From knucklebones to slot machines
The will to gamble
People have thrown dice for thousands of years, and for just as long they have known how it ends. The urge has stayed the same; the dice, the tables and the machines have changed. You get 100 coins and carry them through history: each age hands you its own game, with its real odds.
“When I resolve to play with these no longer, my friends depart from me and leave me lonely. When the brown dice, thrown on the board, have rattled, like a fond girl I seek the place of meeting.”Rigveda, book 10, hymn 34, verse 5 (trans. R. T. H. Griffith, 1896)Start with the knucklebones ↓
About 3,000 years ago
The oldest gambler who speaks to us
Hymn 34 in the last book of the Rigveda is the voice of a man who has lost everything at dice. His dice were nuts from the vibhīdaka tree. His wife holds him aloof and her mother hates him. Other men caress his wife, and his father, mother and brothers say of him: “We know him not: bind him and take him with you.” Still he goes back to the gambling house, “his body all afire”, wondering: “Shall I be lucky?”
Near its end, the hymn gives advice a counsellor might give today: “Play not with dice: no, cultivate thy corn-land. Enjoy the gain, and deem that wealth sufficient.”
Knucklebones are older than the hymn. They are the small ankle bones of sheep and goats, with four sides they can land on. At Neolithic settlements in Anatolia such as Çatalhöyük, archaeologists have found worn knucklebones and read them as game pieces, lucky charms or tools for divination. Greeks and Romans scored the four sides 1, 3, 4 and 6. The worst throw, four ones, was called “the dog”. The best, with all four sides different, was “Venus”.
In 1962 the statistician F. N. David tossed a sheep's knucklebone over and over to measure its sides. Sides 3 and 4 each came up about four times in ten, sides 1 and 6 about once in ten. That makes Venus roughly one throw in 26.
Throw four knucklebones
Each bone lands with the probabilities David measured. We are looking for Venus: a 1, a 3, a 4 and a 6. No coins are at stake here.
That is a game without a house. Whoever wins, wins from someone else at the table. It stayed that way for thousands of years.
The last centuries BCE and the first CE
The state joins the game: 5%
In the Arthaśāstra, the Indian treatise on statecraft attributed to Kauṭilya, gambling is state business. A “Superintendent of gambling” must bring all play into one place, the better to catch spies and thieves; anyone who plays elsewhere is fined 12 paṇas. The house hires out the dice. And from every winner the Superintendent takes “5 per cent”.
The treatise adds, with a realism that has not dated: “gamblers are naturally false players.”
A table in the Superintendent's hall
You and another player each throw two dice. The higher total takes the other's stake, one coin; ties are thrown again. The house keeps 5% of each win.
The dice are fair and your opponent has the same chances as you. Even so, each throw costs you on average 2.5 hundredths of whatever you stake: half of the house's 5%, because you win only half the games. That is before the dice hire and the other fees. It is the oldest “house edge” I have found written down as a rule. From now on the house sits at most tables. You will meet two exceptions along the way.
First century CE
The emperors played too
Tacitus wrote that the Germans play dice sober, as a serious business, and “when everything else is gone, they set their liberties and persons on the last throw.” The loser goes into voluntary servitude and lets himself be bound and sold, however young and strong he is. “They themselves call it honor.”
Roman law banned gambling for money, except bets on athletic contests and during the Saturnalia in December. The emperors paid little attention. Suetonius quotes a letter from Augustus to Tiberius: at the festival of the Quinquatria he “kept the gaming-board warm” all day and lost twenty thousand sesterces. Claudius was so devoted to the game that he wrote a book about it and had a board fitted to his carriage so that the game would not be upset on the road. Nero played for four hundred thousand sesterces a point.
A fourth-century dice tower found in 1985 at Vettweiss-Froitzheim in Germany, now in the museum at Bonn, carries the inscription PICTOS VICTOS · HOSTIS DELETA · LVDITE SECVRI: “The Picts are beaten, the enemy destroyed, play without a care.” The tower had a job: the dice tumble through steps inside, so no hand can guide them.
Constantinople, around 500 CE
The machine at the Hippodrome
In 1834 a block of marble 77 centimetres tall and weighing 290 kilograms was found by the Hippodrome in Constantinople. One side is a stepped track with holes. The others carry a race day in relief: the statue of a horse, an aulos player, attendants drawing lots for the order of the chariots, two four-horse chariots in pursuit, the winner receiving his palm branch. A woman watches from a window. Today the block is in the Bode-Museum in Berlin.
