Fibonacci Roulette System

Leonardo Pisan, better known as Fibonacci, was born in Pisa (now part of Italy) in 1170 A.D. Fibonacci was a member of the Bonacci family and traveled all around the Mediterranean as a boy with his father who held a diplomatic post. His keen interest in mathematics and his exposure to other cultures allowed Fibonacci to excel in solving a wide variety of mathematical problems. Fibonacci is probably best known for discovering the Fibonacci sequence, a sequence of numbers that readily exists in nature. Although, technically not a mathematical system per se, the sequence is often used in a losing or negative progression. The Fibonacci series is as follows:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, …

The next number in the series is simply the sum of the previous two numbers. The starting number is 1. The second number calculated from 0 +1 (no number in front of the first 1) and is 1 again. The next number is 1 +1 or 2, then 1 +2 for 3, then 2 +3 = 5 and 5 +3 = 8, etc. The system works similarly to the Labouchere or cancellation system, only the player starts out with an empty line. If the first bet is won, then the sequence is over and the player has won. No numbers need to be written down. If the first bet is lost, then a line is started and a "1" is written down. The next number in the sequence represents the following wager size. If this bet is lost, then it is added to the end of the line. As each bet is lost, it is added to the end of the series. If a bet is won, the last number in the series is crossed out. An example here will help clarify things:

Our player starts with a one unit loss, so a "1" is recorded to start the line. Another "1" is added after the second wager of one unit loses. The third stake requires a two-unit wager and loses, so a "2" is added. The fourth bet of three units finally wins and the "1-2" can be cancelled from the line. Because each wager adds up to the previous two bets, the last two numbers on the line can be crossed out when a bet wins. The next three bets lose, escalating our eighth stake up to five units. Our player experiences a win at this level, allowing him to cancel out the "2-3" at the end of the line. The ninth bet of two units loses, so the line grows to "1-1-2." A win, loss and win on the tenth, eleventh and twelve wagers finally wipe out the betting line. The player needs and gets a win at this point to go up a net profit of one unit and win the sequence.

With only five wins and eight losses, this particular sequence of wins and losses is tough, but our player is able to pull it out. On the eighth wager, the stake reaches a high of five units. If that bet had lost, our player would be twelve units in the hole. At a $5 unit size, that equates to a $60 deficit. The next wager from here would be eight units and another loss would put him back 20 units total. If you elect to use the Fibonacci, I would highly recommend that you limit your top bet to five units. If you lose your wager at this level, then abandon the series. Things get ugly too quickly from here. Stop and regroup. Let's take the Fibonacci up to twelve straight losses to see how quickly the wagers can mount:

This last example demonstrates how the bets can mount in a losing string of twelve losses. The chances of losing twelve straight on a double zero roulette wheel are (20/38)^12 = 0.0004518, or about 1 shot in 2213. The purpose here was to show a range of cumulative losses and let the system player decide where to draw the line. Some authors show the Fibonacci sequence and omit the first "1" in the series. That's fine, but the shortened version is a little more aggressive than the "full" Fibonacci. You will lose a bit more money on average with this abbreviated variation. Overall, the Fibonacci sequence does not fare to badly. This system can be fun and not too damaging if you limit your top bet to five units.