Di Eudaemons
Physics students, one casino wheel wey dem buy wit cash, and one computer wey small reach to wear go di table.

From 1976 to 1981, one group of physics students for Santa Cruz build digital computers wey dey time di ball and di rotor and name one sector of di wheel while bets still dey open. Dia tests promise 44% advantage and di first long session give about 25%. Di hardware dey fail again and again, electrical noise beat di version wey dem build inside shoe for 1981, and dem win few thousand dollars.
One feeling for one Las Vegas bar, 1975
For di summer of 1975, Norman Packard, one physics student, spend two months to count cards for blackjack for Las Vegas wit one friend, Jack Biles, and dem barely break even. Over di last drink, Biles tok sey e go bet sey physics fit beat roulette, and Packard remember one hidden line for Beat the Dealer by Edward Thorp about method for roulette. Di two of dem borrow tape recorder, stand near wheels for many casinos and tap di microphone each time di ballequipmentBallDi small ball wey dem dey throw for di track against di rotor. Modern balls na ivorine or Teflon, 18–21 mm.Read di whole tin → pass one fixed point. When dem draw am for graph paper, di taps show di ball dey slow and fall for regular way. Di school friend of Packard, Doyne Farmer, graduate student for di University of California, Santa Cruz, call am waste of time until e do di calculation by imself: person wey fit time di ball reach about one tenth of one second suppose, for paper, fit tok where e go land within few numbers.
One wheel for di physics laboratory
For di spring of 1976, Farmer and Dan Browne pay $1,500 cash for one casino wheel wey dem don repair, for one workshop for Reno, and dem tok sey na for fraternity party. For months dem dey carry am for night go di teaching laboratory of di university and measure am wit infrared sensors, one electronic clock wey dem make by demself and one camera wey di sound of di ball as e hit metal dey trigger. Wetin dem find still be good short list of wetin matter for one spin. Na di air dey do most of di slowing, more pass di track. Wheel wey no level, even by one tenth of one inch, dey change where di ball dey leave di track, and for wheel wey tilt, di ball dey like comot for di high side, and dat one make di prediction easy. Balls no be di same: Teflon ball slow two times faster pass ball wey dem make from billiard-ball material. And once di ball don leave di track, e still dey bounce, for average no more pass one quarter to one third of di way round. Dat bounce na di question wey di whole plan hang on, and e no wide reach to scatter di prediction. By di end of di summer dem put di possible advantage for 44%, di figure wey Thorp give for im own device.

Di company and di pie
Dem call di business Eudaemonic Enterprises, from one Greek word for di happiness of life wey person live by reason. Everybody wey work on am go collect pay from di winnings wey go come later, according to di hours wey e put: one slice of wetin dem call di Eudaemonic Pie. Di winnings suppose pay for one community of friends wey go do science di way dem like.
Computer under di arm, 1976–1978
Di first machine grow from one kit computer wey come by mail for September 1976 for $250, wey dem build on di 6502 processor wey Apple computers dey use too. Farmer, wey never program before, write di equations for di ball and di rotorequipmentRotorDi part of di wheel wey dey spin and carry di pockets.Read di whole tin → inside am. Di casino version, dem dey tie am for body, under di arm or, for di women, inside bra. Di player for di wheel dey click switches wit di big toes: one toe dey mark di zerowheelZeroDi one green pocket wey no even-money, dozen or column bet dey cover; na im be di source of di house edge. Dem also dey call am: single zero, 0.Read di whole tin → and den di ball each time dem pass one fixed point, di oda dey move di program between im settings. To fit di program to one particular wheel take about twenty minutes of quiet clicking. Den, few seconds inside each spin, di computer go name one of eight sectorswheelSectorPockets wey follow each oda for one arc of di wheel, no be group for di layout.Read di whole tin → of di wheel, or signal “no bet”, as e dey buzz small plungers against di skin. Second player wey dey far for di table, wey weak radio signal link, go feel di same buzz and cover three or four numbers of dat sector, and sometimes e go change one number to di one wey dey near am for di wheel, so di pattern go hard to read.
Di first trip, to Lake Tahoe and Reno for December 1977, na one long equipment failure. Few weeks later, for di Golden Gate for downtown Las Vegas, Farmer play alone for four and half hours for ten cents one chipmoniChipToken wey stand for one fixed amount, wey you put on top di layout to make bet. Dem also dey call am: check.Read di whole tin →. Di profit small, but for several hundred spins im and Browne put di edge, wit caution, for 25%.

