How the Fibonacci Betting System Works

The Fibonacci betting system is a stake progression: move one position forward after a full loss and two positions back after a win, without going below the first position. It changes stake sizes, not outcome probabilities. In the roulette model used here, expected value remains negative.

Each stake equals your base stake multiplied by the Fibonacci number at the current position. The base stake is the monetary value of one unit; a unit is not automatically a safe percentage of your bankroll.

This guide starts at the first 1 in the sequence:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…

The first two positions have the same stake size, but they are separate positions. With a base stake of $10, the next stake after your first loss is still $10, now at position 2.

Some descriptions start at the second 1. That changes the early stakes and net results. The examples and embedded tools here use the first 1.

What Does an Even-Money Payout Mean in Roulette?

An even-money bet earns net profit equal to the stake when it wins and loses the entire stake on a full loss. A 1:1 payout does not mean a 50% chance of winning.

For example, a winning $10 bet returns $20: your $10 stake plus $10 net profit. A full loss produces a net result of −$10.

On a standard roulette wheel, even-money bets include red or black, odd or even, and the ranges 1–18 or 19–36. Pennsylvania's wheel rules describe 37-pocket and 38-pocket wheels, while its payout rules specify payouts and loss settlement for that jurisdiction. These rules provide a source for the model, not evidence that every casino uses identical rules.

Four rows from the Massachusetts Gaming Commission roulette payout table, including even-money bets

Excerpt from the Massachusetts Gaming Commission's English-language roulette rules dated 24 September 2026, section 2, page 4.

The Massachusetts rules include different settlement provisions for double-zero roulette: a loss can be half or full. The 38-pocket calculation below applies only when zero causes a full loss of the stake.

All tables in this guide treat zero as a full loss. Rules that return half the stake or hold it over for another spin require a separate calculation. The embedded calculator and simulator do not support partial losses, pushes or voids.

Does Returning to the First Position Mean You Are in Profit?

No. In the example below, four losses followed by two wins return you to the first position with a net result of zero. The $10 profit appears only after the third win.

Use a base stake of $10 and the sequence four full losses, then three even-money wins. All monetary figures in the table are in dollars. There are no commissions or partial settlements, and the whole-dollar stakes require no rounding.

To repeat the calculation, subtract the stake from the running net result after each loss and add it after each win. Update the position separately using the “one forward, two back” rule.

The four losses total $70. Winning the $50 stake reduces the loss to $20; winning the next $20 stake brings the result to zero. The following $10 win produces a net profit of $10.

From the third position onward, each Fibonacci number is the sum of the previous two numbers. An even-money win therefore covers the two immediately preceding terms in the sequence, not any accumulated deficit from an arbitrary path of wins and losses.

The calculator tracks results continuously. You can decide in advance to stop or begin a new record at break-even or a chosen target. Reaching the first position alone does not establish a positive net result.

How Much Bankroll Does a Losing Streak Require?

Your bankroll must cover both the stakes already lost and the next full stake if you intend to continue. Every stake must also fit within the table maximum.

With a base stake of $10, the first 12 full losses produce the following amounts. These are whole-dollar calculations without commissions or partial settlements.

For the sequence where F₁ = F₂ = 1:

Sum of the first n units = Fₙ₊₂ − 1.

To fund every bet through the nth loss, you need at least the base stake multiplied by that sum, and each stake must stay within the table maximum. To continue after n losses, add the next stake to the cumulative loss.

Two examples show why remaining money is not the same as enough money to continue:

• $1,000 bankroll, $10 base stake: After nine losses, you have lost $880 and have $120 left. The required next stake is $550, so the progression cannot continue at its full stake even though the bankroll is not zero.
• $300 table maximum, $10 base stake: After eight losses, the cumulative loss is $540. The next stake of $340 exceeds the table maximum, even if you have enough funds.

There is no universal “safe bankroll” of 50 or 100 units. A predeclared stop-loss must account for the possible full loss of the proposed next stake. Depositing more money, restarting the progression or moving to a table with a higher maximum does not remove the accumulated loss.

Why Doesn't Fibonacci Remove the House Edge?

Expected value remains negative because the progression does not change the probabilities of winning and losing. It changes only the amount exposed to those probabilities.

Assume independent spins and an equal probability for every pocket. For a red bet on a single-zero wheel:

• Win probability: p = 18/37 ≈ 48.65%
• Loss probability: q = 19/37
• Expected net result per bet: stake × (2p − 1) = −stake/37
• House edge: 2.70%
• RTP: 97.30%

RTP is the theoretical fraction of turnover returned through payouts, not the frequency of wins. Turnover means the sum of all stakes, not the initial bankroll.

On a double-zero wheel where zero causes a full loss, the win probability is 18/38, the house edge is 5.26%, and RTP is 94.74%. Those figures do not apply to half-loss rules.

For $1,000 in turnover on a single-zero wheel, the expected loss is $27.03. This is a mathematical average rounded to the nearest cent, not a prediction of the remaining funds in a particular session. The house-edge and RTP percentages above are rounded to two decimal places.

The probability of eight consecutive losses from a fixed starting point chosen in advance is:

(19/37)⁸ ≈ 0.4835%.

This is neither the probability of going bust over an entire session nor the probability of encountering eight consecutive losses at some point. Repeated attempts change the question, and insufficient funds can also arise after mixed sequences of wins and losses. Stopping limits further turnover; it does not remove the house edge.

How Does Fibonacci Compare With Other Stake Progressions?

Across the same eight full losses, Fibonacci requires less money than Martingale but more than flat betting or D'Alembert. This compares one specific path, not overall risk or profitability.

The table assumes a starting stake of one unit, a $10 unit, eight consecutive losses, and no bankroll or table-maximum constraint. All amounts are whole dollars.

