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Fibonacci Betting System
Introduction
The Fibonacci betting system is method of betting that usually ensures a session win, at the expense of large losses when things go bad. The system uses the Fibonacci numbers to press bets after a loss. Much like the Labochere, as long as the player wins at least 1/3 of even-money bets, which usually have a 48% to 49.5% chance of winning, then the Fibonacci will result in a session win, as long as the player doesn't run out of money trying.
Fibonacci Numbers
Fibonacci Numbers are a sequence of numbers that appear all over mathematics and nature. One could write a whole book about it. For purposes of understanding the betting system, one just needs to know the sequence.
The first two numbers in the sequence are 1 and 1. After that, each subsequent number is the sum of the previous two numbers. Another way of stating it is if F(n) is the nth Fibonacci Number, then:
- F(1) = 1
- F(2) = 1
- F(n) = F(n-1) + F(n-2), where n>=3
The first 25 Fibonacci numbers are: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025.
That said, I believe most other web sites incorrectly explain how to use the Fibonacci. The way they explain it, many sessions would result in a session push. Nobody uses a betting system to just push. The way I explain it always results in a win of the initial bet.
Here is how to play the Fibonacci:
- Decide on your winning goal and establish a bankroll* you are willing to risk to achieve that goal. Call your winning goal g.
- At any given time using this system, you will be somewhere on the Fibonacci sequence. You will start on the SECOND one**.
- Bet the product of g and your place in the Fibonacci sequence.
- If the result of step 3 is a win, then go back two places on the Fibonacci sequence. If this causes you to fall off the sequence, then walk away a winner.
- If the result of step 3 is a loss, then go up one place on the Fibonacci sequence.
- If you still have money, then go back to step 3.
Footnotes:
*: Ideally, the bankroll should be the sum of consecutive Fibonacci numbers, starting with the second one. The first 25 of such sums are: 1, 3, 6, 11, 19, 32, 53, 87, 142, 231, 375, 608, 985, 1595, 2582, 4179, 6763, 10944, 17709, 28655, 46366, 75023, 121391, 196416.
**: This is where I believe most other sources on the Fibonacci are wrong, which say to start with the first 1 in the sequence. About half the time, this will result in a session push, for example if the first two outcomes are a loss and a win.
Example
The player decides his winning goal is $10.
Example
| Bet Number |
Bet Amount |
Win/Loss | Balance after Bet |
|---|---|---|---|
| 1 | $ 10 | L | $ -10 |
| 2 | $ 20 | L | $ -30 |
| 3 | $ 30 | L | $ -60 |
| 4 | $ 50 | W | $ -10 |
| 5 | $ 20 | L | $ -30 |
| 6 | $ 30 | W | $ 0 |
| 7 | $ 10 | L | $ -10 |
| 8 | $ 20 | L | $ -30 |
| 9 | $ 30 | L | $ -60 |
| 10 | $ 50 | L | $ -110 |
| 11 | $ 80 | L | $ -190 |
| 12 | $ 130 | W | $ -60 |
| 13 | $ 50 | W | $ -10 |
| 14 | $ 20 | L | $ -30 |
| 15 | $ 30 | W | $ 0 |
| 16 | $ 10 | W | $ 10 |
Note that despite winning 6 bets out of 16 only (37.5%), the player finally comes out ahead. Also note he had to wager up to $130 to achieve that. Had the player lost that bet, he would have been down $320. A lot to risk losing for a small win.
Simulation Results
The first simulation is based on betting the Player bet in baccarat. The top row shows the size of the bankroll in units. The simulation size is over 37 billion sessions. As a reminder, the theoretical house edge on the Player bet is 1.235%.
Baccarat Simulation — Player Bet
| Statistic | 11 Units | 19 Units | 32 Units | 53 Units | 87 Units | 142 Units |
|---|---|---|---|---|---|---|
| Probability winning goal reached | 0.911630 | 0.946062 | 0.966720 | 0.979286 | 0.987048 | 0.991879 |
| Average number of bets | 2.615806 | 2.927595 | 3.151269 | 3.318705 | 3.438306 | 3.524126 |
| Average units bet | 4.897283 | 6.383979 | 7.948692 | 9.593549 | 11.303999 | 13.074258 |
| Expected win per session | -0.060439 | -0.078760 | -0.098253 | -0.118545 | -0.139764 | -0.161316 |
| Ratio money won to money bet | -0.012341 | -0.012337 | -0.012361 | -0.012357 | -0.012364 | -0.012338 |
The next simulation is based on betting the Pass bet in craps. The top row shows the size of the bankroll in units. The simulation size is over 100 billion sessions. As a reminder, the theoretical house edge on the Pass bet is 1.414%.
