Myth: Roulette Strategy Wey Dey Always Win
“I get system wey dey win 80% of di time.” E fit be true. E still dey lose moni.
System fit make winning sessions common. E no fit make di expected value positive, becos every bet wey e put na −1/37 of im stake, and expected values dey add up. Di systems wey dey win most often dey lose di most when dem lose.
Di Claim
Di belief: somewhere, roulette strategy dey wey dey always win, one system wey dey change stakes based on past results and turn roulette to game wey you go dey win. Di evidence wey pipo dey bring: run of winning sessions, video on how to win roulette every time, testimony, spreadsheet of one lucky week. Di claim dey usually honest; di person believe am becos e don dey work.
Why E Wrong, for One Line
Expected valuesmathsExpected valueDi average result for each bet for di long run. −1/37 of di stake for every standard European bet.Read di whole tin → dey add up. If every bet get EV = −1/37 of im stake, any sequence of bets get EV = −1/37 of di total wey you stake, no matter di rule wey choose di stakes. System na rule to choose stakes. So every system get EV = −1/37 of turnovermoniTurnoverDi total moni wey you bet for one session or one period, including winnings wey you bet again. Dem also dey call am: handle, action.Read di whole tin →. Dis one na theorem (Doob and Halmos prove am for di 1930s; Thorp 1969 tok di conditions), and e no get exceptions for clever rules. Di one condition wey worth to sabi na minimum bet: di example of Thorp dey bet $1,000 on redbetRedEven-money bet on di 18 red numbers. For French: rouge.Read di whole tin →, then 90 cents, then 9 cents and so on, e dey shrink forever. With chance of 18/37 di first bet go win and di player go stay ahead forever, even though di expected result still be −1/37 of everytin wey e stake. Di minimum of real table dey stop dat one, and with am every hope to stay ahead for di long run.
Wetin Happen for Long Run: Law of Large Numbers for Roulette
Why E Be Like Sey E Dey Work
Negative progressionsstrategyProgressionAny rule wey dey change di stake based on di results wey don pass. Negative progressions dey raise am afta losses, positive ones afta wins.Read di whole tin → dey make winning sessions common. MartingalestrategyMartingaleProgression wey dey double di bet afta every loss. Check di Strategy section to see wetin e dey do and wetin e no dey do.Read di whole tin → from $10 with $500 limit dey end about 80% of sessions of 100 spins ahead by few unitsmoniUnitDi base stake wey system or player dey work with. Dem dey describe progressions in units so dat dem go fit work for any table.Read di whole tin →. Player wey run am for twenty sessions go win sixteen of dem and na dat one e go remember. Each of di four losing sessions dey lose pass wetin ten winning sessions make, and di arithmetic over twenty sessions na negative. Di system no change di mean; e only move di losses go inside fewer, bigger sessions where e easy to call dem bad luck.
Di Test Wey Anybody Fit Run
Di Simulator for Roulette Strategy for dis site dey run 10,000 sessions of any system, or your own code, for one second. Set am to di system wey you believe and read di mean. If di mean positive for any setting, dis page go tok am. Every setting, every system, every table limittableTable limitDi minimum and maximum bet wey dem allow. Na di maximum dey stop progressions wey dey double.Read di whole tin → dey give mean of −2.70% of turnover plus noise. Testimonies na samples of one; di simulator na samples of ten thousand.
System Wey No Fit Lose
For 1997, di poker writer Mike Caro post one roulette system as joke, and Gambling Times publish am again for 2001. Na list of bets wey you go avoid: never red or blackbetBlackEven-money bet for di 18 black numbers. For French: noir.Read di whole tin →, odd or even, or di zeroswheelZeroDi 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 →; no odd red numbers and no even black ones; and notin on 30, or on di long run of pocketsequipmentPocketOne of di 37 small boxes wey get number for di rotor. Dem also dey call am: slot, cup.Read di whole tin → from 11 clockwise round reach 14 for di American wheel. Put di rules togeda and no number remain. Di only pockets wey dey outside dat run na 0, 28, 9, 26, 30 and 2; dem ban 30 by name, and di rest na zero, even and black, or odd and red. Player wey follow di system no go ever bet and no go ever lose. Im edge na zero, and na di only roulette system wey dey honest about how e take reach dia.
Systems Wey Get Name, One Line Each
Systems wey dem dey sell under one name, or as roulette winning formula, no different. Each one na set of bets, and each bet dey pay di wheel im 2.70%. Bollman (2024) work through many of dem for American wheel, where every one dey cost 5.26%; here dem dey for European one.
