Hot Deviations - Marigny de Grilleau Ecart


How you can calculate the Ecart

The statistical ecart or deviation is a quality factor of roulette systems used in the roulette research and was introduced by Marigny de Grilleau. The French mathematician, professional gambler and consultant of the Casino in Monte Carlo tried in the early 20th century to calculate the possibility of gamblers could win permanently huge amounts at the casinos.

Grilleau was mainly focused on the even chances and published his findings in 1926 in his book "Le gain sientifique d'une seule unité" (The scientific winnings of one unit). The ecart is also a tool used to describe how big the deviation between the results of an actual spins sequence and the statistical expectations are.

The formula to calculate the ecart for even chances is:


G…Number of the hits of the chance in focus
C…Total number of observed spins

Let's say you observe the following spins at the roulette table.


According to Grilleau the ecart of 3.0 is quite high and a trend towards the balance of the chances should follow.

You can also use the formula to calculate a quality factor for your roulette system. The higher the ecart is the better, safer and more profitable is the system. In this case the meaning of the variables is as follows:

G…Total amount of won units within your spin sample
C…Total number of placed bets

Solution for other Chances and Progressions

For other chances the formula is a bit more complex:


G…Total amount of won units in your spin sample
C…Total number of placed bets
N...Number of chances bet

  • Even Chance: N=1

  • One Dozen: N=1

  • Two Dozens: N=2

  • One Line: N=1

  • Three Lines: N=3

  • Ten numbers Straight-Up: N=10

S…Number of units placed per bet round.

  • If a progression is used S is the arithmetic average of all bets.

n…Payout rate

  • Even Chance: n=2

  • Dozen / Column: n=3

  • Line Bet: n=6

  • Corner: n= 9

  • Street: n=12

  • Split: n=18

  • Straight-Up: n=36

If you want to know how useful your roulette system is you need to collect thousands of game data and figure out the ecart. If you reach results of E = 4 to E = 5 you have a pretty useful system. With results of E = 6 and above your system becomes less and less likely to fail and may be a long term winner.