Craps Simulation — Pass Bet
| Statistic | 11 Units | 19 Units | 32 Units | 53 Units | 87 Units | 142 Units |
|---|---|---|---|---|---|---|
| Probability winning goal reached | 0.911445 | 0.945909 | 0.966610 | 0.979203 | 0.986989 | 0.991834 |
| Average number of bets | 2.368097 | 2.650841 | 2.853825 | 3.005671 | 3.114277 | 3.192349 |
| Average units bet | 4.434771 | 5.783194 | 7.203172 | 8.696173 | 10.249543 | 11.859770 |
| Expected win per session | -0.062661 | -0.081814 | -0.101862 | -0.123059 | -0.144991 | -0.167709 |
| Ratio money won to money bet | -0.014130 | -0.014147 | -0.014141 | -0.014151 | -0.014146 | -0.014141 |
The next simulation is based on betting the Don't Pass bet in craps. The top row shows the size of the bankroll in units. The simulation size is over 104 billion sessions. As a reminder, the theoretical house edge on the Don't Pass bet is 1.364%.
Craps Simulation — Don't Pass Bet
| Statistic | 11 Units | 19 Units | 32 Units | 53 Units | 87 Units | 142 Units |
|---|---|---|---|---|---|---|
| Probability winning goal reached | 0.911486 | 0.945945 | 0.966636 | 0.979222 | 0.987004 | 0.991845 |
| Average number of bets | 2.435480 | 2.726184 | 2.934764 | 3.090872 | 3.202506 | 3.282736 |
| Average units bet | 4.560666 | 5.946911 | 7.406284 | 8.941055 | 10.537201 | 12.192076 |
| Expected win per session | -0.062165 | -0.081108 | -0.101012 | -0.122033 | -0.143677 | -0.166225 |
| Ratio money won to Money bet | -0.013631 | -0.013639 | -0.013639 | -0.013649 | -0.013635 | -0.013634 |
The next simulation is based on betting any even money bet in double-zero roulette. The top row shows the size of the bankroll in units. The simulation size is over 97 billion sessions. As a reminder, the theoretical house edge on even money bets in double-zero roulette is 5.263%.
Double-Zero Roulette Simulation — Even Money Bet
| Statistic | 11 Units | 19 Units | 32 Units | 53 Units | 87 Units | 142 Units |
|---|---|---|---|---|---|---|
| Probability winning goal reached | 0.895965 | 0.933393 | 0.956825 | 0.971718 | 0.981368 | 0.987675 |
| Average number of bets | 2.464700 | 2.794335 | 3.042827 | 3.237881 | 3.384956 | 3.496308 |
| Average units bet | 4.720054 | 6.309737 | 8.068833 | 10.016054 | 12.152640 | 14.489878 |
| Expected win per session | -0.248416 | -0.332131 | -0.424767 | -0.527211 | -0.639619 | -0.762458 |
| Ratio money won to Money bet | -0.052630 | -0.052638 | -0.052643 | -0.052637 | -0.052632 | -0.052620 |
The next simulation is based on betting any even money bet in single-zero roulette. The top row shows the size of the bankroll in units. The simulation size is over 88 billion sessions. As a reminder, the theoretical house edge on even money bets in double-zero roulette is 2.703%.
Single-Zero Roulette Simulation — Even Money Bet
| Statistic | 11 Units | 19 Units | 32 Units | 53 Units | 87 Units | 142 Units |
|---|---|---|---|---|---|---|
| Probability winning goal reached | 0.906470 | 0.941950 | 0.963570 | 0.976918 | 0.985304 | 0.990611 |
| Average number of bets | 2.400123 | 2.698082 | 2.915528 | 3.080911 | 3.201387 | 3.289492 |
| Average units bet | 4.528809 | 5.954938 | 7.482040 | 9.116027 | 10.847380 | 12.675059 |
| Expected win per session | -0.122356 | -0.160996 | -0.202195 | -0.246408 | -0.293289 | -0.342601 |
| Ratio money won to Money bet | -0.027017 | -0.027036 | -0.027024 | -0.027030 | -0.027038 | -0.027030 |
Video
Please enjoy my video on the Fibonacci betting system.