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.

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.
Waka through di sequence
Loss dey move one step go right. Win dey move two steps back.
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.
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.
- p10 −$500
- p25 −$500
- median −$500
- p75 +$390
- p90 +$480
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 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
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.
Di maximum stake dey lower for di same number of losses, so yes, as di cliff dey come later. Di expectation na di same.
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%.
Sources
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.