Roulette is extremely simple and involves no complicated rules, however, much depends on luck. Fortunately, it is possible to help one’s luck by using mathematics and computer technology.

My proposition

At the left side of the screen there is a miniature and a link to the program "Roulette mathematics" which I wrote, and which provides a statistical analysis of numbers that come up during the game. Results of the analysis are displayed systematically on the screen.

To start playing, it is suffices to run casino software and my program simultaneously. The window of the program can be placed on the left side of the screen and reduced as required, whereas that of the casino can be placed on the right side where we are going to play roulette.

We start off by spinning the wheel. When a number comes up, a corresponding one should be clicked in the program. After a sufficient amount of data has been entered, the program will display a message suggesting when a bet can be placed and the value thereof.

The program is completely safe: it has no internal spyware or destructive features, nor is it linked to any casino. The silverlight plug-in should be installed so that the program can function properly together with a browser. The program  has the following bookmarks: "Roulette mathematics", "Settings" and "Login".
The “Roulette mathematics” bookmark breaks down into the following sections arranged form the top downwards:
      1. History of numbers entered,
      2. Message fields,
      3. Area of red or black buttons (6x6) for entering numbers coming up,
      4. Coloured indicators showing statistics.

Indicators for red or black, even or odd numbers, and number ranges of 1 to 18 or 19 to 36 perform an auxiliary function  and are based on a similar principle of operation. Each indicator consists of 10 blocks positioned one above the other. When a number is clicked, an appropriate block of an indicator is displayed.

For example, if we click number 1 (Red, odd number, 1-18 range), the first block in the indicators for  black, even and 19-36 range numbers will be displayed. Again, if we click 16 (Red, even, 1-18), the second block will be displayed in the indicator for black. The even number indicator will be switched off, and the first block in the odd number indicator will be displayed. Moreover, the second block will be displayed in the 19-36 number range indicator. Further process proceeds in the same way.

The indicators show how many times any number from a given control group has come up in succession. They work out the likelihood of other numbers coming up . If six, red numbers have appeared in succession, the probability of another red one coming up is 1 to 154. Six blocks with an inscription “Black” on them are displayed, and a message “Bet 1€ on Black” appears in the “Message fields” of section 2.

Indicators for dozen and column bets work in a similar way. Successive clicks are counted for each dozen (the first (1..12), the second (13..24) and the third group (25..36)), as well as for columns (the first (1,4,7,10,13,16,19,22,25,28,31,34), the second (2,5,8,11,14,17,23,26,29,32,35), and the third group (3,6,9,12,15,18,21,24,27,30,33,36). If any number from a given dozen or a column comes up six times in succession, a message informing about the opportunity to bet will be displayed. A message, for example “Bet 1€ on Dozen 2”, suggests on which dozen or column a bet should be placed.
In the message field also messages about other possibilities of betting are shown:
- Six Line Bet (two adjoining streets), for example "Bet 1€ on lines of 1,2,3,4,5,6". In this case the chances of winning are slimmer  but the payout is higher /6:1/.
- Four numbers forming a square /Corner Bet/, for example "Bet 1€ on 1,2,4,5". In this case the chances of winning are slimmer  but the payout is higher /8:1/.
- Three numbers on a horizontal line /Street Bet/, for example "Bet 1€ on 1,2,3". In this case the chances of winning are slimmer  but the payout is higher /11:1/.
- two adjoining numbers /Split Bet/, for example "Bet 1€ on 1,2". In this case the chances of winning are slimmer but the payout is higher /17:1/.

The threshold for the first message to be displayed can be set on one’s own in the „Settings” bookmark. It is possible to hasten or delay the displaying.
Theoretical example:
If we assume that a red number is going to come up 13 times in succession, the message “Bet 1€ on Red” will be displayed  after sixth time". To win, it is necessary to place as many as seven bets on the red and increment stakes progressively. If the threshold was lowered by 3 (-3), then the first message “Bet 1€ on Red” would be displayed after the ninth time. Then, it would be necessary to place bets only 4 times in order to win. It is also possible to start off with a higher stake: then the likelihood of winning will be greater. Raising the threshold (+) works the other way.
Changing the position of the slider (raising +) from the default setting causes a larger number of messages to be displayed earlier, whereas lowering means that a smaller number of messages will be shown later.



