Overview
The Fibonacci walks the sequence 1, 1, 2, 3, 5, 8, 13, 21… — each bet the sum of the previous two. Lose a hand, step one number forward; win a hand, step two numbers back. A win therefore recovers exactly the two losses before it, and reaching the start of the sequence means the whole excursion closed at a small profit.
Compared with the Martingale's doubling, the climb is much shallower — seven straight losses demand 13 units instead of 64 — but the trade is time: deep deficits are repaid two steps per win, so digging out of a hole takes a winning run, not a single lucky hand.
How It Works
- 1
Start at one unit
The first two numbers are both 1, so the sequence opens with two identical minimum bets.
- 2
Step forward on a loss
Each loss moves you one number right: 1 → 1 → 2 → 3 → 5 → 8… Bet the number you stand on.
- 3
Step back two on a win
Each win moves you two numbers left — the win just paid for the two losses those numbers represent.
- 4
Close at the start
When a win takes you back past the first number, the excursion is over at a net profit. Start a fresh one at one unit.
- 5
Cap the climb
Decide the deepest index you'll visit — six or seven steps — before you start. Reaching it means the excursion failed; eat the loss and reset.
The Bets
One even-money lane, played every hand — Player keeps recovery amounts exact. Ties push and don't move your position in the sequence.
Example Sequence
An excursion with a $10 base unit on Player:
| Hand | Bet | Result | Net | Running |
|---|---|---|---|---|
| 1 | $10 (step 1) | Loss | −$10 | −$10 |
| 2 | $10 (step 2) | Loss | −$10 | −$20 |
| 3 | $20 (step 3) | Loss | −$20 | −$40 |
| 4 | $30 (step 4) | Win | +$30 | −$10 |
| 5 | $10 (back to 2) | Win | +$10 | $0 |
| 6 | $10 (back to 1) | Win | +$10 | +$10 |
Three losses were unwound by three wins — each win stepping back two — and the closed excursion banked one unit.
The Math
The recovery identity is exact: every Fibonacci number equals the sum of the two before it, so one win at any depth always repays the previous two losses. What it cannot do is repay the losses before those — a deep excursion needs a sustained winning run to close, during which the edge keeps charging its toll on every bet.
The climb outruns bankrolls slower than doubling but still exponentially (each step ≈ 1.618× the last). At a $10 unit, seven straight losses — about a 0.9% event, once per ~116 excursions — put the sequence at $130 with $230 already sunk. The table's $1,000 max meets the sequence at step 12; your stop-loss should meet it far earlier.
Fibonacci trades the Martingale's fast catastrophe for a slow one. The drawdowns arrive later and smaller, but they arrive — and they still dwarf the one-unit profits each excursion chases.
Bankroll Guide
Respecting a seven-step cap, one failed excursion costs $360 all-in — survivable but a full session's damage. Without the cap, step 12 asks for $1,440 the table will refuse.
When to Walk Away
- Any excursion reaches your depth cap
- Session is down 12% of bankroll
- You've closed excursions worth +6% — bank the grind
- You catch yourself skipping the two-step retreat after a win
The gentle climb is a trap of scale, not of kind: like every negative progression, Fibonacci buys frequent small wins with rare large losses. The sequence's elegance changes the pace of ruin, never its direction.
Try it at the table
$5,000 in virtual chips, no sign-up. Run the Fibonacci against a real shoe and let the roads keep score.
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