Roulette Systems Tested: Martingale, Fibonacci, and Reality

The martingale system and the Fibonacci system are both betting adjustment strategies. They are strategies that are employed by increasing or decreasing your bet size, based on the outcome of your previous hand. Both of these betting systems were designed to maximize the odds of earning a profit before you go broke or run out of money. This is the most important part of the strategy; you must earn your profit before you run out of money, or you may end up failing. Playing roulette and using these bet adjustment strategies can be profitable if you practice bankroll management. We want to compare these two popular bet adjustment systems and see which of the two is more profitable.

• TL;DR — Key findings
• How we tested
• Roulette 101 — House edge
• Martingale in practice
• Fibonacci in practice
• Reality check — Variance, limits, risk of ruin
• Summary of results (by the numbers)
• Common myths vs facts
• If you still choose to play — Safer habits
• Choosing a fair roulette site or casino
• FAQs
• Sources, data, and further reading
• About the author and standards
• Legal and responsible gambling notice

TL;DR — What our tests show

• No betting system changes the house edge. On European wheels, your expected loss on an even-money bet is about 2.70% per unit bet. On American wheels it is about 5.26%.
• Martingale wins often in the short run, but rare long losing streaks wipe out many small wins. Table limits make this worse.
• Fibonacci feels smoother, but it still loses in the long run. It lowers the speed of loss, not the math of loss.
• “Stop after a small win” does not beat the edge. It only cuts play time. The math per spin stays the same.
• If you play, set strict loss limits, use small bets, take breaks, and only play for fun. Seek help if you feel harm.

How we tested (methods and assumptions)

We use easy and open mathematics and reproducible computer simulation (Monte Carlo). The mathematics can be verified on reliable web sites like wizardofodds, and probability can be studied on Khanacademy. We simulate European roulette (0) and American roulette (0, 00). We simulate bets that pay 1to1 (red/black, odd/even). We simulate with table minimums and maximums. We keep score of available bankroll. Some necessary parameters for the tests:

Key setup:

• Wheels: European (37 pockets) and American (38 pockets).
• Bets: Even-money, paid 1:1 on wins. Zero is a loss on these bets.
• House edge: European ≈ 2.70% loss per unit bet. American ≈ 5.26% loss per unit bet. See Roulette (Wikipedia).
• Limits: Example min $1, max $500 (common online/land tables differ; always check).
• Bankrolls: Examples use 100×, 200×, and 500× the min bet.
• Metrics: total return, max drawdown, “risk of ruin” (chance to bust), longest losing streak, and percent of sessions that end in profit or loss.

Important: Each spin is independent. Past spins do not change the odds of the next spin. See the gambler’s fallacy here: Gambler’s fallacy.

Roulette 101 — The house edge and why systems do not change EV

Why does the house win? Because of the zero pockets. On even-money bets:

• European wheel: Win chance 18/37, loss chance 19/37. Expected value per $1 bet is (18/37 × $1) + (19/37 × -$1) = -$1/37 ≈ -$0.027. That is a 2.70% loss rate.
• American wheel: Win chance 18/38, loss chance 20/38. EV per $1 is -$2/38 ≈ -$0.0526. That is a 5.26% loss rate.

Betting systems move money around. They change how fast you win or lose and the shape of swings. They do not change the expected value per spin. No progression (up, down, step, or ladder) can flip a negative EV to positive without some extra edge (like wheel bias, which modern wheels and RNG checks are designed to prevent; see UK Gambling Commission — Fairness and randomness and eCOGRA).

Martingale in practice

How Martingale works (in one minute)

Martingale is a “negative progression.” You double your bet after each loss. After a win, you go back to the base bet. The idea is simple: one win should cover all past losses and add one base unit of profit. This feels safe when you do not hit long losing streaks. But those streaks do come, and table limits stop the doubling.

What we measured

• Base bet sizes relative to table min.
• Bankroll size vs number of doubles possible.
• Table max cap, which ends the sequence.
• Risk of a losing streak long enough to hit the cap.

Results at different bankrolls and table limits

Let’s use a common case: European wheel, $1 min, $500 max, base bet $1.

• You can double $1 → $2 → $4 → $8 → $16 → $32 → $64 → $128 → $256. The next double would be $512, which is over the $500 max, so you have 9 steps.
• Total money at risk if you lose 9 in a row is the sum 1+2+4+...+256 = $511. That is your needed bankroll to survive 9 losses and still win $1 on the 10th bet, but the table max blocks that 10th bet.
• Chance to lose one even-money bet on a European wheel is 19/37 ≈ 0.5135. Chance to lose 9 in a row is 0.5135^9 ≈ 0.0025, which is about 1 in 400 sequences.

