Computers for Roulette
How computer dey time di ball, who build di first ones, and how correct e must be.
Roulette computer dey time di ball and di rotor for di first seconds of one spin, and e dey name di part of di wheel where di ball suppose land. Edward Thorp and Claude Shannon build di first one for 1961, and di Eudaemons build digital ones from 1976. Di method need bets wey dem take afta di launch: live studios now dey close betting for di launch, and Nevada don ban dat kind devices since 1985.
How Dem Build Di First Roulette Computer System
Di idea come to Edward Thorp for di spring of 1955, when e be physics graduate student for UCLA: wheel wey dem make too well to get bias suppose send 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 → round as predictable as planet. E film one cheap half-size wheel with stopwatch inside di frame, and e find sey e too irregular to predict; one trip to Nevada for December 1958 show am sey casino wheels dey run smooth. Den blackjack take over. For November 1960, for MIT, e ask Claude Shannon make e send im card-counting paper to di National Academy of Sciences; for di end of di meeting, Shannon ask wetin else e dey work on, and di roulette project move enter Shannon basement. Dem buy regulation wheel from Reno for $1,500, put am on top old slate billiard table, and time di ball against strobe light and clock wey dey read reach one hundredth of second. With practice, dem timing mistakes fall from about 0.03 to 0.01 seconds. By June 1961, di computer get twelve transistors and e big like cigarette pack: switch inside di shoe, wey dem dey press with di big toe, dey time di rotorequipmentRotorDi part of di wheel wey dey spin and carry di pockets.Read di whole tin → and di ball, and sound for one ear dey name one of di 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. For Las Vegas dat summer, Shannon dey time for di wheel and dey write numbers like any system player, while Thorp dey bet dimes for di far end of di table. Di predictions hold, but di wires wey thin like hair wey go di earpiece dey break all di time, and one time one woman wey dey beside Thorp look with fear di speaker wey dey comot from im ear. Dem never bet serious. Thorp announce di roulette computer system for 1966 and publish di details for 1979 and 1984.
Di First Digital Computers
Di machine of Thorp and Shannon na analog: im circuit na im programme, and to change di method mean to rewire am. Di microprocessor remove dat limit. Alan Lewis, student for Caltech, carry digital computer wey e build for house inside camera case go Circus Circus for Las Vegas for 1972, e time wheels from balcony on top di tables and send predictions by radio to partner wey dey below. E run, but e no make moni; later e learn sey e forget di tilt of di wheel. From 1976, one group of physics students for Santa Cruz, di Eudaemons, do di work well well. Dem buy casino wheel, measure di ball, di rotor, di tilt and di bounce, and write equations with five settings wey di player dey adjust for each wheel by clicking toe switches for about twenty minutes before betting. Dem computer dey name one of eight sectors few seconds inside di spin. For real table for January 1978, e give edge wey dem put for 25%; di hardware, wey dem tie for body and later build inside shoes, dey fail more often pass di physics (check Di Eudaemons).
Why Late Bets Matter
Casino fit stop prediction completely if e refuse bets once dem don launch di ball. Thorp find sey almost nobody dey do am: for Reno, Las Vegas, London, Monte Carlo, Nice, Venice and Puerto Rico, di normal practice na to call “no more betsprocedureNo more betsDi call of di dealer (or di prompt for screen) wey dey close betting. Nobody fit put, move or remove chips again.Read di whole tin →” one or two revolutions before di ball drop. Na dat window every prediction scheme since dat time don need, from di Eudaemons to di late calls of di Ritz team for di racetracktableRacetrackDi oval strip for live and electronic layouts wey dey show di numbers for wheel order, wey you dey use to put neighbours and sector bets with one tap.Read di whole tin →. Nevada ban prediction devices for May 1985, and live studios now dey close betting for di launch.
How Casinos Fight Back
For di years when dem still dey take bets afta di launch, casinos fight players wey dem suspect through di dealer. Accounts of di system players of Norman Leigh for Nice for 1966 and of later prediction teams dey describe new croupierpipoCroupierDi dealer for roulette table.Read di whole tin → every spin, ball wey dem change, spins wey dem make short or fast, table wey di casino own pipo full, and at last table wey dem close. Dis stories dey come from di players side and e hard to check dem (Goldman, 2007). Di tactics still make sense: short or fast spin no fit aim di ball for one pocketequipmentPocketOne of di 37 small boxes wey get number for di rotor. Dem also dey call am: slot, cup.Read di whole tin →, but e dey scatter di timing wey predictor dey measure.
