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==============================================   Thursday, June 6, 2002
Mathematical Gambling Systems - Fibonacci and Oscar's Grind - Let's Talk Winning Art Gallery

Hello everyone,

The Fibonacci and the Oscar's Grind systems are often referred to as two mathematical systems.  People tend to use those in various occasions.  This week, we'll have the facts on those systems and clarify in which instances it would make sense to make use of them.


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:
1)  Bet 1 unit and lose: 1,  net: -1 unit
2)  Bet 1 unit and lose: 1-1,  net: -2 units
3)  Bet 2 units and lose: 1-1-2,  net: -4 units
4)  Bet 3 units and win: 1-x-x,  net: -1 unit
5)  Bet 1 unit and lose: 1-1,   net: -2 units
6)  Bet 2 units and lose: 1-1-2,  net: -4 units
7)  Bet 3 units and lose: 1-1-2-3,  net: -7 units
8)  Bet 5 units and win: 1-1-x-x,  net: -2 units
9)  Bet 2 units and lose: 1-1-2,  net:-4 units
10)  Bet 3 units and win: 1-x-x,  net: -1 unit
11)  Bet 1 unit and lose: 1-1,  net: -2 units
12)  Bet 2 units and win: x-x,  net: 0 units
13)  Bet 1 unit and win: stop ,  net:  +1 unit  -Series has been won-

The 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. The 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 the player is able to pull it out. On the eighth wager, the stake reaches a high of five units. If that bet had lost, the 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:

1) Bet 1 unit and lose: 1, net: -1 unit
2) Bet 1 unit and lose: 1-1, net:-2 units
3) Bet 2 units and lose: 1-1-2, net:-4 units
4) Bet 3 units and lose: 1-1-2-3, net:-7 units
5) Bet 5 units and lose: 1-1-2-3-5, net:-12 units
6) Bet 8 units and lose: 1-1-2-3-5-8, net:-20 units
7) Bet 13 units and lose: 1-1-2-3-5-8-13, net: -33 units
8) Bet 21 units and lose: 1-1-2-3-5-8-13-21,net: -54 units
9) Bet 34 units and lose: 1-1-2-3-5-8-13-21-34, net:-88 units
10) Bet 55 units and lose: 1-1-2-3-5-8-13-21-34-55, net:-143 units
11) Bet 89 units and lose: 1-1-2-3-5-8-13-21-34-55-89, net:-232 units
12) Bet 144 units and lose: 1-1-2-3-5-8-13-21-34-55-89-144, net:-376 units

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. Overall, the Fibonacci sequence does not fare too badly. This system can be fun and not too damaging if you limit your top bet to five units.

Oscar's Grind

The first reference I can find regarding this more modern betting system appeared in Allan Wilson's "The Casino Gambler's Guide," copyright 1965. Wilson was intrigued with this system after a dice player named "Oscar" produced detailed records showing modest, but consistent profits. Wilson ran 280,000 sequence simulations on an IBM 790 mainframe computer that was available to him. The analysis showed that while Oscar was a bit on the luckier side, his claims were at least possible. Now remember that Oscar was a pass line bettor only attempting to buck a -1.414% house edge as compared to a -5.263% house edge for double zero roulette. In addition, Oscar had a mega-bankroll and the willingness to risk it all for a one unit per cycle win.

Let's look at the details of the "Grind." The system has the player bet one unit. If he wins, the sequence is over and a new one can be initiated. If the wager is lost, then the next bet will be the same size as the one just lost. Whenever a bet is won, the next stake is one unit larger, unless it causes the bettor to net more than one unit of profit for the sequence. At that point, just enough is wagered to net one unit if the bet wins. That's it! A sample sequence might look like this:

1) Bet 1 unit and lose: -1 unit
2) Bet 1 unit and win: +0 units
3) Bet 1 unit and lose: -1 unit
4) Bet 1 unit and lose: -2 units
5) Bet 1 unit and lose: -3 units
6) Bet 1 unit and win: -2 units
7) Bet 2 units and win: +0 units
8) Bet 1 unit and lose: -1 unit
9) Bet 1 unit and win: +0 units
10) Bet 1 unit and win: +1 unit  -Series has been won-

The player starts with a loss so his second stake remains at one unit. This bet is won, putting him back to even. Because he is only seeking a one-unit win for the progression, he does not escalate his bet to two units. Bets 3 through 5 are losses so he stays with a one-unit stake. After the sixth bet wins, he now increases his wager to two units. The seventh bet also wins, but again he only needs a one unit bet to win the sequence. The eighth bet loses so the ninth wager is one unit. Finally, the tenth bet wins and the player wins the entire progression.

Notice that out of ten total wagers, nine were only one unit in size. This system tends to be more conservative and less volatile. The sequence illustrated above contained five wins and five losses. I like the fact that this system does not quickly escalate your losing wagers and blindside you like some of the others. However, as your losses outnumber your wins, the amount you must wager after a win will steadily mount.

Oscar's Grind will excel in streaky games. The Grind minimizes your betting level if you are amidst a string of losses. It also directs you to gradually increase your wagers during a streak of wins, helping to optimize profits. This can be one of the safer systems to use if you limit your maximum bet size or impose a stop-loss parameter for choppy games. If you plan to use Oscar's Grind, I would recommend a stop-loss of about ten, no more than 12 units per cycle.

Let's Talk Winning - Art Gallery

Let's Talk Winning has now a unique on-line art gallery that you can visit at: http://www.letstalkwinning.com/artgallery.htm.   The graphics are my own works:  images I have produced on a computer screen since the early 80's.  Personal computers then were not as sophisticated as they are today.  I had 16K memory, no hard disk, dual floppy drives, an RGB composite monitor with only 16 colors.  I wrote the program in machine language using escape sequences, addressing every single pixel.  I had added a hardware board, though,  that allowed me to further divide the pixel into a 6 X 6 matrix, using color dithering, enabling me hundreds of colors to work with. 

So, at the time when people were only able to draw boxes and circles on a PC, I was able to come up with abstract images using complex mathematical formulas, that drew the attention of many avant-garde critics in different countries.  The INA (l'Institut National de l'Audiovisuelle) in France wrote a whole book to illustrate my art.  In Italy, my images were used for silk designs.  In Monte-Carlo, I was part of the Imagina show for futuristic art.  And in Montreal, where I live, I exhibited in Images of the Future for 4 years.

My images became the subject of books, magazines, electronic art studios, live concert visuals, and CD covers.  Some companies, such as Ericsson, Microtempus, Royal Bank of Canada have bought some of them to decorate their office buildings. 

The art gallery contains 140 images of mine, displaying four per page.  It's possible for you to purchase an original high-glass print by simply clicking on the image and PayPal will process your order.  The price of each one is $1200.  I will send you a 30 X 40" print to the address you specify within 3 weeks of your order.  If you wish the print to be in a different size or format, such as a transparency, or you would like to have a volume discount if you are decorating your office building for instance,  just send me a note to: webmaster@letstalkwinning.com and I will be pleased to accommodate your request. 

Enjoy the gallery and tell all your art loving friends about it.

Wishing you all the best,
Until next week,


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