tirée au sort dans différentes catégories (animal, ville, prénom, métier...). Ce jeu simple mais efficace développe le vocabulaire, la rapidité d'esprit et la culture générale. Aujourd'hui, la roue des lettres numérique a pris le relais des versions physiques. Les applications web et mobiles offrent une expérience immédiate, avec des animations fluides et des options de personnalisation impossibles avec une roue mécanique. L'exclusion automatique des lettres déjà tirées, l'historique des résultats et le partage en ligne ont modernisé ce classique indémodable. La roue ABC reste un outil polyvalent, aussi utile pour l'éducation que pour le divertissement.

Gift exchange by drawing lots is a tradition deeply rooted in cultures around the world. While the concept of "Secret Santa" as we know it today became popular in English-speaking countries during the 20th century, its roots go much further back in the history of festive exchanges. The Roman Saturnalia, festivals celebrated from December 17 to 23 in honor of the god Saturn, already included gift exchanges among citizens. Social roles were temporarily reversed, and everyone offered symbolic presents — candles, clay figurines, or coins — often drawn by lot among the guests. This tradition survived through the centuries in various forms. In the Middle Ages, the tradition of the "King's Bean" in Epiphany cakes was a form of festive lottery where chance designated a king for the day. In Scandinavia, "Julklapp" (a Christmas gift thrown through the door) added a dimension of surprise and anonymity that foreshadowed the modern Secret Santa. The term "Secret Santa" appeared in the 1970s in the United States, first in businesses and schools. The principle is simple: each participant draws the name of a person to whom they will give a gift, without revealing their identity. A maximum budget is usually set to ensure fairness. This format has conquered the world under different names. In France, it's called "Père Noël secret" or "tirage de cadeaux." In Spain, it's the "Amigo invisible" (invisible friend). In Brazil, "Amigo Secreto" is an essential institution of the holiday season. In Germany, "Wichteln" (from Wichtel, meaning elf) often adds a humorous touch with quirky gifts. With the advent of the Internet and smartphones, gift draws have gone digital. Online tools now make it possible to organize remote draws, add exclusions (to prevent spouses from drawing each other), and reveal results in a fun way. This digital version preserves the magic of chance while adding practicality and accessibility.</p>

Tarot was born in Northern Italy at the beginning of the 15th century, in the princely courts of Milan, Ferrara, and Bologna. The earliest known decks, called "tarocchi" or "trionfi," were aristocratic card games commissioned by the Visconti and Sforza families. The oldest surviving deck, the Visconti-Sforza Tarot (circa 1440–1450), painted by Bonifacio Bembo, is now divided among the Pierpont Morgan Library in New York, the Accademia Carrara in Bergamo, and the Colleoni collection. These 78 cards — 22 "triumphs" and 56 suit cards — were used to play tarocchini, a trick-taking game similar to bridge, which was played in Bologna until the 19th century. The divinatory use of tarot did not emerge until the 18th century, three hundred years after its invention as a game. In 1770, Jean-Baptiste Alliette, a former Parisian wigmaker who reinvented himself under the pseudonym Etteilla (his name spelled backward), published "Etteilla, or a Way to Entertain Yourself with a Deck of Cards," the first treatise on cartomancy using tarot. He invented the cross spread, assigned each card a specific divinatory meaning, and in 1788 created his own deck, the "Grand Etteilla." In 1781, the Freemason scholar Antoine Court de Gébelin claimed in "Le Monde primitif" that tarot was a remnant of the Egyptian Book of Thoth — a theory with no historical basis, but one that permanently anchored tarot in the esoteric imagination. The name "Tarot of Marseille" is actually recent: it was the card maker Paul Marteau, director of the Grimaud company, who established this name in 1930 by standardizing the deck in his book "Le Tarot de Marseille." The cards did not originate in Marseille — the city was simply a major center for playing card production in the 17th and 18th centuries, with workshops like that of Nicolas Conver (1760), whose deck remains the historical reference. Other important production centers existed in Lyon (Jean Dodal, 1701), Rouen, and Paris. The standardization of the "Marseille type" fixed the iconography we know today. The occultists of the 19th century profoundly transformed the reading of tarot. Éliphas Lévi (Alphonse-Louis Constant), in "Dogme et rituel de la haute magie" (1856), established correspondences between the 22 Major Arcana and the 22 letters of the Hebrew alphabet, integrating tarot into the Kabbalistic tradition. In 1909, the British occultist Arthur Edward Waite commissioned the painter Pamela Colman Smith to create a new deck, the Rider-Waite, which for the first time illustrated all 56 Minor Arcana with figurative scenes. Published by Rider & Company in London, this deck would become the best-selling tarot in the world, with over 100 million copies sold. Aleister Crowley created the Thoth Tarot in 1943, painted by Lady Frieda Harris over five years, integrating astrology, Kabbalah, and alchemy. The psychiatrist Carl Gustav Jung took an interest in tarot through his work on archetypes and the collective unconscious. For Jung, the tarot figures — the Magician (persona), the Empress (anima), the Hermit (the inner Sage), the nameless Arcanum (transformation) — represent universal archetypes present in all cultures. In his 1933–1934 seminars on Christiana Morgan's "Vision," Jung directly analyzed tarot imagery as tools for psychological projection. The American psychologist Timothy Leary continued this idea in 1969 in "The Game of Life," linking the 22 Arcana to stages of consciousness evolution. Today, "tarotherapy" is practiced by some psychologists as a tool for introspection, particularly in Italy and Latin America. The 21st century has seen a spectacular tarot revival. The global divination card market reached $793 million in 2024, driven by social media: the hashtag #tarot has accumulated over 40 billion views on TikTok. Artist Kiku Glover created the "Modern Witch Tarot" in 2018, reimagining the Rider-Waite with contemporary, diverse characters — it sold over 500,000 copies in two years. Filmmaker Alejandro Jodorowsky, co-author with Marianne Costa of "The Way of Tarot" (2004), popularized a psycho-symbolic approach to the Tarot of Marseille that influenced an entire generation of practitioners. In France, the "Tarot de Marseille Heritage" shop of Philippe Camoin (a descendant of Nicolas Conver) and Jodorowsky offers a deck restored from historical documents, considered the most faithful version to the 18th-century originals.

