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Ion Saliu's Paradox Applied to Roulette

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Written on September 3, 2002; © SALIU.COM

• 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! Non! 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 on 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 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%.

There are advantages of Ion Saliu's Paradox applied to the game of roulette.

Copyright © MMII Ion Saliu

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This is a mathematical presentation of the casino game of roulette.