Roulette Numbers and Roulette Wheel Bias.

Roulette Number Pairing Analysis — Is There a Mechanical Wheel Bias?

By Ion Saliu, Founder of Roulette Mathematics

Roulette Real casino spins and roulette wheel system.

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An analysis of roulette number pairing, roulette wheel bias, with real casino roulette  spins from Hamburg casino or Spielbank.

• The main roulette strategy page analyzes the so–called roulette wheel bias. If there is such a thing as the wheel bias, then a few roulette numbers will be drawn significantly more often than the other numbers. Also, each roulette number will be immediately followed by a limited universe of other roulette numbers. The latter parameter is known at this web site as number pairing. It is common in lottery (you can read here about the 'wonder grid' in lotto games).

A pairing in roulette is a roulette number AND the number drawn in the very next spin. In the case of a consecutive hit, a roulette number is followed by itself. Let it be said that each roulette number can be followed by itself with an equal frequency to a pairing consisting of a different number. The probability is the same.

I noticed, however, that a repeat is less frequent than a heterogeneous pairing. I included two statistical reports based on real casino roulette spins. I analyzed 1968 real spins recorded at the Hamburg, Germany casino, February 1 – 6, 2000. File name: HAMB00.DAT freeware from my FTP download site. By the way, that file is a precious item now. I have been unable to access the casino database again. My requests for real roulette spins have remained unanswered by the casinos. I doubt that the casinos will make their roulette databases available again! We need go to the casinos, stand near a roulette marquee, and painstakingly record every spin, for many hours.

Editor's note
In an apparent change of heart, the Hamburg casino (Spielbank) offers online roulette results for free. I no longer offer links in clickable format, as they change way too often (especially after I write a successful material!)

http://www.spielbank-hamburg.de/spielsaal/permanenzen.php4
HTML title: "Spielbank Hamburg - Real Game. Real Money."
Google translates Spielbank as gaming house; that is, casino, kasino.
The link appears now in a Google search and does lead to roulette spins results. I cannot guarantee the accuracy of data. But I may not doubt the integrity of spielbank-hamburg.de.

The results are categorized by the following parameters, in order:
Roulette Table or Wheel (Tisch) – Day (Tag) – Month (Monat) – Year (Jahr).

I downloaded the results for one table or wheel (#1) for the entire month of January 2006. File name: HAMB0106.WH1; 7990 lines (draws or spins) in text format; the last draw of 31 January 2006 is at the very top of the file (line #1). The file contains roulette numbers (spins) only, one number per line. The casino results files have also other data, such as frequency and various statistics. The files also have dashed lines (----) which probably represent dealer changes.

HAMB0106.WH1 represents the best recording format: table by table. Do not mix the spins from different roulette wheels in the same file.

See the roulette number pairings reports for the HAMB0106.WH1 spins file. The first report is for the most recent 1000 spins: approximately 4 days worth of spinning or January 27 to 31, 2006. The second report analyzes all 7990 roulette spins for the month of January 2006. I do not see any bias according to the normal probability rule.

There is a number of 54 consecutive repeats in 1968 spins. That amounts to about 27 roulette numbers in 1000 spins. There are 37 roulette numbers in the single-zero game (as in Hamburg, Germany). It means that a few roulette numbers did not hit in consecutive spins for the duration of a 1000-spin session. But each roulette number was followed in the very next spin by a different number at least 2 times in 1000 spins.

For example, the roulette number 0 was followed by itself (0 again) in the very next draw (spin) once in 1968 spins. Roulette number 0 was followed by roulette #1 in the very next spin 6 times in 1968 spins.

Roulette number 1 was followed by itself (1 again) in the very next draw (spin) once in 1968 spins. Roulette number 1 was followed by roulette #29 in the very next spin 5 times in 1968 spins.

Roulette number 5 was followed by itself (5 again) in the very next spin 0 times in 1968 spins. Roulette number 5 was followed by roulette #21 in the very next spin 4 times in 1968 spins.

Even if there are clear discrepancies, they are within 3 standard deviations from the norm. Therefore the statistical data is still compliant with the rule of the normal probability. The discrepancy should have been two times wider to turn into suspicious bias; e.g. from 0 to 12.

