Step by Step: One Martingale Session
Ten dollars on red, double am afta every loss, for $500 table. Spin by spin, including di spin wey end am.
One Martingale session wey we simulate from $1,000 bankroll. Forty-one small wins, then six losses one afta di oda and di table refuse di seventh bet. Di session end $220 down afta e don go up reach $410, and na wetin di system dey do be dat.
Di Plan
Bet $10 on redbetRedEven-money bet on di 18 red numbers. For French: rouge.Read di whole tin →. Afta you lose, double am. Afta you win, go back to $10. Table limittableTable limitDi minimum and maximum bet wey dem allow. Na di maximum dey stop progressions wey dey double.Read di whole tin → na $500, so di stakes na 10, 20, 40, 80, 160, 320 and then $640 bet wey di table go refuse. Six losses one afta di oda go break di system; every attempt get (19/37)⁶ ≈ 1.8% chance to do am, and one session of 100 spins get about 50 attempts. Wetin we expect: about 60% chance sey e go break inside 100 spins, and loss of $630 when e happen.
Spins 1–30
Normal 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 →: strings of one to three losses, and every one end with win wey bring +$10. By spin 30 we don get 17 wins, each one close one cycle, and we dey $170 up. Di biggest stake so far na $80 afta three losses. E be like machine wey dey print $10 notes.
Spins 31–60
More of di same, with one cycle of four losses (stakes reach $160, then one win) wey put $310 for di table for small time and e be like courage. Afta 60 spins: 41 cycles complete, $410 up, and di lowest point of di 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 → since spin 30 na $1,040. Di histogram of every Martingale session dey look like dis for most of im length.
Spins 61–66
L L L L L L. Stakes 10, 20, 40, 80, 160, 320: $630 don lose. Di next bet go be $640; di limit na $500. Di system don break. We fit bet $500 (and if e win, we still dey $130 down for di cycle) or go back to $10 and accept di loss. Six blacksbetBlackEven-money bet for di 18 black numbers. For French: noir.Read di whole tin → or 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 → one afta di oda get probabilitymathsProbabilityDi chance of one outcome, from 0 to 1 or from 0% to 100%. One number: 1/37 = 2.70%.Read di whole tin → of 1.8% for every cycle. We don run about 45 cycles. Di chance to reach dis point somewhere inside 45 cycles na about 55%. E no be bad luck; na di median.
- p10 −$1,000
- p25 −$1,000
- median −$1,000
- p75 +$790
- p90 +$1,690
Di Accounts
$410 up afta 60 spins, $220 down afta 66. Di total wey we bet: about $2,100 for 66 spins, compared to $660 for person wey dey bet flat $10. 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 → on $2,100 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 → na $57; our −$220 dey about one third of standard deviationmathsStandard deviationSquare root of variance; di normal distance between one result and di expected value.Read di whole tin → below am, and dat one no strange for system wey im distribution get long left tail. If we stop for spin 60 with stop-winstrategyStop-winOne profit target wey you set before, wey you go end di session when you reach am.Read di whole tin → of $400, we for comot $410 up, and di next session for still carry di same 1.8% for every cycle.
Wetin Di Session Show
Martingale dey turn 48.65% bet into sequence wey dey win 98% of im cycles and lose 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 di oda 2%. E no dey change di expected loss for every dollar; e dey multiply di dollars. Di person wey dey bet flat for our side bet one third as much and lose, for average, one third as much. Di player wey run dis system for one year go win most evenings and lose di year.
How often losing streak dey come
Even-money bet for single-zero wheel dey lose 19 spins out of 37. Each row na di chance sey one particular run of spins go lose finish, and how much Martingale player, wey dey double afta every loss, don lose by dat time.
| losses wey follow each oda | chance | about 1 for | wetin you don lose so far | di next 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 na 19/37 wey you multiply by imself once for every loss, counting from one particular spin. Long session get plenty spins where dat kind run fit start, so for one evening e dey happen more often well well pass wetin one row show.
Questions wey pipo dey ask
Nine losses go break am instead of six: 0.25% for every cycle, and $5,110 go lose when e happen. Di cliff go rare pass, e go high pass, but na di same −2.70%.
E for win 48.65% of di time and still leave di cycle for −$130. No good move dey afta Martingale don break; na only di stake wey you go choose next dey.
Yes, for dat session. No be for di mean over all sessions.
Play with Maths
Try dem by yourself first. Each solution dey folded; open am when you ready.
For table of $1 to $500, 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 → player dey start with $1 on redbetRedEven-money bet on di 18 red numbers. For French: rouge.Read di whole tin → for single-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 → wheel. How many losses wey follow each oda go stop di doubling, how much e don lose by dat time, and how often e dey happen?
Show di solution
Answer Nine losses: $511 don go, and di next bet for be $512. E dey happen once for about 403 sequences.
Di stakes na 1, 2, 4, 8, 16, 32, 64, 128 and 256: togeda $511. Di tenth one for be $512, wey pass di limit. $500 bet wey win still go leave di player $11 down; one wey lose go leave am $1,011 down.
Red dey lose with chance 19/37, so nine losses wey follow each oda get chance of (19/37)⁹ ≈ 0.25%, once for about 403 sequences. Each sequence wey complete dey win $1, so di player dey expect about $402 of small wins before di one $511 loss, and for average e still dey lose di 2.70% of everytin wey e bet.
For double-zero wheel, di chance na (20/38)⁹, once for about 323. Bollman (2021) print “about 1 in 833”, wey be (18/38)⁹, di chance of nine wins wey follow each oda.
Small laugh
Forty-one small wins and one big loss. Na di whole system be dat.
Sources
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Thorp, E. O. “Optimal gambling systems for favorable games.”