Walkthrough: A Fibonacci Climb

The plan

Stake the first FibonaccistrategyFibonacciProgression that follows the sequence 1, 1, 2, 3, 5, 8, 13…: one step forward after a loss, two steps back after a win.Read full → number, $5. After a loss, move one step right in the sequence. After a win, move two steps left. A cycle is cleared when we are back at the start and one unitmoneyUnitThe base stake a system or a player works in. Progressions are described in units so they apply at any table.Read full → up. Compared with MartingalestrategyMartingaleProgression that doubles the bet after each loss. See the Strategy section for what it does and does not do.Read full → the stake grows by ×1.6 instead of ×2, so the cliff is further away and the climb back is slower: a win does not end the cycle, it only steps back.

Spins 1–40

Eleven cycles cleared, the longest reaching the fifth term ($25). Each cleared cycle nets exactly $5; the bookkeeping is pleasant and the stakes stayed small. Net +$55. It feels like a Martingale with the panic removed.

Spins 41–70

Five more cycles clear by spin 60 (+$25). Then the cycle that does not clear. L L L L L L L W L L: stakes 5, 5, 10, 15, 25, 40, 65 (seven losses, −$165), a win at $105 (+$105, step back two to $40), then two losses at $40 and $65. We are now at the eighth term, $105, with −$165 in the cycle, and the next loss would send us to $170 against a $200 table limittableTable limitMinimum and maximum bet allowed. The maximum is what stops doubling progressions.Read full →. Net for the stretch −$140.

Roulette Table Limits

Spins 71–90

L L: $105 and then $170 lost, and the cycle stands at −$440. The next stake would be $275, over the limit, so at spin 72 we abandon the cycle and restart at $5. That is the cliff. The remaining eighteen spins clear four more cycles. Final −$340; the bankrollmoneyBankrollThe total amount set aside for play. Bankroll management is deciding how much of it to risk per bet and per session.Read full →’s low point was −$360.

The accounts

Total wagered about $1,200 against $450 flat. Expected lossmathExpected lossExpected value times total amount wagered; the average amount lost over a session or a period.Read full → on $1,200 is $32; actual −$340 is about one and a half standard deviationsmathStandard deviationSquare root of variance; the typical distance of a result from the expected value.Read full → below, a bad session, and the kind of session Fibonacci produces nearly one time in five at this length. The cleared cycles paid $5 each; the bad cycle cost eighty-eight of them.

What the session shows

Fibonacci spreads the Martingale’s cliff over several spins and pushes it further out, which makes it both safer and more deceptive: the sequence of stakes looks reasonable right up to the one that is not. The expected loss per dollar is unchanged; the extra turnovermoneyTurnoverThe total amount wagered over a session or period, counting re-bet winnings. Also: handle, action.Read full → from the climb is where the money goes.

Questions