An old commentary explains what it was for: the betting parties put four balls of different colours at the top of the track and let them run down through the holes, and whichever ball came out of the last hole first won for whoever had bet on it. The museum calls the object a “luxury version” of such gambling machines and says it was “certainly” used at the Hippodrome for betting.
Pick a colour
Four bettors put in a coin each, one on each ball. Whoever's ball comes out first takes all four coins. At the Hippodrome the rival factions were the Blues and the Greens.
We don't know whether the organisers kept anything from the pot. As played here, the game is perfectly fair: in the long run each colour wins one time in four.
The emperor Justinian banned both the dice and the machines. A law given at Constantinople on 22 September 529 says that dice, once allowed only at contests, had become “a calamity”: some people played without knowing anything of the game except the names of the numbers on the dice, “and have lost their property by playing day and night with silver, precious stones and gold.” The law banned play in public and in private. Anyone who had lost could reclaim the money, even fifty years later. Five sports stayed legal, among them leaping, javelin and wrestling, with a stake of no more than one gold piece, “although he is very rich”. The next law in Justinian's Code also bans the game with “wooden horses” (equi lignei), which the museum identifies with machines like this one, and houses where these games were played were to be confiscated. The Berlin museum dates the ban on machines of this kind to 534, the year of the revised Code.
The Ethnographic Atlas
Almost everywhere. Not quite everywhere.
The Qur'an sets strong drink and games of chance, maysir, side by side: “In both is great sin, and (some) utility for men; but the sin of them is greater than their usefulness” (2:219). In China, the code of the Tang dynasty gave a hundred blows to anyone who gambled for goods, but spared bets on archery and wagers of food and drink. In Wallachia, the law code Îndreptarea legii of 1652 stripped priests who played at harjeți of their office and excommunicated lay players. The critical edition glosses harjeți as “knucklebones, dice”.
In 1907 Stewart Culin catalogued the games of the native peoples of North America. He found dice games among 130 tribes of 30 language families, “and from no one tribe does it appear to have been absent.” Chess and other games of pure strategy, on the other hand, were entirely missing.
The map below shows all 486 societies in Murdock's Ethnographic Atlas for which anthropologists recorded what games were played.
Games of chance appear in 310 of the 486 societies, nearly two in three. They are in all 79 of the south-western United States, all 42 in the Atlas's “Western Canada” and “Eastern Canada” regions, and 15 of the 17 in Eastern Europe. They are missing in all 17 societies in Brazil, all 6 in Australia and 12 of the 14 in New Guinea and its neighbouring islands. Only 26 societies had no games at all.
Part of what the map shows depends on who did the writing. The Atlas holds far more communities from North America than from anywhere else. Each dot describes one group at the date an ethnographer studied it, and a game the ethnographer never saw is not there. With those caveats, Australia has other evidence behind it: a 2008 thesis finds no games of chance in traditional Aboriginal society, and card games seem to have arrived with traders from Makassar.
In 1959 the anthropologists John Roberts, Malcolm Arth and Robert Bush noticed, across 50 societies, that games of chance turn up more often where people believe in gods and spirits who are benevolent and can be persuaded. Throwing dice was sometimes a way of asking the sky.
Paris, 1654
Probability was born at the gaming table
In the summer of 1654 Blaise Pascal wrote to Pierre de Fermat about the Chevalier de Méré. Méré knew that it pays to bet on throwing at least one six in four throws of a die: the advantage is “as 671 is to 625”. But with two dice, the bet on at least one double six in 24 throws loses. To Méré this seemed impossible. Pascal wrote that this was “his great scandal”, and that Méré had taken to saying that arithmetic had lost its mind.
Probability theory grew out of the letters of that summer, above all out of the question of how to split the stakes of an interrupted game.
The Chevalier's bets
The stake is one coin and a win pays the same. Pick a bet and throw.
The gap is too small for a gambler to feel at the table. Pascal's letter shows only that Méré objected to the arithmetic; it says nothing about lost money. The first bet is the only one on this page that favours you. The gambling houses learned the lesson quickly.
1567–1906
The lottery: luck with a state ticket
Elizabeth I announced England's first state lottery in 1567 to raise money for repairing the harbours. A ticket cost ten shillings, and the draw took place in 1569 at St Paul's. From 1612, the Virginia Company kept its American colony alive largely on lotteries. Lotteries also raised money for Harvard in 1745 and for the college that grew into Columbia University.
In Romania, the state lottery goes back to a law promulgated by King Carol I on 29 May 1906, which raised a fund for villagers' medical care. Caragiale had already published, in 1898, the story of Lefter Popescu, who hunts desperately for his winning tickets, finds them, resigns his job, and learns at the counter that the numbers had been misprinted in the paper. From 1901 he called it “Two Lottery Tickets” (Două loturi).