    We must remember that a roulette program was also created by a programmer. I assume that it was written in such a  way that the casino can win. Knowing strategies and modes of writing such programs, I suggest that tactics, strategies, modes of playing and thresholds be changed quite often. This will mislead the casino analyser (provided it exists) and raise the chances of winning.

Some theory

Roulette is a French name for a gaming wheel which determines outcomes of the game. It features small pockets numbered randomly 0 to 36. They are red or black, and the zero pocket is green. The game consists in the croupier spinning the wheel in one direction and then spinning a ball over it in the opposite direction. When the wheel loses its impetus, the ball lands in one of the pockets. If it stops in a pocket of a colour and/or number on which a bet was placed, this means that the player wins. If not, the player loses.

Bets can be placed in various ways which determine the likelihood of winning and the payout value:

    - Straight Bet: single number bet – 35 to1
    - Split Bet: two (adjoining) numbers – 17 to 1
    - Street Bet: three numbers – 11 to 1
    - Corner Bet: four numbers – 8 to 1
    - Six Line Bet: two adjoining streets – 6 to1
    - Column Bet – 2 to 1
    - Dozen Bet: 1-12, 13-24, 25-36 – 2 to1
    - Even, Odd – 1 to 1
    - 1st 18, 2nd 18, Numbers 1-18 and 19-36 – 1 to 1
    - Red, Black- 1 to 1
Let us suppose that we have placed a bet of 1€ on the red, and 3 (red) is the winning number. Then, we win 2€, therefore, the money staked is doubled with us gaining 1€. Of course, if the bet had been placed on the red, and 26 (black) had come up, the money staked would be lost.

Imagine us playing at a table with a minimum stake of 1€. Maximum stake for this table is 50 €. This time bets are going to be placed on black numbers:
1€ bet placed on the red; 5 is the winning number: we lose.
2€ bet placed on the red; 1 is the winning number: we lose a total of 3€.
4€ bet placed on the red; 36 is the winning number: we lose a total of 7€.
8€ bet placed on the red; 12 is the winning number: we lose a total of 15€.
16€ bet placed on the red; 0 is the winning number: we lose a total of 31€.
32€ bet place on red; 16 is the winning number: we have already lost a total of 63€.
Now we would have to place a bet of 64€ but this is not possible since the limit is 50€!


There are several developed strategies of playing roulette. Using coloured indicators showing statistics, the player can adopt each of them. A progression strategy is employed to display sizes of stakes in the messages.
In  the program , I have employed system of management for displaying in messages fo largeness of rates:
-    strategy of progression - system a ‘la Martingale,
-    system cascade,
-    system Labouchere,
-    system d’Alembert,
-    system Fibinacci,
-    others.

Progression strategy

The idea behind the progression strategy is to increment stakes until the desired result is achieved. The program enumerates and displays stakes automatically.
Only after a few close numbers have come up in a row should the first bet be placed on an opposite group! This program records, analyses and signals such situations.

In the case of dozen (1-12,13-24,25-36) or column bets, stakes should be put when at least 8 close numbers have come up.  In the case of the black/red number, first eighteen number range/last eighteen number range, even/odd number bets, stakes should be put when at least 6 close numbers have come up. These threshold can be of course experimentally lowered or raised. By lowering them we increase the chances of winning, whereas if they are raised, the chances become slimmer.
I suggest starting off with a 1€ bet and doubling it in the case of losses until the desired outcome. Then, the player should again place a 1€ bet. Moreover, it is advisable to start playing at a table with a 50€ limit.