The use of spinning objects to designate a person or predict the future dates back to antiquity. In ancient Greece, the strophalos — a pierced disk spun on a cord — served as a divination tool, described by the poet Theocritus in his second Idyll around 270 BC. The Romans used the turbo, a ritual spinning top, and the teetotum (totum), a polyhedral die mounted on an axis that was spun to produce a random result. In China, divination through rotating objects is attested as early as the Shang dynasty (approximately 1600–1046 BC), where oracular practices involved positioning objects by rotation. The fundamental principle — entrusting a choice to a spinning object — thus spans civilizations long before the bottle became the instrument of reference. In the Middle Ages, the teetotum became a common game instrument throughout Europe, mentioned in illuminated manuscripts from the 13th century. In Germany, the Kreisel (spinning top) served not only as a toy but also as a decision-making tool in taverns to determine who would buy the next round. The Renaissance saw the rise of aristocratic parlor games: in Italy, the gioco della bottiglia appears in 16th-century chronicles as entertainment at Venetian festivals. In France, "forfeit games" — where a spinning object designated the person who had to perform a forfeit — appeared in 17th-century literature, notably in descriptions of the salons at the Hôtel de Rambouillet, where socialites competed in wit and eloquence. It was in the United States, in the parlors of the Victorian bourgeoisie during the 19th century, that "Spin the Bottle" took its modern form. The earliest documented mentions appear in the 1860s, in parlor game guides such as those published by George Routledge. At the time, the game remained relatively tame: the chosen person had to recite a poem, tell an anecdote, or answer a question. The glass bottle, ubiquitous in households of the industrial era, gradually replaced spinning tops and rotating dice. In 1897, Harper's Bazar magazine mentioned a variant called "Bottle Fate" in its descriptions of New York garden parties. The game crossed the Atlantic at the beginning of the 20th century, establishing itself first in England and then across the rest of Europe. The true explosion in popularity came in the 1950s, driven by the emergence of American teen culture. The postwar baby boom created a generation of teenagers who, for the first time, had their own social spaces — finished basements, sock hops, and drive-ins. Hollywood films of the era cemented the game in the collective imagination, and the comedy "The Seven Year Itch" (1955) starring Marilyn Monroe alluded to it. Sociologist James Coleman, in his book "The Adolescent Society" (1961), analyzed the role of party games like Spin the Bottle in shaping adolescent social norms. In France, the game became popular during the "surprises-parties" of the 1960s and 1970s, becoming a staple of youth gatherings. The "Truth or Dare" variant, combined with the bottle to designate players, appeared in the 1980s and further reinforced the game's playful dimension. The physics of a spinning bottle obeys the laws of classical mechanics described by Leonhard Euler in the 18th century. The final angle depends on three main variables: the initial angular velocity (ω₀), the coefficient of friction between the bottle and the surface (μ), and the mass distribution of the bottle. An empty bottle has its center of mass approximately at its geometric center, producing a more regular spin, while a bottle containing residual liquid sees its center of mass shift chaotically. Physicist Robert Matthews showed in 1995 that sensitivity to initial conditions makes the outcome effectively unpredictable for a human observer, confirming the perceived fairness of the game. In probability theory, if N players are arranged in a circle, each has a 1/N probability of being selected — provided the spin is energetic enough to complete several full rotations. Today, "Spin the Bottle" is enjoying a second life thanks to digital versions. Mobile apps of the "Spin the Bottle" type have accumulated tens of millions of downloads on iOS and Android platforms. The game regularly appears in contemporary popular culture: in the series "Stranger Things" (season 1, episode 2, 2016), in "Riverdale" (season 1, 2017), and in Greta Gerwig's film "Lady Bird" (2017). Teachers have adapted the concept to create interactive educational activities — the "question wheel" is a direct variant. In business, team-building coaches use adapted versions to break the ice at seminars. Social psychologist Robert Cialdini notes that the game exploits the principle of "chance as social arbiter": by delegating the choice to an object, participants more readily accept a situation they would not have voluntarily chosen.