Di Honest Version
Systems dey change di shape of one session: how often you dey win, how big di wins be, how bad di worst case fit be. Dis ones na real choices, and player fit prefer one shape pass anoda. Wetin systems no dey change na di price, wey be 2.70% of everytin wey you bet, and becos progressions dey bet more pass flat bettingstrategyFlat bettingTo bet di same amount every spin. Na di baseline wey dem dey compare every progression with.Read di whole tin →, dem dey pay more of am.
Questions wey pipo dey ask
Six months of sessions every week na about 25 sessions. Martingale dey win 80% of dem. Di losing sessions dey come, and dem big pass.
Di stop rule dey reduce turnover, and so e dey reduce expected lossmathsExpected lossExpected value times di total moni wey you bet; di average amount wey you go lose for one session or one period.Read di whole tin →. E no dey make am positive.
No be for fair wheel. For biased wheellabBiased wheelWheel wey get physical defect wey make some pockets come out pass 1/37. E rare, and you fit only find am with thousands of spins wey you record.Read di whole tin →, and dat one na physics problem, no be system.
Play with Maths
Try dem by yourself first. Each solution dey folded; open am when you ready.
Di joke system of Mike Caro from 1997 for di American wheel ban redbetRedEven-money bet on di 18 red numbers. For French: rouge.Read di whole tin → and blackbetBlackEven-money bet for di 18 black numbers. For French: noir.Read di whole tin →, odd and even, and di zeroswheelZeroDi 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 →; odd red numbers and even black ones; di number 30; and every pocketequipmentPocketOne of di 37 small boxes wey get number for di rotor. Dem also dey call am: slot, cup.Read di whole tin → for di run from 11 clockwise go round reach 14. Apply di rules one by one. Which numbers remain to bet?
Show di solution
Answer Notin. Di system no dey ever bet, so im edge na exactly zero.
To ban red, black, odd, even and di zeros go leave single numbers and small groups among 1 to 36.
No odd reds and no even blacks go leave di even reds (12, 14, 16, 18, 30, 32, 34, 36) and di odd blacks (11, 13, 15, 17, 29, 31, 33, 35): sixteen numbers. To ban 30 go leave fifteen.
For di American wheel, di run from 11 clockwise reach 14 dey cover 32 out of di 38 pockets. Di six wey dey outside am na 0, 28, 9, 26, 30 and 2. All di fifteen wey remain dey inside di run, so di last rule go remove dem too. System wey no dey ever bet na di only one wey no dey ever lose, and na dat one be di point of Caro.
Kryptos dey run three MartingalesstrategyMartingaleProgression wey dey double di bet afta every loss. Check di Strategy section to see wetin e dey do and wetin e no dey do.Read di whole tin → at once, one for each pair of even-money betsbetEven-money betRed/black, odd/even, high/low. 18 numbers, e dey pay 1:1.Read di whole tin → (high or low, odd or even, red or black), with stakes 1, 2, 4, 8, 16, 32 and e dey stop afta six losses. Take one of di three for European wheel. How often e dey lose all six bets, wetin one cycle dey earn for average, and which share of di moni wey you stake be dat?
Show di solution
Answer E dey lose all six about once for 55 cycles, 1.83% of di time, and dat one dey cost 63 unitsmoniUnitDi base stake wey system or player dey work with. Dem dey describe progressions in units so dat dem go fit work for any table.Read di whole tin →. For average, one cycle dey lose about 0.17 units out of 6.42 units wey you stake: 2.70%, di price of every bet for di wheel.
One bet dey lose with chance 19/37, zero inside. Six wey follow each oda: (19/37)⁶ = 0.0183, about 1 for 55, and then di stakes 1 + 2 + 4 + 8 + 16 + 32 = 63 don go. If not, di cycle go end with win and +1 unit.
Average: 1 × (1 − 0.0183) − 63 × 0.0183 = 1 − 64 × 0.0183 = −0.17 units.
Moni wey you stake: you dey always put di first bet, di second only afta loss, and so on: 1 + 2 × (19/37) + 4 × (19/37)² + … + 32 × (19/37)⁵ = 6.42 units. And −0.17/6.42 = −2.70%.
Di six spins wey dem record only dey decide which side each bet go dey, and di wheel no fit sabi dem. To run all three dey triple di moni wey you stake and di average loss with am. Bollman (2024) work di system for American wheel, where each of dem dey lose six one afta di oda 2.1% of di time.
Small laugh
To win often and to win moni na different numbers.
Sources
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Doob, J. L. “Note on probability.”
- Halmos, P. R. “Invariants of certain stochastic transformations: the mathematical theory of gambling systems.”
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.
- Bollman, M. Basic Gambling Mathematics: The Numbers Behind the Neon, 2nd ed.