Martingale doubles the stake after a full loss and returns to the base stake after a win. D'Alembert adds one unit after a loss and subtracts one after a win. Flat betting keeps the stake unchanged.

The chart illustrates 20 shared random outcomes, using a $10 base stake, $500 starting funds and a 48.6% win probability. It does not check whether funds are sufficient, so balances can become negative. Martingale has a $1,280 stake cap in this chart.

It is therefore not an empirical study or a model that stops when a player cannot afford the next bet. Slower stake growth across an identical losing streak does not make a method universally safer or profitable.

How Do You Test a Sequence in the Calculator?

The calculator lets you record wins and full losses manually and see the next stake. It does not check whether your bankroll can fund that stake.

To reproduce the first five bets from the worked example:

1. Enter 10 in the Base Bet ($) field.
2. Click Start Simulation to begin the calculation.
3. Click I Lost four times.
4. Check the result: −70 running net result, 50 next stake and position 5.
5. Click I Won once. The running net result becomes −20, the next stake becomes 20, and the position becomes 3.
6. Optionally, click I Won twice more. The first click brings the result to 0 with a next stake of 10; the second produces +10, again with a next stake of 10.

These actions assume full losses and even-money wins, with the sequence starting at the first 1. The calculator does not model commission or partial settlement.

English Fibonacci calculator after four full losses, showing a running net result of −70 and next stake of 50 with a base stake of 10

The local calculator interface after four full losses. This shows the tool's operation, not a test of the published website.

English Fibonacci calculator after four full losses and one win, showing a running net result of −20 and next stake of 20

The same local interface after winning the 50 stake. Part of the loss has been recovered, but the running net result remains negative.

Read the calculator's indicators separately:

• “Bankroll” is an interface label. Here it shows the signed running net result, starting at zero—not your remaining allocated gambling funds. This calculator has no starting-bankroll field.
• Next stake and position show movement through the sequence. They do not confirm that you can afford the next bet.
• “Total at Risk” is an interface label. It is based on preceding terms in the sequence, not the actual cumulative loss after an arbitrary mixed path.

Use the undo control to correct the last recorded outcome. The reset control returns to setup; it does not undo real losses.

The tool contains only 15 positions, ending at 610 units. Further losses repeat that final position rather than extending the sequence indefinitely. There are no controls for available funds or the table maximum, and no calculations for pushes, voids or partial losses.

How Do You Use the Simulator and Interpret Its Limits?

The simulator generates random sequences using your chosen win probability and tracks remaining funds. It is a separate calculation, not a continuation of the manual calculator's running net result.

For an educational example, enter these values in the corresponding fields:

Then click Run Simulation. Here, 48.6% is the rounded probability entered into the model, not the exact value of 18/37. No particular random result is promised for this run.

The model generates independent wins with the specified probability. A win adds the stake to the remaining funds; a loss subtracts it. If the calculated stake exceeds the remaining funds, the tool reduces the stake to the entire available balance. That is an all-remaining-funds bet, not a stop because the full progression stake is unaffordable.

The simulator also repeats the final, 15th position at 610 units. It has no table maximum and does not model pushes, voids, commission or changing odds.

If a bust rate is shown, it is the share of simulated sessions that reached zero in this implementation. It is not the probability of being unable to afford the next full stake. Likewise, the proportion of profitable sessions and the average result from just five simulations do not establish precise probabilities or prove that the system is profitable.

Does Fibonacci Work for Sports Betting and Other Games?

The progression can be applied to other bets, but the loss-recovery arithmetic shown above assumes that a win earns net profit equal to the stake. Different odds and settlement rules change the result.

Take the same four-loss, three-win path with stakes of $10, $10, $20, $30, $50, $20 and $10, but use constant decimal odds of 1.91:

• The first four losses total $70.
• The three winning stakes total $80.
• Net profit on each winning bet equals its stake × 0.91.
• The final net result is +$2.80, not the +$10 produced at decimal odds of 2.00.

At odds of 1.91, the payout is stake × 1.91 and includes the returned stake. With no pushes, voids or commission, the break-even win probability is 1/1.91 ≈ 52.36%. Monetary results and the percentage are rounded to two decimal places.

On other paths, returning to the first position can leave an outstanding loss. Sports betting also has different probabilities, relationships between outcomes and settlement rules from the independent-spin roulette model. A stake progression does not identify valuable predictions.

Baccarat with commission and special tie rules, and blackjack with pushes, doubles, splits and different payouts, cannot be reduced to this binary model. Variable payouts in slots and multiplier games do not automatically fit it either. For a different stake calculation, you can use the staking plan calculator, but changing stake sizes does not replace analysis of probabilities and settlement rules.

What Should You Check Before the Next Bet?

Continue only within conditions set in advance. If the next full stake would breach them, stop rather than deposit more money to chase recovery.

Use this order of checks:

1. Learn the calculation without wagering money. Work through the table and make sure you distinguish the payout from the net result.
2. Set the unit and bankroll before the first bet. Specify your allocated funds, the table maximum, a time limit and a stop-loss.
3. Check the full next stake before every bet. It must fit both your remaining funds and the table maximum.
4. Check the possible loss. Losing the entire proposed stake must not take you beyond your predeclared loss limit.
5. Stop if any condition fails. Do not raise the limit, deposit more funds or move to another table just to keep the progression going.

For more on allocating funds and setting limits, see the bankroll management guide.

Real-money gambling is restricted to adults who meet the applicable local requirements and the operator's terms. Check the rules for your location and the specific service; there is no universal permission covering every country.

Fibonacci makes the changing financial exposure after wins and losses easy to see. It does not guarantee recovery, make a return to the first position profitable, or remove negative expected value.