Bad Homburg, Baden-Baden, 1843–1867
A single zero
In 1843 the brothers François and Louis Blanc introduced a roulette wheel with a single zero at the casino in Bad Homburg. From 1863 Monte Carlo became François Blanc's business. On a single-zero wheel, a bet on red wins 18 times in 37; the house edge is 1 in 37, or 2.7%.
Dostoevsky first played roulette at Wiesbaden in 1863 and kept at it, on and off, until 1871. In October 1866, under a contract that would have taken the rights to his works, he dictated The Gambler, set in an invented spa called Roulettenburg, to the stenographer Anna Snitkina in 26 days. The next year they married. On their honeymoon in Baden-Baden, by her account, they pawned her wedding ring, earrings and brooch, then his overcoat.
One coin on red
If red comes up you win a coin. Black or zero, you lose it.
San Francisco, the 1890s to now
The machine that plays by itself
Some time between 1894 and 1899 (sources disagree on the year), a San Francisco mechanic, Charles Fey, built the Liberty Bell: three reels with horseshoes, diamonds, spades, hearts, stars and a cracked bell. The machine paid out by itself, in coins. No opponent, no croupier, no other person was needed.
Mechanical reels had a fixed number of positions, so even the biggest prizes could not be very rare. In 1984 Inge Telnaes patented the answer: a random number generator picks a position on a much longer “virtual” reel, which is then translated into a position on the real one. One physical position, the patent says, can stand for “one or several” virtual ones. That means the designer decides how often each symbol appears, and above all where.
In 2009 Kevin Harrigan and Mike Dixon obtained, through freedom-of-information requests, the technical sheets for some machines in Ontario. One is Double Diamond Deluxe: 22 real positions on the reel and 72 virtual ones. The Double Diamond symbol at position 8 has a single virtual stop. The blanks just above and just below it have five each.
The first reel, exactly as built
This is the real map of reel 1, all 72 virtual stops, including the ones the machine nudges past the line. Reels 2 and 3 were never published, so nothing is won here. Just count how often the Double Diamond lands on the line, and how often right next to it.
The eye sees the diamond “one step away” from the line ten times as often as on it. Researchers call this a near-miss. It is written into the reel map. Across the whole reel, counting the second diamond and the stops the machine nudges past the line, the ratio is 7.5 to 1.
Play Double Diamond Deluxe
One coin is the three-credit stake. Payouts come straight from the machine's published table, across all 373,248 combinations. It returns 92.6% of what goes in on average, and something pays on one spin in seven. The symbols aren't shown because the maker never published them.
If gambling has stopped being a game for you or someone close to you: in Britain, the National Gambling Helpline, 0808 8020 133, free, 24 hours a day (GamCare).
Losses that sound like wins
Video machines can play 15 lines at once. On Lucky Larry's Lobstermania, another machine from the same study, a player betting all 15 lines “wins” something on a third of spins. But 61% of those wins are smaller than the stake. The machine flashes and plays its tune, and you have less money than before. In 2010 Mike Dixon and colleagues measured players' skin conductance: it rose for these “wins” just as it did for real ones.
A hundred 15-line spins, drawn from the published frequencies:
The zone
The anthropologist Natasha Dow Schüll spent some fifteen years with machine gamblers in Las Vegas. The heaviest players described a state they call “the zone”, in which worries and even the sense of their own bodies fade. They play simply to keep playing. The industry, her book Addiction by Design (2012) shows, designs its machines, venues and loyalty schemes for one goal: “time on device”.
Speed does the rest. A mechanical reel spins about once every six seconds, 600 spins an hour. A video machine at three seconds manages 1,200 an hour. Australia's Productivity Commission calculated in 2010 that at the highest permitted stake and that speed, a player could lose on average $1,200 an hour.
Neuroscience
Why we like not knowing
Dopamine neurons in the monkey brain respond above all to surprise: to a reward better than expected. When the reward is certain, they are quiet; when it fails to come, their activity dips. Wolfram Schultz and colleagues described this “prediction error” signal in the 1990s. In 2003 his lab found, in two monkeys, a signal that grew largest when the chance of reward was exactly 50%, when uncertainty is greatest. The authors spoke cautiously of a “possible role” in risk-taking, and the interpretation is still debated.
In people, Luke Clark and colleagues showed in 2009 that near-misses feel worse than clear losses, yet they increase the desire to play and light up brain regions that also respond to real wins. Ellen Langer found in 1975 that people asked more than four times as much for a lottery ticket they had chosen as for one they were handed, although the odds were identical.
