Fibonacci System Calculator

Defaults: Base Bet $10, Sequence Step 6. The engine builds the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, … and treats `step` as how far along that list you have already travelled. For step 6 it takes the first six multipliers 1, 1, 2, 3, 5, 8, multiplies each by the $10 base, and sums them: $10+$10+$20+$30+$50+$80 = $200.00. That is Sequence Total — the money already staked if you lost every step from the start of the sequence through the sixth term. Next Bet is the sixth term times base: 8 × 10 = $80.00, i.e. the stake that corresponds to being on step 6.

If that $80 even-money bet wins, typical Fibonacci practice is to walk two terms back (from 8 to 3), not to reset to 1 as Martingale does after a win. This calculator does not simulate that walk; it only reports the sum through `step` and the current term. After six losing steps you are $200 in the hole at the current stake of $80. A win at $80 even money returns $80 profit on that spin, which does not fill a $200 hole — unlike Martingale, Fibonacci is not designed to recover the entire streak on one hit. That is why people call it “gentler,” and why it still loses: gentler is not plus-EV.

Common mistakes: starting the sequence at 0, 1, 1 instead of 1, 1, 2 (the engine starts 1, 1); thinking step 6 means the 6th win; and comparing $200 with Martingale’s $310 after five doubles as if fewer dollars meant a better system. Different lengths, different recovery rules. Next, set step to 2: total $20, next $10 (the second 1). Set step to 10: first ten Fibonacci numbers 1,1,2,3,5,8,13,21,34,55 sum to 143 units × $10 = $1430, next bet $550. The growth is slower than powers of two and still exponential enough to hit a table limit.

Read $200 / $80 as exposure and current unit, not as a forecast that the next spin wins. On a European even-money bet you still lose 19/37 of spins. Fibonacci staking does not change 19/37. Try the same base on step 8 versus step 4 to feel how the triangular-looking early terms suddenly steepen after 8, 13, 21.

The Fibonacci betting system is a slower negative progression used almost exclusively on even-money roulette chances (red/black, odd/even, high/low). After a loss you move one term forward; after a win you move two terms back. This calculator does not play that dance. It freezes the sequence at a step you choose and tells you the sum of stakes so far and the current stake. Historians, system-debunkers, and players who saw “Fibonacci roulette” on a blog use it to price the path before they touch a felt.

Leonardo of Pisa published the sequence in Liber Abaci in 1202, as a rabbit-population story, not as a casino method. The betting overlay is centuries later, a cousin of Martingale for people who found doubling too violent. Nineteenth- and twentieth-century roulette manuals listed it alongside d’Alembert and Labouchère as a “scientific” progression. It is not scientific. The even-money bet remains negative expectation; the sequence only changes the size of the packets you send into that expectation.

Who it is for: comparing exposure with Martingale at similar streak lengths, checking whether an $80 sixth-term stake fits a table minimum/maximum pair, teaching that “slower” is not “safer” over a long session. Who it is not for: anyone hoping Liber Abaci contains a proof that red is due. The golden ratio is irrelevant to a 37-pocket wheel. There is no field for wheel type on this page because the engine is purely a sequence sum; probability of the losing path is not computed here (unlike the Martingale calculator).

What it does not do: apply the two-step-back win rule, compute house edge, or tell you when to reset. It will not simulate 200 spins. It will not protect you from a table max at the 13 or 21 term. Limitations are honest: Sequence Total assumes you posted every term from the first 1 through step, all losses. If you arrived at step 6 by a mix of wins and losses, your actual cash-in-the-hole is not $200. Type the step you are on, not a fantasy of a perfect losing run, unless that is the scenario you want to stress-test.

Educational sequence arithmetic. Not a way to beat roulette. Not financial advice. The $200 default is six Fibonacci units of $10, nothing more.

Leonardo of Pisa published the sequence in Liber Abaci in 1202 as a rabbit-breeding exercise, not as a casino staking plan. The betting overlay is centuries later: a slower negative progression than doubling, used almost exclusively on even-money chances. With F = 1, 1, 2, 3, 5, 8 as the first six terms and a base of 10 at step 6, each term is multiplied by the unit. Sequence total is 10 + 10 + 20 + 30 + 50 + 80 = 200 dollars, the money already posted if every step from the first 1 through the sixth term was a loss. The current stake, the sixth term times base, is 80 dollars.

Closed form belongs in the lecture before any folklore about gentleness. The nth Fibonacci number with F(1) = F(2) = 1 satisfies the partial-sum identity Sum = F(n + 2) − 1. After that sentence, for n = 6 one needs F(8) = 21, so 21 − 1 = 20 units, times base 10 equals 200, matching the walk. The next stake 80 is 8 × 10, the last of those six terms. Typical table practice after a win is to walk two terms back, from 8 toward 3, rather than to reset to 1. That walk is path-dependent. A single even-money win at 80 returns 80 of profit on the spin and does not fill a 200-dollar hole. Unlike Martingale, Fibonacci is not designed to recover an entire streak on one hit.

Expectation does not become positive because the stakes grow more slowly. On European even money each spin has win probability 18 / 37 and loss probability 19 / 37. Unit expected value is minus 10 × 1 / 37; at the sixth term it is minus 80 × 1 / 37. Linearity says the sequence of sizes does not matter: session expected value is house edge times turnover. Liber Abaci 1202 contains no derivation that produces plus expected value at a thirty-seven-pocket wheel. Binet’s formula F(n) ≈ φ^n / √5 with φ = (1 + √5) / 2 explains why later terms steepen; the golden ratio is a growth rate for the stake, not a lucky constant of the wheel. The system is not plus-EV.

Nineteenth- and twentieth-century roulette manuals listed Fibonacci beside d’Alembert and Labouchère as a “scientific” progression. It is not scientific. It is an 18th–20th century casino fashion. Five or six consecutive even-money losses are the same events priced at a few percent on a doubling lecture; Fibonacci does not make them rarer. Table maxima still clip the 13, 21 and 34 terms. If the path to step 6 mixed wins and losses, live cash in the hole is not 200. The 200 and the 80 assume a monotone losing prefix from a fresh start at base 10, step 6, F = 1, 1, 2, 3, 5, 8.

Assumptions: those six terms were posted as losses, the current stake is the term at step 6 rather than a win-adjusted index, no table maximum, no pocket probability in the arithmetic. House edge remains about 2.70 percent European even money, 5.26 percent American, untouched by rabbits. Sum = F(n + 2) − 1 is the reason the total is 200 rather than an accident of addition. Educational sequence arithmetic, not a method for extracting 80 dollars from the next spin.