Below there are chances of any number from a given group coming up in succession, for example odd numbers, black numbers, and the first eighteen numbers:

2 numbers in a row- 23.66 % - 1 to 4.22
3 numbers in a row – 11.55 % - 1 to 8.65
4 numbers in a row - 5.60 % - 1 to 17.85
5 numbers in a row - 2.72 % - 1 to 36.76
6 numbers in a row - 1.32 % - 1 to 75.75
7 numbers in a row - 0.65 % - 1 to 154
8 numbers in a row - 0.31 % - 1 to 322
9 numbers in a row - 0.15 % - 1 to 666
10 numbers in a row - 0.074 % - 1 to 1350
11 numbers in a row - 0.036 % - 1 to 2780
12 numbers in a row - 0.017 % - 1 to 5900

If we enter the game when for example a black number has come up 5 times in succession, then the probability that a bet placed on a red number will be unsuccessful is only 2.72 %.  If we enter the game when for example a black number has come up 6 times in succession, then the probability that a bet placed on a red number will be unsuccessful is only 1.32 %.
So far we have discovered how mathematical rules can be applied to situations in which a limit of a table may be reached.


Progressive method

Progressive method is one of most popular system in all hazard games. In basic version it  relies on doubling invested rate in each case a played through and reverting to the  basic rate in case a winning. This manner allows cover in played through contets last win rates.

However , it is not prescribed basic progressive system excessively, because it is related with relatively big risk. Property of heavy stock of cash is indispensable condition and the winnings are not  high that . Additinal it is possible to hit in certain moment on limit of the table, even owning heavy stock financial, that will be tied with defeat.


I use modified in my program versions of progressions a’la Martingale. After the played through the  program does not double rate. What prompts belong to put once again, in order to recover played through and surpass level of loss.
It allows to extend game and boost chances on a winning.

Program results after established by player mathematical roulette number begin displaying suggestion spins, a win has not fell in with the chosen bet. If player l put and he will play through, the  program will prompt belong to put what once again, in order to recover played through and gain minimally.


 Amount of suggestion of program will be different depending on bet. Amount of rate results from tables in  suggestion below. Setting up, that we begin game from 1 € and limit of the table is 50 €,
that amount of suggestion will be for bets:

Red - black 6
Even - odd 6
Low - high
6
Dozens
10
Column 10
Lines 23
Four numbers 38
Three numbers 51
Two numbers 76
One number 155


Cascade

Cascade plays it on 4 spins. Win if we will win in  1,2,3 or 4 spins or we return it at the beginning of cascade  In cascade played through number 1, we proceed for cascade number 2 and we play according to served in table number of counter. If we don’t win in cascade number 2 we go to  cascade number 3 and  further likewise. In case of  victory in cascade number 2,3 etc., we return at the beginning of win cascade number 2,3 etc. System of cascade it is  progression on  different levels.



Level of  cascade value of counters in draft 4  spins
Cascade number 1
1
2
4
8
Cascade number 2
2
3
6
12
Cascade number 3
3
4
8
16
Cascade number 4
4 5
10
20
Cascade number 5
5
6
12
24
Cascade number 6
6
7
14
28
Cascade number 7
7
8
16
32

It concerns system on simple bets cascade game only :  Colour Bet,  Even/Odd,  Low/High Number. For bets remaining simple number - Straight,  Split,  Street,  Corner, l Six Line,  Dozen, Column, the program prompts according to system a’la Martingale.

System Labouchere

We write down that growing pull of  numbers . Program takes advantage pull 1 2 3 4 5 6 7.  Value of rate it is amount of first and last number. If I win, I  will cross out ultra numbers. If I play through I will add the played through rate at the end of range.
 We treat falling out zero as played through also. It concerns system on simple
bets game only system Labouchere.


System d’ Alembert

In case played through we bring up about one rate unit , when we win we go down rate  about one unit . We treat falling out  as played through 0 also and we boost rate. It concerns system on simple bets game only d’Alembert .


System Fibonacci


There is amount former two  within each number Fibonacciego 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 etc. If we play through we remove  in right side about the 1 place , if we win about 2 places in left side.

We treat falling out zero as the played through also.
System Fibonacci  concerns on simple bets game only : Colour bet ,  Even/Odd,  Low/High Number. For bets remaining :  Straight,  split, Street, Corner, Six Line, Dozen


Combinations of  game

The  program enables the game on a combination of number compact , lying beside on circle.
  - Voisins du lodge - great series it includes beside on circle 17 numbers put, concentrated circle of zero. It is surrounded 9 counters.
-    Tiers du cylindre - Small series dozen includes  12 numbers so called eighth. There  are  numbers from 27 for 33  concentrate around eight . It is surrounded  6 counters.
-     Les orphelins - ORPH – it is combination 8 numbers contens from two grups interleaving great and series small. It surrounds it 5 counters.

