Step-by-step: a Martingale session
Ten dolla pon red, double afta evry loss, at a $500 table. Spin by spin, an di spin weh end it too.
A simulate Martingale session fram a $1,000 bankroll. Forty-one small win, den six loss inna a row an a seventh bet weh di table refuse. Di session end down $220 afta wi did up $410, an a dat di system do.
Di plan
Bet $10 pon redbet demRedEven-money bet pon di 18 red numba. Inna French: rouge.Read di whole ting →. Afta a loss, double. Afta a win, back to $10. Table limitpon di tableTable limitDi minimum an maximum bet dem allow. Di maximum a weh stop progression weh double up.Read di whole ting → $500, suh di stake dem a 10, 20, 40, 80, 160, 320 an den a $640 bet weh di table wi refuse. Six loss back to back bruk di system; evry try have (19/37)⁶ ≈ 1.8% chance fi do dat, an a 100-spin session have bout 50 try. Wah fi expec: roughly a 60% chance fi bruk inna 100 spin, an a loss a $630 wen it happen.
Spin 1–30
Regular 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 →: string a one to tree loss, an a win end each one an net +$10. By spin 30 wi get 17 win, each one close a cycle, an wi up $170. Di bigges stake suh far did a $80 afta tree loss. It feel like a machine weh print $10 bill.
Spin 31–60
More a di same, wid one four-loss cycle (stake go up to $160, den a win) weh put $310 pon di table fi a likkle while an feel like courage. Afta 60 spin: 41 cycle done, up $410, an di lowes point a di bankrollmoney mattaBankrollAll di money yuh set aside fi play. Fi manage yuh bankroll mean yuh decide ow much a it yuh a go risk pon evry bet an evry session.Read di whole ting → since spin 30 did a $1,040. Di histogram a evry Martingale session look like dis fi most a it length.
Spin 61–66
Lose Lose Lose Lose Lose Lose. Stake 10, 20, 40, 80, 160, 320: $630 gone. Di nex bet woulda be $640; di limit a $500. Di system bruk. Wi can bet $500 (an if it win, wi still $130 down pon di cycle) or go back to $10 an tek di loss. Six blackbet demBlackEven-money bet pon di 18 black numba. Inna French: noir.Read di whole ting → or 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 → inna a row have a probabilitymathsProbabilityDi chance fi a result, fram 0 to 1 or 0% to 100%. One numba: 1/37 = 2.70%.Read di whole ting → a 1.8% evry cycle. Wi did run bout 45 cycle. Di chance fi reach dis point somewhere inna 45 cycle did deh bout 55%. It neva bad luck; it did jus a di median.
- p10 −$1,000
- p25 −$1,000
- median −$1,000
- p75 +$790
- p90 +$1,690
Di account
Up $410 afta 60 spin, down $220 afta 66. Total bet: bout $2,100 ova 66 spin, gainst $660 fi a flat $10 bettor. 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 → pon $2,100 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 → a $57; fi wi actual −$220 deh bout a third a a standard deviationmathsStandard deviationDi square root a variance; ow far a result usually deh fram di expected value.Read di whole ting → below dat, an dat a nutten strange fi a system weh distribution have a long lef tail. If wi did stop at spin 60 wid a stop-winstrategy demStop-winA profit target weh yuh set fram bifo, an wen yuh reach it yuh end di session (di win weh mek yuh stop).Read di whole ting → a $400, wi woulda leave up $410, an di nex session woulda carry di same 1.8% evry cycle.
Wah di session show
Martingale turn a 48.65% bet inna a sequence weh win 98% a di cycle dem an lose 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 di odda 2%. It nuh change di expected loss pon evry dolla; it multiply di dolla dem. Di flat-bettin playa beside wi bet a third as much an lose, pon average, a third as much. Di playa weh run dis system fi a year wi win most evenin an lose di year.
Ow often a losin run come
A even-money bet pon a single-zero wheel lose 19 spin outta 37. Evry row a di chance seh a certain run a spin all lose, an wah a Martingale playa, weh double afta evry loss, lose by den.
| loss inna a row | chance | bout 1 outta | lose so far | nex bet |
|---|---|---|---|---|
| 1 | 51.4% | 2 | $1 | $2 |
| 2 | 26.4% | 4 | $3 | $4 |
| 3 | 13.5% | 7 | $7 | $8 |
| 4 | 7.0% | 14 | $15 | $16 |
| 5 | 3.6% | 28 | $31 | $32 |
| 6 | 1.8% | 55 | $63 | $64 |
| 7 | 0.94% | 106 | $127 | $128 |
| 8 | 0.48% | 207 | $255 | $256 |
| 9 | 0.25% | 403 | $511 | $512 |
| 10 | 0.13% | 784 | $1,023 | $1,024 |
| 11 | 0.065% | 1527 | $2,047 | $2,048 |
| 12 | 0.034% | 2974 | $4,095 | $4,096 |
| 13 | 0.017% | 5792 | $8,191 | $8,192 |
| 14 | 0.0089% | 11279 | $16,383 | $16,384 |
| 15 | 0.0046% | 21965 | $32,767 | $32,768 |
Di chance a 19/37 multiply by itself one time fi evry loss, count fram one given spin. A long session have nuff spin weh dat kinda run can start, suh ova a evenin it far more likely dan one row show.
Question dem
Nine loss bruk it instead a six: 0.25% evry cycle, an $5,110 gone wen it happen. Rarer cliff, higher cliff, same −2.70%.
It woulda win 48.65% a di time an lef di cycle at −$130 anyway. Nuh good move nuh deh afta a Martingale bruk; only di stake yuh choose nex.
Yes, fi dat session. Nuh fi di average ova all session.
Fun wid maths
Try dem yuhself fus. Evry ansa fold up; open it wen yuh ready.
At a $1 to $500 table, a 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 → playa start at $1 pon redbet demRedEven-money bet pon di 18 red numba. Inna French: rouge.Read di whole ting → pon a single-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 → wheel. Ow much loss inna a row stop di doublin, ow much lose by den, an ow often it happen?
Show di ansa
Ansa Nine loss: $511 lose, an di nex bet woulda be $512. It happen one time inna bout 403 sequence.
Di stake dem a 1, 2, 4, 8, 16, 32, 64, 128 an 256: togedda $511. Di tenth one woulda be $512, ova di limit. A $500 bet weh win still lef di playa $11 dung; one weh lose lef dem $1,011 dung.
Red lose wid chance 19/37, suh nine loss inna a row have a chance a (19/37)⁹ ≈ 0.25%, one time inna bout 403 sequence. Evry sequence weh finish win $1, suh di playa can expec bout $402 a small win bifo di one $511 loss, an di 2.70% a evryting weh bet still lose pon average.
Pon a double-zero wheel di chance a (20/38)⁹, one time inna bout 323. Bollman (2021) print “about 1 in 833”, weh a (18/38)⁹, di chance a nine win inna a row.
Sumting fi laugh
Forty-one small win an one big loss. Dat a di whole system.
Source dem
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. “Optimal gambling systems for favorable games.”