A second take is in tall order: Mechanics. There should not be any discrepancy between a mechanical roulette wheel (as in the casinos) and a random number generator (as in roulette software). The bias against an immediate roulette number repeat is less pronounced in random generation of roulette spins. A short explanation: The croupier (dealer) places the roulette ball in the slot that hit last. The probability is lower to have the roulette ball come exactly in the same slot as in the previous spin. We are dealing here with two simultaneous probabilities. If the dealer would place the roulette ball randomly on the wheel, the unfavorable repeat bias would be less present.

Even if within the normal probability rule, the bias could burn the casino out. A roulette player could play the top 10-12 pairings of each roulette number. For example, every time number 0 (the green) was drawn, the player would play the following 10 roulette numbers: 1 15 25 9 3 20 8 30 32 33. They followed roulette number 0 in the next spin a total of 35 times out of 61 hits. That represents 57% of all cases when the roulette number 0 hit. It comes down to playing only the top pairings of each spin and winning 50% of the time! Play 12 numbers — and hit once, miss once. The total of 24 units in cost yields a win of 36 units straight–up. That would be 12 units net win in two spins; or an average of 6 units in net profit in every spin! A profit of 600 units per 100–spin sessions...

The problem is we don't know IN ADVANCE which numbers will be the top 12 pairings for each roulette number. The skips of the pairings themselves must be determined as well. Only a computer program can determine the skips in real-time — mission impossible inside a casino!

Otherwise, of course, the roulette wheel could be extremely biased due to wear. We analyzed the previous 1000 roulette spins (recorded by hand!) and we are certain of the bias. Meanwhile the casino executives have no clue of such bias! In my opinion, that is NOT a realistic expectation. The casinos always analyze the roulette spins and look for possible biases due to wear. I am not sure they perform pairing analysis because I have not given anybody my specialized roulette software. Still, there are several statistical methods to hunt wheel biases.

Why do the casinos refuse to make their roulette spins databases available to the public? Just a rhetorical question, kokodrilo...

• Apparently, only the German casinos publish the actual roulette spins: Hamburg casino (Spielbank) and Wiesbaden Casino (Spielbank). They do sometimes … then they remove the links! They say, in various languages: "Ion Saliu scared the hell out of us kasinos...casinos..."

http://www.spielbank-hamburg.de/spielsaal/permanenzen.php4
http://www.spielbank-wiesbaden.de/DE/621/Permanenzen2.php

Wish them in your best language: "Requiescat in pace!" "Rest in peace!"

Play the best roulette number pairing system.

          Roulette Numbers Hitting in Consecutive Spins (Play-Last-Number)

# Consecutive Hits:  54  times in 1968  spins
* Skips:  68  35  135  101  9  15  9  65  46  3  33  6  49  3  17  11  26  17  71  44  15  8  0 
* Sorted Skips:  0  1  1  1  2  3  3  3  5  6  7  8  8  9  9  11  15  15  16  17  17  17  18  
* Median Consecutive Skip:  22 



                                Roulette Pairings Report
                                Pairing = Number + Number in NEXT Spin
                                Data File: HAMB00.DAT; 1968 Spins
                                Date: 11-30-2005

       Roulette Number:  0     Hits:   61   ( 3.1 %)
 With #: 1  15 25 9  3  20 8  30 32 33 22 6  26 19 12 21 34 35 24 14 5  28 18 0  11 7  13 36
 Hits:   6  4  4  3  3  3  3  3  3  3  2  2  2  2  2  2  2  2  1  1  1  1  1  1  1  1  1  1
 Pairs total: 61


       Roulette Number:  1     Hits:   58   ( 2.9 %)
 With #: 29 30 17 20 23 25 26 4  14 8  11 24 12 13 0  5  36 3  22 6  7  1  15 10 18 31 32 33 19
 Hits:   5  4  3  3  3  3  3  3  3  2  2  2  2  2  2  2  2  1  1  1  1  1  1  1  1  1  1  1  1
 Pairs total: 58


       Roulette Number:  2     Hits:   60   ( 3 %)
 With #: 8  9  16 7  19 23 27 32 36 1  0  22 12 13 14 33 15 4  26 5  29 30 2  20 34 35 3
 Hits:   7  5  4  3  3  3  3  3  3  2  2  2  2  2  2  2  2  1  1  1  1  1  1  1  1  1  1
 Pairs total: 60


       Roulette Number:  3     Hits:   63   ( 3.2 %)
 With #: 0  12 18 8  13 11 24 32 16 17 6  19 20 22 7  25 28 14 34 35 36 10 5  1  31 2  33 3  21 15
 Hits:   5  4  4  3  3  3  3  3  2  2  2  2  2  2  2  2  2  2  2  2  2  1  1  1  1  1  1  1  1  1
 Pairs total: 63


...