Choosing option the  game on a combination of numbers we can get the suggestions in bet on 12 numbers.  - Dozen, Columns and on 18 numbers bets : beta Colour,  Even/Odd,  Low/High Number.
Suggestions are switched off for the bets  - Straight,  split,  Street,  Corner, Six Line.

Others

Program enables surrounding of DOZEN variant 3 line.
Instead of Dozen 1 ( 1st12) we surround 1,2  and 3 lines  (together 12 numbers)
Instead of Dozen 2 ( 2nd12 ) we surround 4,5 and 6 lines  (together12 numbers )
Instead of Dozen 3 ( 3rd12) we surround 7,8 and 9 lines  (together12 numbers )

The program enables /HIGH surrounding LOW variant 6 threesomes also.
Instead of low  ( 1-18 )  we surround 1,2,3,4,5 and 6 threesome  (together 18 numbers )
Instead of high (19-36) we surround  7,8 9,10,11  and 12 threesome (together18 numbers)
Such combinations allow to diversify game and change value the winnings.


The Grid
                             
Colour Bet, Even-Odd, Low-High Number    

Nr gry/Bet Number Stawka/Your Bet Wygrana/Your Win Twój zysk/Your Profit
1
€1 2 1
2
€2 4 1
3
€3 8 1
4
€4 16 1
5
€5 32 1
6
€6 64 1


Column, Dozen

Nr gry/Bet Number
Stawka/Your Bet Wygrana/Your Win Twój zysk/Your Profit
1
 € 1 3
2
2
 € 2
6
3
3
 € 3
9
3
4
 € 4
12
2
5
 € 6
18
2
6
 € 9
27
2
7
 € 13
39
1
8
 € 20
60
2
9
 € 30
90
2
10
 € 45
135
2
     
            
Six Line 

Nr gry/Bet Number Stawka/Your Bet Wygrana/Your Win Twój zysk/Your Profit
1
€ 1 6 5
2
€ 1 6 4
3
€ 1 6 3
4
€ 1 6 2
5
€ 1 6 1
6
 € 2 12 5
7
 € 2 12 3
8
 € 2 12 1
9
€ 3 18 4
10
€ 3 18 1
11
€ 4 24
3
12
€ 5 30
4
13
€ 6 36
4
14
 € 7 42
3
15
 € 8 48
1
16
€ 10 60
3
17
€ 12 72
3
18
€ 14 84
1
19
€ 17 102
2
20
€ 21 126
5
21
€ 25 150
4
22
€ 30 180
4
23
€ 36 216
4

     
Corner 

Nr gry/Bet Number Stawka/Your Bet Wygrana/Your Win Twój zysk/Your Profit
1
€ 1 9
8
2
€ 1 9
7
3
€ 1 9
6
4
€ 1 9
5
5
€ 1 9
4
6
€ 1 9
3
7
€ 1 9
2
8
€ 1 9
1
9
€ 2 18
8
10
€ 2 18
6
11
€ 2 18
4
12
€ 2 18
2
13
 € 3 27
8
14
 € 3 27
5
15
 € 3 27
2
16
 € 4
36
7
17
 € 4 36
3
18
 € 5
45
7
19
 € 5
45
2
20
 € 6
54
5
21
 € 7
63
7
22
 € 8
72
8
23
 € 9
81
8
24
 € 10
90
7
25
 € 11
99
5
26
 € 12
108
2
27
 € 14 126
6
28
 € 16
144
8
29
 € 18
162
8
30
 € 20
180
6
31
 € 22
198
2
32
 € 25
225
4
33
 € 28
252
3
34
 € 32
288
7
35
 € 36
324
7
36
 € 40
360
3
37
 € 45
405
3
38
 € 51
459
6


