Step by Step Sessions · Step by Step · 7 min

Step by Step: One Fibonacci Climb

Stakes of 1, 1, 2, 3, 5, 8, 13 on blackbetBlackEven-money bet for di 18 black numbers. For French: noir.Read di whole tin →, and you go back two steps afta you win. One slower Martingale, and how im cliff dey come.

Short answer

One Fibonacci session wey we simulate for 90 spins, $5 for one unit. Twenty cycles clear for $5 each, and one bad run reach di ninth term ($170 stake) and leave di session $340 down. E gentle pass doubling until e no gentle again.

unit
$5 on black
sequence
1 1 2 3 5 8 13 21 34
cliff
$170 stake for di ninth term
result
−$340 for 90 spins

Waka through di sequence

Loss dey move one step go right. Win dey move two steps back.

11235813213455Lose
di next stake1di result till now0spins0

Stakes and results dey in units of di base bet.

Di Plan

Stake di first FibonaccistrategyFibonacciProgression wey dey follow di sequence 1, 1, 2, 3, 5, 8, 13…: one step forward afta you lose, two steps back afta you win.Read di whole tin → number, $5. Afta you lose, move one step to di right for di sequence. Afta you win, move two steps to di left. One cycle don clear when we come back to di start and we dey one unitmoniUnitDi 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 → up. Compared to 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 →, di stake dey grow by ×1.6 instead of ×2, so di cliff dey far pass and di climb back dey slow pass: one win no dey end di cycle, e only dey step back.

Spins 1–40

Eleven cycles clear, and di longest one reach di fifth term ($25). Every cycle wey clear dey bring exactly $5; di bookkeeping sweet and di stakes still small. Net +$55. E be like Martingale wey dem remove di panic from.

cyclesequencestakesnet
1W5+$5
2L W W5, 5, 5 → e clear+$5
3L L W L W W5, 5, 10, 5, 5, 5+$5
4L L L W W W5, 5, 10, 15, 5, 5+$5
5–11max na 5th term ($25)≤ 25+$35
afta 40 spins11 cycles clear+$55

Spins 41–70

Five more cycles clear by spin 60 (+$25). Then di cycle wey no clear come. L L L L L L L W L L: stakes 5, 5, 10, 15, 25, 40, 65 (seven losses, −$165), one win for $105 (+$105, step back two to $40), then two losses for $40 and $65. Now we dey di eighth term, $105, with −$165 inside di cycle, and di next loss go send us to $170 when di table limittableTable limitDi minimum and maximum bet wey dem allow. Na di maximum dey stop progressions wey dey double.Read di whole tin → na $200. Net for dis stretch na −$140.

Dis session and nine oda ones wey be like amresult vs where you start
+$595$0−$500+$480−$2500125250375500spinsresult
1,000 sessions × 500 spins · violet p10/p25/p75/p90, light blue median, 83 faint samples · move mouse on top di chart to see quantiles for one spin
  • p10 −$500
  • p25 −$500
  • median −$500
  • p75 +$390
  • p90 +$480
1,000 sessions × 500 spins · we cut di y-axis for 1st–99th percentile (di extremes na −$500 to +$700) · 500 spins · $5 base · even-money bet
Di climb slow pass Martingale, and di cliff high pass and come later. Di lines wey fall dey fall far, and dem dey fall over many spins instead of one.

Table Limits for Roulette

Spins 71–90

L L: we lose $105 and then $170, and di cycle don reach −$440. Di next stake go be $275, wey pass di limit, so for spin 72 we abandon di cycle and start again from $5. Na dat one be di cliff. Di eighteen spins wey remain clear four more cycles. Di final na −$340; 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 → na −$360.

Di stakes dey grow by about 1.6 afta every loss; for di eighth step, di next one no fit enter under di limit again.

Di Accounts

Di total wey we bet na about $1,200, compared to $450 for flat betting. 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 $1,200 na $32; wetin happen, −$340, dey about one and half standard deviationsmathsStandard deviationSquare root of variance; di normal distance between one result and di expected value.Read di whole tin → below. Na bad session, and na di kind session wey Fibonacci dey produce almost one time out of five for dis length. Di cycles wey clear pay $5 each; di bad cycle cost eighty-eight of dem.

Wetin Di Session Show

Fibonacci dey spread di cliff of Martingale over many spins and push am go far, and dat one make am both safer and more deceptive: di stakes for di sequence dey look reasonable until di one wey no reasonable. Di expected loss for every dollar no change; di extra 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 → from di climb na where di moni dey go.

Questions wey pipo dey ask

Why you go back two steps afta you win?

Becos one win for term n dey recover di losses for terms n−1 and n−2, wey add up to am. Dem build di sequence for dis rule.

E safe pass Martingale?

Di maximum stake dey lower for di same number of losses, so yes, as di cliff dey come later. Di expectation na di same.

Which term go first pass $500 limit?

Di twelfth one, with $5 unit: 5, 5, 10, 15, 25, 40, 65, 105, 170, 275, 445, then 720.

Small laugh

Di golden ratio na 1.618. Di house edge still be 2.70%.

Di golden ratio na 1.618. Di house edge still be 2.70%.

Sources

  1. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010. Chapter 13, roulette.
we check am 2026-09-28model: European wheel, single zerohow we work am ↗where we get am ↗