The strangest evidence comes from medicine. Some Parkinson's patients treated with drugs that mimic dopamine start to gamble compulsively. In a study of more than 3,000 patients, 17.1% of those on such drugs had an impulse-control disorder, against 6.9% of the others. Since 2013 the American diagnostic manual, DSM-5, has placed gambling disorder alongside substance addictions: the first addiction without a substance it recognises.
Who plays
Why mostly young men
The Lancet Commission on gambling gathered studies from around the world in 2024. In the past year, 49.1% of men and 37.4% of women gambled. The big gap is in the harm: 11.9% of men show at least one sign of risky gambling, against 5.5% of women. Problem gambling or gambling disorder affects 2.2% of men and 1% of women.
A 2011 meta-analysis by Catharine Cross, Lee Copping and Anne Campbell, across 277 studies, suggests where the gap may come from, though it does not measure gambling itself. Men seek thrills more, and women are more sensitive to the threat of punishment or loss. On sensitivity to reward, the sexes barely differ. Applied to gambling, that would mean the appetite for winning is the same, and losing simply stops men less.
Age matters as much as sex. Sensation seeking rises through adolescence and peaks around 19, while self-control matures only at about 23 to 26. In a well-known experiment by Margo Gardner and Laurence Steinberg, adolescents took twice as many risks in a driving game when two friends were in the room. In adults the effect was much weaker.
There are evolutionary explanations too. In 1985 Margo Wilson and Martin Daly proposed a “young male syndrome”: at the age when competition for status and partners is fiercest, risk would have paid. It is an influential hypothesis and a hard one to test. Testosterone, the usual suspect, comes out of the studies badly: the links found are inconsistent, and large experiments that gave volunteers the hormone found no effect on risk.
Then there is the market. The Lancet Commission writes that social media advertising can target young men specifically. In the 2022–23 Premier League season, 40% of shirt sponsors were betting firms. A sports bet also gives young men the feeling that they are playing with their heads, because they know football. Among adults who bet on sport, about one in eleven has problem gambling or gambling disorder; among adolescents who bet, one in six.
Romania, today
The slot hall on the corner
In Videle, a town of about 10,000, the only secondary school stands at a crossroads with about eight gambling halls, Ariana Coman reported in “At the crossroads of slot machines” (PressOne, April 2024). That same month, on 17 April 2024, Romania promulgated a law banning gambling halls in places with fewer than 15,000 inhabitants, which is more than 90% of the country's localities. Since February 2026 an emergency ordinance has let local councils approve, ban or limit gambling in larger towns too. The mayor of Slatina said his town had 70 halls and three libraries.
According to the Court of Accounts audit of the gambling regulator, ONJN, reported by Mediafax in July 2026, Romanians staked about 96.1 billion lei in 2024, 60.1 billion of it on machines. Most of that comes back as prizes. What the operators kept, the players' net loss, was 19.1 billion lei: 9.8 billion online and 7.8 billion on hall machines.
A 2016 government decision requires hall machines to pay out at least 85% of what they take. Put the other way, the law lets a machine keep, on average, up to 15 bani of every leu played. Counted the same way, the Superintendent of the Arthaśāstra took 2.5: six times less.
The Lancet Commission also notes that Eastern Europe has the highest share of gamblers showing signs of risky gambling of any region in the world, for men and for women alike.
The world, 2024
2.3 billion
The Lancet Commission estimates that 46.2% of the world's adults gambled in the past year: about 2.3 billion people. Gambling is legal in some form in more than 80% of countries, and online it can be reached from almost anywhere. Players' net losses are projected to reach nearly $700 billion a year by 2028.
Each dot below stands for 10 million people who gambled in the past year.
A Canadian study cited by the Commission found that the most active 20% of gamblers account for 90% of online casino play. The business rests on a few people, and the machines are designed to keep them in their seats as long as possible.
The reckoning
What history took from you
You started with 100 coins. Here is what happened to them, game by game, next to what each game's arithmetic says: the stake times the house edge, added up over all your plays.
| Game | Plays | Your result | Expected |
|---|
An example: 100 pulls on Double Diamond Deluxe at one coin each. The machine returns 92.6%, so on average you lose 100 × 7.4% = 7.4 coins. Over a small number of pulls, though, anything can happen: after 1,000 pulls, the machine's sheet gives anywhere from 59% to 126% of what went in. Only at a million pulls is it sure to sit between 91.5% and 93.6%.
