Myth: a roulette strategy weh always win
“Mi have a system weh win 80% a di time.” Maybe yuh do. It still lose money.
A system can mek winnin session common. It cyaan mek di expected value positive, cause evry bet it put dung a −1/37 a it stake, an expected value add up. Di system dem weh win most often lose di mos wen dem lose.
Wah dem claim
Di belief: somewhere out deh a roulette strategy deh weh always win, a system a changin stake based pon past result weh turn roulette inna a game yuh win. Di evidence dem gi: a run a winnin session, a video bout ow fi win at roulette evry time, a testimonial, a spreadsheet fram a lucky week. Di claim usually honest; di person believe it cause it did a work.
Why it wrong, inna one line
Expected valuemathsExpected valueDi average result pon evry bet inna di long run. −1/37 a di stake fi evry standard European bet.Read di whole ting → add up. If evry bet have EV = −1/37 a it stake, any sequence a bet have EV = −1/37 a di total stake, no matter wah rule choose di stake dem. A system a a rule fi choose stake. Suh evry system have EV = −1/37 a turnovermoney mattaTurnoverAll di money yuh bet ova a session or a period, countin di winnins yuh bet again (all di money yuh bet, roun afta roun). Nex name: handle, action.Read di whole ting →. Dis a a theorem (Doob an Halmos prove it inna di 1930s; Thorp 1969 lay out di condition dem), an it nuh have nuh exception fi clever rule. Di one condition weh worth fi know a a minimum bet: Thorp example bet $1,000 pon redbet demRedEven-money bet pon di 18 red numba. Inna French: rouge.Read di whole ting →, den 90 cent, den 9 cent an suh on, a get smaller forever. Wid chance 18/37 di fus bet win an di playa stay ahead fi good, even though di expected result still a −1/37 a evryting weh stake. A real table minimum stop dat, an wid it, evry hope fi stay ahead inna di long run.
Why it look like it work
Negative progressionstrategy demProgressionAny rule weh change di stake based pon di result dem weh pass. Negative progression raise it afta loss, positive progression afta win.Read di whole ting → mek winnin session common. Martingalestrategy demMartingaleProgression weh double di bet afta evry loss. Look inna di Strategy section fi see wah it do an wah it nuh do.Read di whole ting → fram $10 at a $500 limit end bout 80% a 100-spin session ahead by a few unitmoney mattaUnitDi base stake weh a system or a playa work wid. Dem describe progression inna unit suh dem work at any table.Read di whole ting →. A playa weh run it fi twenty session win sixteen a dem an memba dat. Di four losin session each lose more dan wah ten winnin session mek, an di arithmetic ova twenty session negative. Di system neva change di average; it move di loss dem inna fewer, bigger session weh it easier fi call dem bad luck.
Di test anybaddy can run
Di Strategy Simulator pon dis site run 10,000 session a any system, or yuh own code, inna one second. Set it to di system yuh believe inna an read di average. If di average did positive fi any settin, dis page woulda seh suh. Evry settin, evry system, evry table limitpon di tableTable limitDi minimum an maximum bet dem allow. Di maximum a weh stop progression weh double up.Read di whole ting → gi a average a −2.70% a turnover plus noise. Testimonial a sample a one; di simulator a sample a ten tousand.
A system weh cyaan lose
Inna 1997 di poker writer Mike Caro put up a roulette system as a joke, an Gambling Times publish it again inna 2001. It a a lis a bet fi stay weh fram: neva red or blackbet demBlackEven-money bet pon di 18 black numba. Inna French: noir.Read di whole ting →, odd or even, or di zeropon di wheelZeroDi one green pocket weh no even-money, dozen or column bet nuh cover; a weh di house edge come fram. Nex name: single zero, 0.Read di whole ting → dem; nuh odd red numba an nuh even black one; an nutten pon 30, or pon di long run a pocketgearPocketOne a di 37 compartment wid numba pon di rotor. Nex name: slot, cup.Read di whole ting → fram 11 clockwise roun to 14 pon di American wheel. Put di rule dem together an nuh numba nuh lef. Di only pocket outside dat run a 0, 28, 9, 26, 30 an 2; dem ban 30 by name, an di res a a zero, even an black, or odd an red. A playa weh follow di system neva bet an neva lose. Di edge a zero, an it a di only roulette system weh honest bout ow it get deh.
System wid name, one line each
System dem sell unda a name, or as a roulette winnin formula, nuh different. Each one a a set a bet, an each bet pay di wheel it 2.70%. Bollman (2024) work tru a few a dem fi a American wheel, weh evry one cost 5.26%; yah so dem deh pon a European one.
