Mathematics proves that every roulette number repeats based on probability.

Roulette Basics, Betting, Systems, Methods, Gambling Strategies

Ion Saliu's Paradox and Roulette

Roulette is a game of chance (casino gambling) ruled by theory of probability.

Written on September 3, 2002.

• Consider this your start on the way to win consistently at any roulette table (except for the fraudulent online casinos). There are many Internet searches on roulette: win at roulette, winning roulette systems, successful betting at roulette, making money at roulette, beat the queen of casino games, bet to win roulette, etc. On one hand, there are strongly negative opinions on the probability of winning consistently at the roulette table. Summarize: the player will lose no matter what system he/she uses at the roulette table. Nobody can predict the roulette wheel, unless it is biased! On the other hand, there are hilariously positive opinions and systems to win at roulette. “100% guaranteed to win roulette!”

Roulette is a game of chance ruled by theory of probability. This web site offers plenty of information on theory of probability, theory of games, gambling mathematics. Mathematics of roulette is extensively analyzed here. The cornerstone is the Fundamental Formula of Gambling (FFG). It is a mathematical fact that every roulette number has a repeat cycle based on FFG. In a least 50% of the wins, a roulette number repeats after 25-26 spins. Look at the end of this page. The single-zero roulette number '36' recorded 44 hits in 1968 spins (at the Hamburg casino, Germany). More than half of its repeats were under 27 spins. The probability median calculated by FFG is 25. This represents one simple, the simplest winning system at roulette. My main roulette page offers two more winning systems, both free, both more powerful than this simple idea.

The end of this page shows the links to follow. Please do check the web pages of this site dedicated to roulette. You will see how mathematics can get “involved” in a game such as roulette. I offer two free systems and free software to test the systems. The software can analyze other roulette systems as well. You can either generate thousands of random spins, or analyze thousands of real casino spins (single zero or double zero). There is a data file of roulette spins recorded at the Hamburg casino (Germany).

Keep in mind that my gambling theory has provoked serious hostility from casino executives and other gambling theorists. Even a casino chairman felt compelled to threaten me in my forum. Please read that message carefully. Why would casinos care about roulette or casino or gambling systems if the systems don't win?

• Ion Saliu's Paradox and Roulette

'Ion Saliu's Paradox of N Trials' is presented in detail at, especially the probability theory page and the mathematics of gambling formula. If p = 1 / N, we can discover an interesting relation between the degree of certainty DC and the number of trials N. The degree of certainty has a limit, when N tends to infinity. That limit is 1 — 1/e , or approximately 0.632…

If you play 1 roulette number for the next 38 spins, common belief was that you expected to win once. NOT! Only if you play 38 numbers in 1 spin, your chance to hit the winning number is 100%. Here is an interesting table, which includes also The Free Roulette System #1 presented at the main roulette site.

Type of Play Winning Chance % Cost in Units Gain for Saliu's Paradox %
Play 1 # in 38 Spins 63.7% 38 -
Play 38 #s in  1 Spin 100% 38 1 - .637 = 36.3%
Play 34 #s in  1 Spin 89.5% 34 28.8%

The maximum gain comes when playing 38 numbers in one spin: 36.3%. Obviously, it makes no sense to play that way because of the house advantage. On the other hand, a so-called wise gambler is more than happy to play one number at a time. What he does is simply losing slowly! Not only that, but losing slowly is accompanied by losing more. That cautious type of gambling is like a placebo. A roulette system such as 'Free #1' scares most roulette gamblers. "Play 34 or 33 numbers in one shot? I'll have a heart attack!" In reality, the 'Free System #1' offers a 28.8% advantage over playing singular numbers in long sessions. That's mathematics, and there is no heart to worry about.

You can also use SuperFormula.EXE to calculate all kinds of probabilities and advantage percentages. The option L — At least M successes in N trials is a very useful instrument. If you play 19 numbers in one spin, the probability to win is 50%. If you play 19 numbers in 2 consecutive spins, the probability to win at least once is 75%.

Super Formula software calculates odds, probabilities, including casino roulette.

I put together all my roulette software, systems and strategies in a comprehensive package named BrightR.exe. The winning roulette systems, strategies and software are free at this website with a (nominal) paid membership fee to download them all.

The roulette software, systems, strategies, free betting systems, in one package.

Advantages of Ion Saliu's Paradox in the game of roulette.

Copyright © MMII, Ion Saliu. All rights reserved worldwide.

Ion Saliu's Theory of Probability Book founded on mathematics applied to roulette, systems, strategy. Read Ion Saliu's first book in print: Probability Theory, Live!
~ Founded on mathematical discoveries, also applied to roulette, systems, strategy, win - loss streaks; detailed analysis, also based on real-life cases (casino playing).

Roulette: Software, Content, Resources, Systems, Super Strategy.
See a comprehensive directory of the pages and materials on the subject of roulette, software, systems, and the Super Strategy.

  • Free Roulette Systems, Software — The Main Roulette Page.
  • The Super Roulette Strategy: The Best Winning Roulette Systems Free In 2005.
  • An inventory of free and outrageously priced roulette systems.
  • Roulette Software, Systems: Wheel Positioning (Slots, Sectors), The Birthday Paradox.
  • "Roulette System that Won Millions!"
    ~ Ion Saliu's roulette theory, systems, and software were pirated by an Australian gambling group.

  • Probability, Odds to Win Roulette in Various Number of Spins: To Be Ahead And Quit.
  • The James Bond roulette system in the Taliban Desert.
  • Roulette Systems And Threats From A Casino Chairman.
  • Anti-gambler advice from John Patrick, casino mole extraordinaire and conspirator.
  • Wizard of Odds Had High Praise For Ion Saliu's Gambling Theory.
  • Casinos pay troubled individuals to intimidate intelligent gambling system authors.

    Roulette systems, software, odds, winning in casino.

    Roulette mathematics, free systems, strategy, software.

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