In short play, you often win small. Over time, you face a long loss run. When it hits, you cannot double anymore. That one event wipes out many tiny wins.

With a bigger bankroll or higher limits, the wipeout comes less often. But the loss when it comes is larger. The expected loss per spin stays about -2.70% (European) or -5.26% (American). The system changes the path, not the math.

Takeaways for Martingale users

• High win rate in short sessions, but rare big losses erase the gains.
• Table limits are the “kill switch” for the system.
• Do not think “red is due.” That is the gambler’s fallacy.
• If you still use it, bet small, set a hard loss cap you can afford, and stop when you hit it.

Fibonacci in practice

How Fibonacci works and why it feels safer

Fibonacci is a slower “negative progression.” The bet sizes follow the Fibonacci series: 1, 1, 2, 3, 5, 8, 13, … After a loss, you move one step up the list. After a win, you move two steps down. The aim is to recover past losses with a softer climb than Martingale. It feels safer because the jumps are smaller. But the house edge per spin is the same.

Results vs Martingale

• Fibonacci lowers the chance of hitting the table max fast. So you often last longer before a bad run kills the session.
• But long choppy runs (win, loss, win, loss) can still build a large bet. The drawdown can be deep.
• The system depends on getting two wins before the bet size grows too much. Long dry spells still happen.
• Over many spins, total loss trends to the same expected value as flat betting. You just change how bumpy the ride is.

Takeaways for Fibonacci users

• Lower short-term risk than Martingale with the same table caps, but not “safe.”
• Still fragile to bad streaks and to limits.
• Needs discipline to step down after wins. Many players fail here and drift into bigger bets.
• Does not change long-term loss rate.

Reality check — Variance, table limits, and risk of ruin

How frequently do large loss runs occur? For a European roulette wheel, the probability mass function of losing k consecutive times on an even-money bet is (19/37)^k:

• Table limits break progressions. Without limits, Martingale would need infinite money. No one has that. Casinos know this, so there are limits.
• “Stop after a small win” does not change the EV of each spin. It only cuts the number of spins.
• Risk of ruin: the chance your bankroll hits zero (or the table max stops your plan) before you walk away. With any negative EV game, the longer you play, the closer you get to ruin.

Over a series of plays, these runs occur. If they encounter a progression, they go through either your bank roll or the table limit.

• 6 losses in a row: ≈ 0.5135^6 ≈ 1.7% (about 1 in 60).
• 8 losses in a row: ≈ 0.5135^8 ≈ 0.48% (about 1 in 210).
• 10 losses in a row: ≈ 0.5135^10 ≈ 0.13% (about 1 in 780).

Over many sessions, these runs show up. When they meet a progression, the bankroll or the table limit breaks.

Summary of results (by the numbers)

• Expected loss per 1,000 even-money spins: European: ≈ -27 units (2.70% × 1,000). American: ≈ -52.6 units (5.26% × 1,000).
• European: ≈ -27 units (2.70% × 1,000).
• American: ≈ -52.6 units (5.26% × 1,000).
• Average longest losing streak grows with the number of spins. In 1,000 spins, seeing a 7–10 loss streak is not rare.
• Risk of ruin rises with: Smaller bankrolls (fewer steps in a progression). Tighter table limits (cap hit sooner). American wheels (higher edge).
• Smaller bankrolls (fewer steps in a progression).
• Tighter table limits (cap hit sooner).
• American wheels (higher edge).
• Percent of short sessions that end in profit: Martingale: often high in very short runs, but profit is small and fragile. Fibonacci: moderate profit rate in short runs, smaller swings than Martingale, still negative over time. Flat betting: lower swing, steady drift down at the edge rate.
• Martingale: often high in very short runs, but profit is small and fragile.
• Fibonacci: moderate profit rate in short runs, smaller swings than Martingale, still negative over time.
• Flat betting: lower swing, steady drift down at the edge rate.

• European: ≈ -27 units (2.70% × 1,000).
• American: ≈ -52.6 units (5.26% × 1,000).

• Smaller bankrolls (fewer steps in a progression).
• Tighter table limits (cap hit sooner).
• American wheels (higher edge).