Street 

Nr gry/Bet Number Stawka/Your Bet Wygrana/Your Win Twój zysk/Your Profit
1
€ 1 12
11
2
€ 1 12 10
3
€ 1 12 9
4
€ 1 12 8
5
€ 1 12 7
6
€ 1 12 6
7
€ 1 12 5
8
€ 1 12 4
9
€ 1 12 3
10
€ 1 12 2
11
€ 2
24
12
12
€ 2 24
10
13
€ 2 24
8
14
€ 2 24
6
15
€ 2 24
4
16
€ 2 24
2
17
€ 3
36
11
18
€ 3 36
8
19
€ 3 36
5
20
€ 3 36
2
21
€ 4
48
10
22
€ 4 48
6
23
€ 4 48
2
24
€ 5
60
9
25
€ 5
60
4
26
€ 6
72
10
27
€ 6
72
4
28
€ 7
84
9
29
€ 7
84
2
30
€ 8
96
6
31
€ 9
108
9
32
€ 10
120
11
33
€ 11
132
12
34
€ 12 144
12
35
€ 13 156
11
36
€ 14 168
9
37
€ 15 180
6
38
€ 16 192
2
39
€ 18 216
8
40
€ 20
240
12
41
€ 22
264
14
42
€ 24
288
14
43
€ 26
312
12
44
€ 28
336
8
45
€ 30
360
2
46
€ 33
396
5
47
€ 36
432
5
48
€ 39
468
2
49
€ 43
516
7
50
€ 47
564
8
51
€ 51
612
5


Split  

Nr gry/Bet Number Stawka/Your Bet Wygrana/Your Win Twój zysk/Your Profit
1
€ 1 18
17
2
€ 1 18 16
3
€ 1 18 15
4
€ 1 18 14
5
€ 1 18 13
6
€ 1 18 12
7
€ 1 18 11
8
€ 1 18 10
9
€ 1 18 9
10
€ 1 18 8
11
€ 1 18 7
12
€ 1 18 6
13
€ 1 18 5
14
€ 1 18 4
15
€ 1 18 3
16
€ 1 18 2
17
€ 2 36 18
18
€ 2 36 16
19
€ 2 36 14
20
€ 2 36 12
21
€ 2 36 10
22
€ 2 36 8
23
€ 2 36 6
24
€ 2 36 4
25
€ 2 36 2
26
€ 3
54
17
27
€ 3
54 14
28
€ 3
54 11
29
€ 3
54 8
30
€ 3
54 5
31
€ 3
54 2
32
€ 4
72
16
33
€ 4
72 12
34
€ 4
72 8
35
€ 4
72 4
36
€ 5
90
17
37
€ 5
90 12
38
€ 5
90 7
39
€ 5
90 2
40
€ 6
108
14
41
€ 6
108
8
42
€ 6
108
2
43
€ 7
126
13
44
€ 7
126
6
45
€ 8
144
16
46
€ 8
144
8
47
€ 9
162
17
48
€ 9
162
8
49
€ 10
180
16
50
€ 10
180
6
51
€ 11
198
13
52
€ 12
216
19
53
€ 12 216
7
54
€ 13
234
12
55
€ 14
252
16
56
€ 14
252
2
57
€ 15
270
5
58
€ 16
288
7
59
€ 17
306
8
60
€ 18
324
8
61
€ 19
342
7
62
€ 20
360
5
63
€ 21 378
2
64
€ 23 414
15
65
€ 24 432
9
66
€ 25 450
2
67
€ 27 486
11
68
€ 28 504
1
69
€ 30
540
7
70
€ 32
576
11
71
€ 34
612
13
72
€ 36 648
13
73
€ 38
684
11
74
€ 40
720
7
75
€ 42
756
1
76
€ 45
810
10

          