If you are ahead, that isn't a mistake. The machine's technical sheet shows that after 1,000 pulls a player can be holding anything from 59% to 126% of what went in. Only after a million pulls is the machine sure to sit around 92.6%. The house edge is too small for one person to see. The owner sees it, adding up millions of pulls by everyone.
The urge that pulled the man in the Rigveda back to the table is the one that made you pull once more. Only what sits on the other side of the table has changed: a friend, then an official taking 5%, then a marble ball, a wheel with one zero, a reel with 72 stops, and a machine that never sleeps.
If you or someone close to you can't stop: in Britain, the National Gambling Helpline is free and open around the clock on 0808 8020 133 (GamCare). In Romania, Asociația Joc Responsabil offers free, confidential counselling on 0800 800 099 (weekdays, 9–17).
Sources
- Rigveda 10.34, trans. Ralph T. H. Griffith, The Hymns of the Rigveda (1896), sacred-texts.com. Vibhīdaka nuts: W. Norman Brown, “The Indian Games of Pachisi, Chaupar, and Chausar”, Expedition (1964), Penn Museum.
- Knucklebones at Çatalhöyük: Çatalhöyük Archive Report 2003. Measured probabilities: F. N. David, Games, Gods and Gambling (1962), ch. 1.
- Arthaśāstra III.20, trans. R. Shamasastry (1915), Wikisource.
- Tacitus, Germania 24, Project Gutenberg. Suetonius, Lives of the Caesars (Augustus 71, Claudius 33, Nero 30), trans. J. C. Rolfe, LacusCurtius. The Vettweiss-Froitzheim dice tower, LVR-LandesMuseum Bonn.
- The Hippodrome machine: Staatliche Museen zu Berlin, museum-digital and Google Arts & Culture (commentary translated by Dieter Roderich Reinsch).
- Justinian's Code 3.43, trans. Fred H. Blume, Annotated Justinian Code, University of Wyoming.
- Qur'an 2:219, trans. Pickthall, quran.com. Tang Code, art. 402, Wikisource. Îndreptarea legii (1652), glava 104, Academy edition (1962), archive.org.
- Stewart Culin, Games of the North American Indians (1907), archive.org. Ethnographic Atlas, variable EA035 (“Games”), D-PLACE, with codes following the SCCS codebook. Australia: M. Fogarty, PhD thesis, Charles Darwin University (2008). Roberts, Arth and Bush, “Games in Culture”, American Anthropologist 61 (1959), summarised by HRAF.
- Pascal to Fermat, 29 July 1654, in Oeuvres de Fermat; APS News.
- The 1567 lottery: History Today. Loteria Română: loto.ro. Caragiale, “Două loturi”, Wikisource.
- François Blanc and single-zero roulette: M. Braude, Making Monte Carlo (2017). Dostoevsky: “The Gambler (novel)” and “Anna Dostoevskaya”; the pawned items from Anna's diary, via Bookforum.
- Liberty Bell: Wikipedia, charlesfey.com. Telnaes patent, US 4,448,419 (1984), Google Patents.
- K. A. Harrigan and M. Dixon, “PAR Sheets, probabilities, and slot machine play”, Journal of Gambling Issues 23 (2009), PDF. Its tables 2, 5 and 6 drive the games on this page.
- M. J. Dixon et al., “Losses disguised as wins in modern multi-line video slot machines”, Addiction 105 (2010). N. D. Schüll, Addiction by Design (Princeton, 2012). Productivity Commission, Gambling (2010), vol. 1.
- Fiorillo, Tobler and Schultz, Science 299 (2003). Clark et al., Neuron 61 (2009). Langer, J. Pers. Soc. Psychol. 32 (1975). Weintraub et al. (the DOMINION study), Archives of Neurology 67 (2010).
- Cross, Copping and Campbell, Psychological Bulletin 137 (2011). Steinberg et al., Developmental Psychology 44 (2008). Gardner and Steinberg, Developmental Psychology 41 (2005). Wilson and Daly, Ethology and Sociobiology 6 (1985). Stanton et al., Psychological Science 22 (2011). Testosterone administration studies: Hormones and Behavior (2024) and PNAS (2025), doi:10.1073/pnas.2508519122.
- H. Wardle et al., “The Lancet Public Health Commission on gambling”, Lancet Public Health 9 (2024), open access.
- Ariana Coman, “La răscruce de păcănele”, PressOne, 21 April 2024. Ovidiu Cornea, Europa Liberă, 17 April 2024 and 28 February 2026. Cezar Moldovan, Mediafax, 2 July 2026. Government Decision 111/2016, art. 84, anaf.ro.
The games use random numbers generated in your browser and the exact odds from the sources above. No money is involved, and the coins never leave the page.