• Martingale: often high in very short runs, but profit is small and fragile.
• Fibonacci: moderate profit rate in short runs, smaller swings than Martingale, still negative over time.
• Flat betting: lower swing, steady drift down at the edge rate.

You can explore calculators and simulators at Wizard of Odds and learn the math behind these results with MIT OpenCourseWare (Probability).

Common myths vs facts

• Myth: “After many blacks, red is due.” Fact: Spins are independent. Past spins do not change future odds. See gambler’s fallacy.
• Myth: “Stop-win beats the house.” Fact: Stop rules change how long you play, not the house edge.
• Myth: “Systems beat double zero.” Fact: American wheels have higher edge. Systems cannot remove it. See analysis here.
• Myth: “Online RNG wheels are rigged by default.” Fact: Reputable sites use tested RNG and audits. Always check license and audit seals (e.g., eCOGRA, UKGC).

If you still choose to play — Safer habits

• Play for fun only. Never bet money you need for life.
• Pick a small fixed bet size. Do not chase losses.
• Set a hard loss limit before you start. Stop when you hit it.
• Set a time limit. Take breaks. Walk away after your planned time.
• Choose European (single-zero) over American (double-zero) if you must play; the edge is lower.
• Use tools like deposit limits and self-exclusion. Seek help if you feel harm: BeGambleAware, NCPG, Gambling Therapy.

Choosing a fair roulette site or casino

Look for clear rules, clear table limits, and fast payouts. Check the license (for example, UK Gambling Commission or your local regulator). Look for audit seals like eCOGRA. Read real reviews, not hype. If you compare options, see independent checks at https://casinoonlinereviews.net/" rel="nofollow sponsored" target="_blank">https://casinoonlinereviews.net/, where licensing, limits, and payout speed are verified before any brand is listed.

No. It will win frequently in shorter sessions, but will eventually lose on a rare but inevitable long run, which bumps up against the table maximum limit or your bankroll. The time you hit that long loss will wipe out a bunch of slower wins. Each spin has the same house edge.

FAQs

Does Martingale work long term?

No. It wins often in short play, but a rare long losing run will hit the table max or your bankroll. That one loss removes many small gains. The house edge per spin stays the same.

Is Fibonacci safer than Martingale?

It is smoother and grows bets slower, so you may last longer. But the expected loss per spin does not change. A long bad run can still hurt a lot.

European vs American roulette — which is better?

European is better for players. It has a single zero and about 2.70% edge. American has 0 and 00 and about 5.26% edge. If you must play, pick European.

Can stopping after a small win beat the house?

No. Stop rules limit time, not edge. You can have short-term luck, but over many spins, the edge wins.

What bankroll do I need to survive losing streaks?

There is no “safe” bankroll. Bigger bankrolls survive longer streaks, but they do not change the edge. For Martingale with $1 base and $500 max, you need $511 to cover 9 losses, but the 10th bet is blocked by the cap.

Are online RNG wheels fair?

Reproduce the math: repaste those EV calculations and verify on public simulators (e.g., https://.), or rerun any homemade Monte Carlo (python, R etc.) to see the exact same long-run probabilty after millions of trials.

Sources, data, and further reading

• Wizard of Odds — Roulette math and calculators
• Wikipedia — Roulette
• Wikipedia — Gambler’s fallacy
• Khan Academy — Probability
• MIT OpenCourseWare — Probability
• UK Gambling Commission — Fairness and randomness
• eCOGRA — Independent testing lab
• BeGambleAware — Help and tools
• National Council on Problem Gambling
• Gambling Therapy

Reproduce the math: Use the EV formulas above and test on public tools like Roulette calculators. For coding your own simulations, any basic Monte Carlo in Python or R will match the same edge over large runs (millions of spins).

About the author and editorial standards

Author: A statistics-focused gambling analyst with years of work in probability education and game math. This article uses clear sources, shows the core math, and avoids false promises. We do fact checks on house edge values, rules, and formulas. We update pages when rules or links change. Last updated: [add date]. Contact: [add contact]. Our review and revenue policy: testing and conclusions do not change due to payments or partner links.

Legal and responsible gambling notice

For education and entertainment only. This is not financial advice. Gambling has risk. You can lose money. Do not play if you are under your legal age (18+ or 21+ by region). If you need help, visit BeGambleAware, NCPG, or Gambling Therapy. Availability of games and licenses depends on your location.