Di honest version
System change di shape a a session: ow often yuh win, ow big di win dem, ow bad di wors case. Dem a real choice an a playa might prefer one shape ova anodda. Wah system nuh change a di price, weh a 2.70% a evryting weh bet, an cause progression bet more dan flat bettinstrategy demFlat bettinFi bet di same amount evry spin. Di baseline weh dem compare evry progression gainst.Read di whole ting →, dem pay more a it.
Question dem
Six month a session evry week a bout 25 session. Martingale win 80% a dem. Di losin session dem a come, an dem bigger.
Di stop rule cut di turnover an suh it cut di expected lossmathsExpected lossExpected value times all di money yuh bet; di average amount yuh lose ova a session or a period (di loss yuh fi expec pon average).Read di whole ting →. It nuh mek it positive.
Nuh pon a fair wheel. Pon a bias wheellabBias wheelA wheel weh have physical defect weh mek some pocket more likely dan 1/37. It rare, an yuh can only find it out wid thousands a spin weh yuh write dung.Read di whole ting →, an dat a a physics problem, nuh a system.
Fun wid maths
Try dem yuhself fus. Evry ansa fold up; open it wen yuh ready.
Mike Caro 1997 joke system fi di American wheel ban redbet demRedEven-money bet pon di 18 red numba. Inna French: rouge.Read di whole ting → an blackbet demBlackEven-money bet pon di 18 black numba. Inna French: noir.Read di whole ting →, odd an even, an di zeropon di wheelZeroDi one green pocket weh no even-money, dozen or column bet nuh cover; a weh di house edge come fram. Nex name: single zero, 0.Read di whole ting → dem; odd red numba an even black one; di numba 30; an evry pocketgearPocketOne a di 37 compartment wid numba pon di rotor. Nex name: slot, cup.Read di whole ting → inna di run fram 11 clockwise roun to 14. Use di rule dem one at a time. Which numba lef fi bet?
Show di ansa
Ansa None. Di system neva bet, suh di edge a exactly zero.
Fi ban red, black, odd, even an di zero dem lef single numba an small group inna 1 to 36.
Nuh odd red an nuh even black lef di even red dem (12, 14, 16, 18, 30, 32, 34, 36) an di odd black dem (11, 13, 15, 17, 29, 31, 33, 35): sixteen numba. Fi ban 30 lef fifteen.
Pon di American wheel, di run fram 11 clockwise to 14 cover 32 a di 38 pocket. Di six outside it a 0, 28, 9, 26, 30 an 2. All fifteen weh survive deh inside di run, suh di las rule tek dem out too. A system weh neva bet a di only one weh neva lose, an dat a did Caro point.
Kryptos run tree Martingalestrategy demMartingaleProgression weh double di bet afta evry loss. Look inna di Strategy section fi see wah it do an wah it nuh do.Read di whole ting → at di same time, one pon each pair a even-money betbet demEven-money betRed/black, odd/even, high/low. 18 numba, pay 1:1.Read di whole ting → (high or low, odd or even, red or black), wid stake 1, 2, 4, 8, 16, 32 an a stop afta six loss. Tek one a di tree pon a European wheel. Ow often it lose all six bet, wah one cycle earn pon average, an wah share a di money weh bet dat a?
Show di ansa
Ansa It lose all six bout one time inna 55 cycle, 1.83% a di time, an dat cost 63 unitmoney mattaUnitDi base stake weh a system or a playa work wid. Dem describe progression inna unit suh dem work at any table.Read di whole ting →. Pon average a cycle lose bout 0.17 unit outta 6.42 unit weh bet: 2.70%, di price a evry bet pon di wheel.
A bet lose wid chance 19/37, di zero included. Six inna a row: (19/37)⁶ = 0.0183, bout 1 inna 55, an den di stake dem 1 + 2 + 4 + 8 + 16 + 32 = 63 gone. Odda wise di cycle end wid a win an +1 unit.
Average: 1 × (1 − 0.0183) − 63 × 0.0183 = 1 − 64 × 0.0183 = −0.17 unit.
Money weh bet: di fus bet always get put dung, di second only afta a loss, an suh on: 1 + 2 × (19/37) + 4 × (19/37)² + … + 32 × (19/37)⁵ = 6.42 unit. An −0.17/6.42 = −2.70%.
Di six spin weh dem record only decide which side each bet deh pon, an di wheel cyaan know dem. Fi run all tree triple di money weh bet, an di average loss wid it. Bollman (2024) work di system pon a American wheel, weh each one a dem lose six inna a row 2.1% a di time.
Sumting fi laugh
Fi win often an fi win money a two different numba.
Source dem
- 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.