Introduction

To be precise, ‘even money’ bets have a 48.65% chance of winning in European Roulette, and 47.37% in American roulette. Due to the high probability of those bets, the payout for them is 1:1. The other outside bets are Column and Dozen, both of which cover 12 numbers on the table. Roulette's a really old game, but you can't play the time-honored style in California. Sure, the state allows roulette, just not in the traditional style. Roulette has always been a stylish and regal game, unlike craps, which is a tougher, more aggressive game. However, neither game is allowed in California, and there's a good reason. FBSD - Flat Bet Single Dozen Roulette System. 30,000 Roulette Dozens by Perry B. 3D-RB 3 Dozens - Relative Betting Roulette System. DS4-5 Roulette Systems. WRS - 6 Window Roulette Systems. FRS - Favorite Roulette System (Roulette contest winner!) Rose Garden. Wave System for Even Bets. And stay in the thrill of the game until the last second. Turn the odds of the game in your favour with just taps on the most competitively-priced odds! Here's what our mobile users are saying. Try it now at m.OBET33.com 'It is very simple but effective' Unlike other betting apps, it’s a no nonsense, straight to the point design.

The Gambler's Fallacy is the mistaken belief that if an independent event has not happened in a long time, then it becomes overdue and more likely. It is also equally incorrect that if an outcome has happened a disproportionate number of times lately, compared to statistical expectations, then it becomes overheated and less likely to occur the next time. An example of this fallacious thinking might be that if the number 23 hasn't been drawn in a 6-49 lottery the last 100 games, then it becomes more likely to be drawn during the next drawing.

Many worthless betting strategies and systems are based on belief in the Gambler's Fallacy. I got the idea for writing about this after reading an 888 online roulette article by Frank Scoblete entitled How to Take Advantage of Roulette Hot Spots. In that article, Scoblete recommends taking a count of each outcome for 3,700 spins in single-zero roulette and 3,800 spins in double-zero roulette in the hunt for 'hot numbers.' Never mind that this would take about 100 hours to make this many observations, assuming the industry standard of 38 spins per hour.

Before going further, let me say that I strongly believe modern roulette wheels made by top brands like Cammegh are extremely precise and any bias would be minuscule compared to the house advantage. Thus, testing a modern roulette for bias would be a total waste of time. Now, testing a 30-year-old hand-me-down wheel in a banana republic might be another story. However, you're on your own if you win a lot of money from said casino and try to leave with it.

That said, if you track 3,800 outcomes in single-zero roulette, the average number of times any number will hit is 3800/38=100. I ran a simulation of over 1.3 trillion spins, counting how many times each number was hit, sorting the outcomes to find the most frequent number and how many times it was observed, and keeping a count of how many times the most frequent number in each simulation was seen.

Hottest Number in 3,800 Spins of Double-Zero Roulette

As a former actuary, I hate to use a layman's term like the 'hottest number,' but that is how gamblers talk so will go with that. That said, following are the results of the count of the hottest number in millions of 3800-spin simulations.

Count of the Hottest Number in 3,800 Spins on Double-Zero Wheel

Statistic	Value
Mean	122.02
Median	121
Mode	120
90th Percentile	128
95th Percentile	131
99th Percentile	136
99.9th Percentile	142

Here is what the table above means in plain simple English.

• The mean, or average, count of the hottest number is 122.02.
• The median count of the most frequent number is 121. This means that over 50% of time the most frequent number appeared 121 times or less, as well as 121 times or more. This is possible because the probability of 121 observations is in both groups.
• The mode, or most count of the hottest number is 120, which happens 8.29% of the time.
• The 90th percentile is the smallest number such that the probability the count of the hottest number is at least 90% .
• The 95th percentile is the smallest number such that the probability the count of the hottest number is at least 95%.
• The 99th percentile is the smallest number such that the probability the count of the hottest number is at least 99%.
• The 99.9th percentile is the smallest number such that the probability the count of the hottest number is at least 99.9%.

Hottest Number in 3,700 Spins of Single-Zero Roulette

The results are very similar with 3,700 spins tracked on a single-zero wheel. Following is a summary of the results.

Count of the Hottest Number in 3,700 Spins on Single-Zero Wheel

Statistic	Value
Mean	121.90
Median	121
Mode	120
90th Percentile	128
95th Percentile	131
99th Percentile	136
99.9th Percentile	142

The following table shows the full results of the simulation on both wheels. The two commulative columns show the probability that the count of the hottest number is the number on the left column or more. For example, the probability the hottest number in 3,700 spins of single-zero roulette is 130 or more is 0.072044.