Di summer of 1978
Dat summer di group play in shifts for weeks, for downtown and for di Strip, two sessions every day and never di same casino two nights one afta di oda. Dem keep notebook for each casino: im wheels and how far dem no level, im workers, im shift changes. Las Vegas wheels come tilt well well, and di late-night games slow, and na wetin di computer need, becos slow rotor and fast ball dey leave more time to measure and to bet. Good nights dey. For Circus Circus, change of croupierpipoCroupierDi dealer for roulette table.Read di whole tin → for two o’clock for morning turn one session wey dey lose to several hundred dollars, for 25 cents one chip. And failures dey come steady: loose wires, radio links wey dey shift wit di temperature, electric shocks from di antenna wires wey dem sew inside dia shirts. One night di plungers hang, di wiring too hot, and Ingrid Hoermann continue to play wit burn instead to leave table wey dey win. Casino workers notice di winning but dem never notice di method; one time one croupier, wey vex becos of di stack of chips wey dey grow, grab di wheel wey dey turn and force am round.
Inside thirteen months dem make eight trips go Nevada and, as dem dey bet mostly dimes and quarters, dem win few thousand dollars. One session for di California Club for December 1978 bring more pass $1,000 inside three hours and convince dem sey di method deserve better hardware.
Packard and Biles dey time roulette balls wit tape recorder for Las Vegas.
Dem buy casino wheel for Reno; one summer of measurements; di first kit computer.
Di first casino trip, Lake Tahoe and Reno. Di equipment fail.
Golden Gate, Las Vegas: four and half hours wit dime stakes, dem put di edge for 25%.
Weeks of play for Las Vegas wit di computer for body.
California Club: more pass $1,000 inside three hours.
Dem rebuild di computer to enter inside shoe.
Las Vegas: electrical noise cover di radio link. Di project stop.
Nevada ban prediction devices. The Eudaemonic Pie come out.
Di computer inside shoe, 1980–1981
To remove di wires from dia body, dem decide to put everytin inside shoes. Mark Truitt, new physics graduate wey waka comot from job interview for military radar work, spend one and half years on am. Di idea wey make am fit come from one technician for di university: off di computer between predictions, and e go need far less batteries. Truitt put di chips on two circuit boards wey e etch by imself, turn one on top di oda and fill di space wit hard wax, and dat one make one block of about two inches by four and half inch thick, wey person fit waka on top. Batteries, antenna and two of di three buzzers enter di heel. Three buzzers for three speeds give nine signals: eight sectors and “no bet”. One shoemaker dig inside ordinary leather shoes and e no ask any question.
For November 1981, Farmer and di writer Thomas Bass carry di shoes and $2,500 go Las Vegas. For di first table, di first prediction hit, den di buzzers begin fire anyhow. Casinos full wit electrical noise, from security cameras, neon signs and slot machines, and e cover di weak radio link between di shoes; one television for di motel room do di same tin. Days of repairs by four pipo no fit cure am, and di project stop there. Di equipment enter one trunk for one basement for Santa Cruz.