Straight 

Nr gry/Bet Number Stawka/Your Bet Wygrana/Your Win Twój zysk/Your Profit
1
€ 1
35
35
2
€ 1
35
34
3
€ 1
35
33
4
€ 1
35
32
5
€ 1
35
31
6
€ 1
35
30
7
€ 1
35
29
8
€ 1
35
28
9
€ 1
35
27
10
€ 1
35
26
11
€ 1
35
25
12
€ 1
35
24
13
€ 1
35
23
14
€ 1
35
22
15
€ 1
35
21
16
€ 1
35
20
17
€ 1
35
19
18
€ 1
35
18
19
€ 1
35
17
20
€ 1
35
16
21
€ 1
35
15
22
€ 1
35
14
23
€ 1
35
13
24
€ 1
35
12
25
€ 1
35
11
26
€ 1
35
10
27
€ 1
35
9
28
€ 1
35
8
29
€ 1
35
7
30
€ 1
35
6
31
€ 1
35
5
32
€ 1
35
4
33
€ 1
35
3
34
€ 1
35
2
35
€ 2
70
34
36
€ 2 70
32
37
€ 2 70
30
38
€ 2 70
28
39
€ 2 70
26
40
€ 2 70
24
41
€ 2 70
22
42
€ 2 70
20
43
€ 2 70
18
44
€ 2 70
16
45
€ 2 70
14
46
€ 2 70
12
47
€ 2 70
10
48
€ 2 70
8
49
€ 2 70
6
50
€ 2 70
4
51
€ 2 70
2
52
€ 3
105
34
53
€ 3 105 31
54
€ 3 105 28
55
€ 3 105 25
56
€ 3 105 22
57
€ 3 105 19
58
€ 3 105 16
59
€ 3 105 13
60
€ 3 105 10
61
€ 3 105 7
62
€ 3 105 4
63
€ 3 105 1
64
€ 4
140
32
65
€ 4 140 28
66
€ 4 140 24
67
€ 4 140 20
68
€ 4 140 16
69
€ 4 140 12
70
€ 4 140 8
71
€ 4 140 4
72
€ 4 140 0
73
€ 5
175
30
74
€ 5 175
25
75
€ 5 175
20
76
€ 5 175
15
77
€ 5 175
10
78
€ 5 175
5
79
€ 6
210
34
80
€ 6 210
28
81
€ 6 210
22
82
€ 6 210
16
83
€ 6 210
10
84
€ 6 210
4
85
€ 7
245
32
86
€ 7 245
25
87
€ 7 245
18
88
€ 7 245
11
89
€ 7 245
4
90
€ 8
280
31
91
€ 8 280
23
92
€ 8 280
15
93
€ 8 280
7
94
€ 9
315
33
95
€ 9 315
24
96
€ 9 315
15
97
€ 9 315
6
98
€ 10
350
31
99
€ 10
350
21
100
€ 10
350
11
101
€ 10
350
1
102
€ 11 385
25
103
€ 11 385
14
104
€ 11 385
3
105
€ 12 420
26
106
€ 12 420
14
107
€ 12 420
2
108
€ 13 455
24
109
€ 13 455
11
110
€ 14 490
32
111
€ 14 490
18
112
€ 14 490
4
113
€ 15 525
24
114
€ 15 525
9
115
€ 16 560
28
116
€ 16 560
12
117
€ 17 595
30
118
€ 17 595
13
119
€ 18 630
30
120
€ 18 630
12
121
€ 19 665
28
122
€ 19 665
9
123
€ 20
700
24
124
€ 20 700
4
125
€ 21 735
18
126
€ 22 770
31
127
€ 22 770
9
128
€ 23
805
1
129
€ 24
840
32
130
€ 24
840
8
131
€ 25
875
18
132
€ 26 910
27
133
€ 26 910
1
134
€ 27 945
9
135
€ 28 980
16
136
€ 29 1015
22
137
€ 30
1050
27
138
€ 31 1085
31
139
€ 32 1120
34
140
€ 32 1120
2
141
€ 33 1155
4
142
€ 34 1190
5
143
€ 35 1125
5
144
€ 36 1260
4
145
€ 37 1295
2
146
€ 39 1365
33
147
€ 40
1400
28
148
€ 41
1435
22
149
€ 42
1470
15
150
€ 43 1505
7
151
€ 45 1575
32
152
€ 46 1610
21
153
€ 47 1645
9
154
€ 49 1715
30
155
€ 50 1750
15

However, we should be aware of one risk!! For safety’s sake, players are warned not to proceed to a table with a higher limit unless the amount in their accounts exceeds a few times the limit of the table at which they are currently playing. This reduces the risk of losing!
It is advisable to play much just for fun, which makes it possible to sense the game and then use the experience acquired.


Due to the cost of the website maintenance, I must charge fees for making the program available. Payments can be made in the "Payments" bookmark.


Roulette mathematics

Good luck
Ryszard Tustanowski