How Good Di Prediction Must Be
Thorp (1984) calculate how much prediction worth when im mistake dey follow bell curve: for normal spin, di pocket wey e predict dey off by σ pockets one way or di oda. Bet di number wey e predict alone, or am and two neighboursbetNeighboursOne number and di two pockets for each side of am for di wheel, five straight-up chips.Read di whole tin → for each side, and di edge go depend on σ alone. Perfect prediction go win every straight upbetStraight upOne single number, e dey pay 35:1.Read di whole tin →. For σ = 10 pockets, di accuracy wey Thorp and Shannon reach, straight up dey return about +44%, di figure wey Thorp give for dem device; im 1998 account put am on di eighth of di wheel wey dem favour pass. Di edge dey fall quick as di mistake dey grow, and e don finish for about 17 pockets for European wheel and 16 for American one, when di prediction dey miss by almost half di wheel. Di error budget of Thorp imself dey show why dat limit near: separate mistakes of 1.4 and 5.5 pockets from timing di rotor and di ball, 7 from di fall of di ball across di deflectorsequipmentDeflectorOne of di metal tins for di apron wey dey scatter di ball as e dey fall. Dem also dey call am: canoe, diamond, pin.Read di whole tin → and 6 from di bounce for di pockets, join togeda to about 10.8.
Questions wey pipo dey ask
No. Ball no dey. Na software dey draw di number before di animation.
Timing go fit beat dem, and na why nobody dey run any one like dat.
Play with Maths
Try dem by yourself first. Each solution dey folded; open am when you ready.
NeighboursbetNeighboursOne number and di two pockets for each side of am for di wheel, five straight-up chips.Read di whole tin → call dey put 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 → on one number and on di two pocketsequipmentPocketOne of di 37 small boxes wey get number for di rotor. Dem also dey call am: slot, cup.Read di whole tin → for each side of am for di wheel: five chips. How often prediction must land inside dose five pockets to break even, and wetin e go earn if e correct one time for five?
Show di solution
Answer E dey break even for 5 for 36, 13.9%, against 13.5% by chance alone. If e correct one time for five, e dey return 44% more pass wetin e stake.
If di call hit, one chip dey win 35 to 1 and e dey come back with im winnings, 36 chips, and di oda four dey lose. So one hit dey return 36 for 5 wey you stake, and di call dey break even if e hit 5 times for 36, 13.9%. By chance e dey hit 5 times for 37, 13.5%. Dat small gap, wey no reach half of one percentage point, na where di whole 2.70% dey come from.
For one hit for five, 0.2 × 36 = 7.2 chips dey come back for every 5 wey you stake, +44%. For one for four, +80%.
Na why small gain for accuracy dey worth so much, and why casinos dey close call betstableCall betBet wey you announce give di dealer instead of to put am with your hand, usually bet on one sector of di wheel like voisins or tiers. Dem also dey call am “announced bet”.Read di whole tin → early when di stakes high: dat small gap na di whole margin of di house. Dem report sey di Ritz players of 2004 bet dis way.
Thorp list four errors wey no dey depend on each oda for im prediction, in pockets: 1.4 from timing di rotorequipmentRotorDi part of di wheel wey dey spin and carry di pockets.Read di whole tin →, 5.5 from timing 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 →, 7 from how di ball fall across di deflectorsequipmentDeflectorOne of di metal tins for di apron wey dey scatter di ball as e dey fall. Dem also dey call am: canoe, diamond, pin.Read di whole tin → and 6 from di bounce inside di pockets. How big di total be, and how much di two timing errors dey add?
Show di solution
Answer About 10.8 pockets in all. Without di timing errors e go be 9.2, so di two timings dey add only 1.6.
Errors wey no dey depend on each oda no dey add up directly; na dia squares dey add. Di normal size of di total na di square root of di sum of di squares: 1.4² + 5.5² + 7² + 6² = 1.96 + 30.25 + 49 + 36 = 117.2, and √117.2 ≈ 10.8.
Without di two timing errors: √(49 + 36) = √85 ≈ 9.2.
Total of 10.8 pockets dey inside di 17-pocket limit for di table for dis page and e worth about +34% for one number. Di lesson wey Thorp draw: once di fall across di deflectors na di biggest error, better timing no dey buy much.
Small laugh
Di physics dey work. Di betting window don close.
Sources
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Thorp, E. O. “The invention of the first wearable computer.”
- Bass, T. A. The Eudaemonic Pie.
- Small, M. & Tse, C. K. “Predicting the outcome of roulette.”
- Goldman, N. Great Gambling Scams.
- Nevada Revised Statutes, chapter 465.