       Roulette Number:  21    Hits:   45   ( 2.3 %)
 With #: 6  28 3  8  10 14 15 16 18 21 4  30 32 33 19 13 22 24 26 1  29 7  31 2  5  34 35
 Hits:   4  4  2  2  2  2  2  2  2  2  2  2  2  2  1  1  1  1  1  1  1  1  1  1  1  1  1
 Pairs total: 45


       Roulette Number:  22    Hits:   46   ( 2.3 %)
 With #: 0  14 17 26 31 1  3  18 8  11 35 7  15 16 5  9  19 20 21 22 23 24 25 10 27 29 30 6  12 36
 Hits:   3  3  3  3  3  2  2  2  2  2  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 Pairs total: 46


       Roulette Number:  23    Hits:   57   ( 2.9 %)
 With #: 29 11 1  13 22 27 2  30 35 19 3  23 25 6  14 16 33 17 0  26 18 28 10 15 5  24 36
 Hits:   5  4  3  3  3  3  3  3  3  2  2  2  2  2  2  2  2  2  1  1  1  1  1  1  1  1  1
 Pairs total: 57


       Roulette Number:  24    Hits:   40   ( 2 %)
 With #: 0  4  12 24 30 2  14 1  27 8  31 5  13 6  16 7  26 3  28 9  11 32 34 36
 Hits:   3  3  3  3  3  2  2  2  2  2  2  1  1  1  1  1  1  1  1  1  1  1  1  1
 Pairs total: 40


       Roulette Number:  25    Hits:   62   ( 3.2 %)
 With #: 0  7  15 19 6  16 1  20 24 5  8  10 4  26 27 29 31 36 25 9  3  28 11 30 12 32 33 35 13
 Hits:   5  5  4  4  3  3  3  3  3  2  2  2  2  2  2  2  2  2  1  1  1  1  1  1  1  1  1  1  1
 Pairs total: 62


       Roulette Number:  26    Hits:   60   ( 3 %)
 With #: 2  3  1  12 25 26 29 5  13 14 16 17 21 6  9  28 11 33 20 7  22 23 24 8  0  10 4  30 19 34 35
 Hits:   5  5  3  3  3  3  3  2  2  2  2  2  2  2  2  2  2  2  1  1  1  1  1  1  1  1  1  1  1  1  1
 Pairs total: 60


       Roulette Number:  27    Hits:   50   ( 2.5 %)
 With #: 2  14 25 0  16 3  10 18 23 6  27 33 34 35 20 21 12 24 1  26 7  28 29 31 17 4  19
 Hits:   4  4  4  3  3  3  2  2  2  2  2  2  2  2  1  1  1  1  1  1  1  1  1  1  1  1  1
 Pairs total: 50


       Roulette Number:  28    Hits:   56   ( 2.8 %)
 With #: 3  4  36 17 25 35 8  19 20 23 7  26 27 31 34 5  6  12 13 15 28 29 30 0  32 33 1  9  11
 Hits:   4  4  4  3  3  3  3  2  2  2  2  2  2  2  2  2  2  1  1  1  1  1  1  1  1  1  1  1  1
 Pairs total: 56

...

       Roulette Number:  35    Hits:   49   ( 2.5 %)
 With #: 10 12 16 3  19 25 26 30 2  11 8  9  36 20 21 23 24 7  17 27 18 31 34 35 1
 Hits:   4  4  4  3  3  3  3  3  2  2  2  2  2  1  1  1  1  1  1  1  1  1  1  1  1
 Pairs total: 49


       Roulette Number:  36    Hits:   44   ( 2.2 %)
 With #: 9  10 11 15 4  6  1  16 23 25 34 2  5  17 18 19 21 22 3  24 12 27 28 29 30 32 33 13 36
 Hits:   3  3  3  3  2  2  2  2  2  2  2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 Pairs total: 44

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