Wetin 44% mean
For American wheel, straight upbetStraight upOne single number, e dey pay 35:1.Read di whole tin → dey win once in 38 spins for average and e dey pay 35 to 1, and dat one dey cost di player 5.26%. 44% advantage na wetin di same bet worth when e dey win once in 25 spins: 36 chips dey come back for every 25 wey you stake. So di computer no need sabi di number. E only need make di numbers wey e choose show about one and half times as often as chance allow.
Why big edge still feel like gambling
Edge for 35 to 1 dey pay slow and e no dey even. One of di advisers of di group warn sey player wey dey stake $100 for one number fit don lose $10,000 or $20,000 before di advantage show, and di arithmetic agree: wit 44% edge on single numbers, player still dey behind afta 100 spins almost one time in four. Na why di Eudaemons start wit dimes and build dia bankrollmoniBankrollDi total moni wey you set aside for play. Bankroll management na to decide how much of am you go risk for each bet and for each session.Read di whole tin → from winnings, and why Alan Lewis, wey join dem for 1978, spend im time on how much to bet. Farmer later think sey dem too careful. Small stakes keep dem safe, and dem also mean sey years of work bring very small moni.
Wetin e cost and wetin e pay
About $15,000 go into parts, tools and di pay of Truitt, most of am from Farmer and from Letty Belin, one lawyer wey later marry am. Dem give Farmer credit for 3,500 hours of work, Truitt 3,000 and Packard 2,000. Against dat one, na di few thousand dollars wey dem win wit small stakes. For 1983 Farmer advertise for one gambling magazine for investors, as e describe one prototype wit casino advantage of 20 to 40% wey dem don prove. When di Eudaemons dey play, di search wey Belin do for Nevada law no find anytin wey ban to predict game; for May 1985 di state make am crime to use device for dat. Wetin last na di science. To build di computers train Farmer, Packard and dia friends for di study of chaos, and na there dem make dia name.
To read di book today
Thomas Bass, wey put di bets for di last trip, tell di story for The Eudaemonic Pie (1985), wey e build on long interviews wit di group, and na di source for dis page. Im short history of roulette no safe like im account of di project. E repeat di story of di six clerks wey Jagger hire, wey go back to one book of 1901 and no further (see Joseph Jagger), and e put di casino test of Thorp and Shannon for 1962, where di own accounts of Thorp tok di summer of 1961.
Questions wey pipo dey ask
No. Dem win few thousand dollars wit dime and quarter stakes, and dem spend about $15,000 and many thousands of hours.
When dem dey play, Nevada no get law against to predict game wit device. E don get one since 1985, and most places wey get casinos get am now.
No for places where betting dey close as dem throw di ball, as e dey happen for live studios, and to carry such device enter casino na crime for most jurisdictions.
Play with Maths
Try dem by yourself first. Each solution dey folded; open am when you ready.
Di Eudaemons calculate sey dia computer worth 44% for straight upbetStraight upOne single number, e dey pay 35:1.Read di whole tin → for American wheel, where di bet dey pay 35 to 1. How often di number wey dem choose must win make dat one be true? And how many of di 38 pocketsequipmentPocketOne of di 37 small boxes wey get number for di rotor. Dem also dey call am: slot, cup.Read di whole tin → prediction go need to rule out, if di ballequipmentBallDi small ball wey dem dey throw for di track against di rotor. Modern balls na ivorine or Teflon, 18–21 mm.Read di whole tin → get equal chance to land for any of di rest?
Show di solution
Answer Once for 25 spins. Dat one na di same as to rule out 13 pockets and leave 25.
ChipmoniChipToken wey stand for one fixed amount, wey you put on top di layout to make bet. Dem also dey call am: check.Read di whole tin → wey win dey come back with 35 more: 36 chips. If di number win once for n spins, n chips wey you stake dey bring 36 back, so di bet worth 36/n − 1.
Make dat one equal 0.44: 36/n = 1.44, so n = 25. Without prediction, n na 38 and di bet worth 36/38 − 1 = −5.26%.
Now imagine sey prediction rule out k pockets and di ball get equal chance to land for each of di oda 38 − k. Chip on one of dose ones dey win once for 38 − k spins. For 44% we need 38 − k = 25, so k = 13: e pass one third of di wheel small.
For di book, dem quote Farmer sey 40% dey come from to rule out eight pockets. For dis simple model, eight dey give 36/30 − 1 = 20%, so di real picture must don dey uneven: some of di pockets wey remain get chance well well pass di oda ones.
pockets wey dem rule outpockets wey remainhow much straight up worth038−5.26%2360%830+20%1325+44%1919+89%Imagine sey your number really dey win once for 25 spins for 35 to 1, 44% edge. You dey bet one chip every spin. How likely you go dey behind afta 100 spins? Afta 500?
Show di solution
Answer About 23% afta 100 spins and still about 6% afta 500.
Afta 100 spins you don stake 100 chips, and each win dey bring back 36. Two wins dey bring 72, loss of 28; three dey bring 108, gain of 8. So you dey behind if you win two times or less.
Di chance of no win for 100 spins na (24/25)¹⁰⁰ = 1.7%. Exactly one win: 100 × (1/25) × (24/25)⁹⁹ = 7.0%. Exactly two: 4,950 × (1/25)² × (24/25)⁹⁸ = 14.5%. Togeda 23.2%.
Afta 500 spins you need 14 wins to dey ahead (14 × 36 = 504), and di average na 20. Di chance of 13 or less na about 6.2%.
Dis na di oda side of long-odds bet. Di edge big, and for about one run of 100 spins out of four, e no dey show. Player wey no sure sey di edge dey there no fit separate bad run from computer wey spoil, and na di position wey di Eudaemons dey often find demself.
spinswins wey you need to dey aheadchance sey you go dey behind50240.1%100323.2%200618.6%500146.2%Di book tok sey with 44% edge, $100 wey you stake 50 times every hour suppose earn $2,200 every hour. Check am. Then work out wetin di same edge earn for di stakes wey di group really play: one dime for each spin.
Show di solution
Answer $2,200 correct for $100 for each spin. For one dime for each spin, na $2.20 every hour.
Edge na share of everytin wey you stake. For $100 for each spin and 50 spins every hour, you don stake $5,000, and 44% of dat one na $2,200.
For 10 cents for each spin, you don stake $5 for one hour, and 44% of $5 na $2.20. Even if dem cover four numbers with one dime each, na $8.80 every hour for two pipo.
Di group play small becos dem dey build bankrollmoniBankrollDi total moni wey you set aside for play. Bankroll management na to decide how much of am you go risk for each bet and for each session.Read di whole tin → from notin and becos, as di puzzle wey dey up show, 44% edge for 35 to 1 fit dey lose for hours. Di price of dat caution be sey di method fit dey work perfectly and still pay less pass work.
Small laugh

Di physics work. Di neon win.
Sources
- Bass, T. A. The Eudaemonic Pie.
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. “The invention of the first wearable computer.”
- Nevada Revised Statutes, chapter 465.