Summary of the Count of the Hottest Number in 3,700 Spins of Single-Zero Roulette and 3,800 spins of Double-Zero Roulette

Count	Probability Single Zero	Cummulative Single Zero	Probability Double Zero	Cummulative Double Zero
160 or More	0.000001	0.000001	0.000001	0.000001
159	0.000000	0.000001	0.000000	0.000001
158	0.000001	0.000001	0.000001	0.000001
157	0.000001	0.000002	0.000001	0.000002
156	0.000001	0.000003	0.000001	0.000003
155	0.000002	0.000005	0.000002	0.000005
154	0.000003	0.000009	0.000003	0.000008
153	0.000005	0.000013	0.000005	0.000013
152	0.000007	0.000020	0.000008	0.000021
151	0.000012	0.000032	0.000012	0.000033
150	0.000017	0.000049	0.000018	0.000051
149	0.000026	0.000075	0.000027	0.000077
148	0.000038	0.000114	0.000041	0.000118
147	0.000060	0.000174	0.000062	0.000180
146	0.000091	0.000265	0.000092	0.000273
145	0.000132	0.000397	0.000137	0.000409
144	0.000195	0.000592	0.000199	0.000608
143	0.000282	0.000874	0.000289	0.000898
142	0.000409	0.001283	0.000421	0.001319
141	0.000580	0.001863	0.000606	0.001925
140	0.000833	0.002696	0.000860	0.002784
139	0.001186	0.003882	0.001215	0.003999
138	0.001652	0.005534	0.001704	0.005703
137	0.002315	0.007849	0.002374	0.008077
136	0.003175	0.011023	0.003286	0.011363
135	0.004355	0.015378	0.004489	0.015852
134	0.005916	0.021295	0.006088	0.021940
133	0.007939	0.029233	0.008196	0.030136
132	0.010601	0.039834	0.010908	0.041044
131	0.013991	0.053824	0.014384	0.055428
130	0.018220	0.072044	0.018757	0.074185
129	0.023498	0.095542	0.024114	0.098299
128	0.029866	0.125408	0.030603	0.128901
127	0.037288	0.162696	0.038228	0.167130
126	0.045771	0.208467	0.046898	0.214027
125	0.055165	0.263632	0.056310	0.270337
124	0.064853	0.328485	0.066020	0.336357
123	0.074178	0.402662	0.075236	0.411593
122	0.081929	0.484591	0.082885	0.494479
121	0.087158	0.571750	0.087696	0.582174
120	0.088520	0.660269	0.088559	0.670734
119	0.084982	0.745252	0.084406	0.755140
118	0.076454	0.821705	0.075245	0.830385
117	0.063606	0.885312	0.061851	0.892236
116	0.048069	0.933381	0.046111	0.938347
115	0.032432	0.965813	0.030604	0.968952
114	0.019117	0.984930	0.017664	0.986616
113	0.009567	0.994496	0.008614	0.995230
112	0.003894	0.998390	0.003420	0.998650
111	0.001257	0.999647	0.001065	0.999715
110	0.000297	0.999944	0.000243	0.999958
109	0.000050	0.999994	0.000038	0.999996
108 or Less	0.000006	1.000000	0.000004	1.000000

Count of the Hottest Numbers in 300 Spins in Double-Zero Roulette

What if you don't want to spend 100 hours gathering data on a single wheel? Some casinos are kind enough to give you, on a silver platter, the number of times in the last 300 spins the four 'hottest' and 'coolest' numbers occurred. The image at the top of the page shows an example taken on a double-zero wheel at the Venetian.

In 300 spins, the average number of wins on a double-zero wheel for any number is 300/38=7.9. As you can see from the image above, the four hottest numbers were 20, 5, 29, and 2, which occurred 15, 14, 13, and 12 times respectively. Is this unusual? No. In a simulation of over 80 billion spins, the most frequent number, in 300-spin experiments, appeared most frequently at 14 times with a probability of 27.4%. The most likely total of the second, third, and fourth most frequent numbers was 13, 12, and 12 times respectively, with probabilities of 37.9%, 46.5%, and 45.8%. So the results of the 'hottest' numbers in the image above were a little more flat than average.

The following table shows the probabilities of the four hottest numbers in 300 spins of double-zero roulette. For example, the probability the third most frequent number happens 15 times is 0.009210.

Count of the Hottest Four Numbers in 300 Spins on a Double-Zero Wheel

Observations	Probability Most Frequent	Probability Second Most Frequent	Probability Third Most Frequent	Probability Fourth Most Frequent
25 or More	0.000022	0.000000	0.000000	0.000000
24	0.000051	0.000000	0.000000	0.000000
23	0.000166	0.000000	0.000000	0.000000
22	0.000509	0.000000	0.000000	0.000000
21	0.001494	0.000001	0.000000	0.000000
20	0.004120	0.000009	0.000000	0.000000
19	0.010806	0.000075	0.000000	0.000000
18	0.026599	0.000532	0.000003	0.000000
17	0.060526	0.003263	0.000060	0.000001
16	0.123564	0.016988	0.000852	0.000020
15	0.212699	0.071262	0.009210	0.000598
14	0.274118	0.215025	0.068242	0.011476
13	0.212781	0.379097	0.283768	0.117786
12	0.067913	0.270747	0.464748	0.457655
11	0.004615	0.042552	0.168285	0.383900
10	0.000017	0.000448	0.004830	0.028544
9	0.000000	0.000000	0.000001	0.000020
Total	1.000000	1.000000	1.000000	1.000000

The next table shows the mean, median, and mode for the count of the first, second, third, and fourth hottest numbers in millions of 300-spin simulations of double-zero roulette.

Summary of the Count of the Four Most Frequent Numbers in 300 Spins of Double-Zero Wheel

Order	Mean	Median	Mode
First	14.48	14	14
Second	13.07	13	13
Third	12.27	12	12
Fourth	11.70	12	12

Count of the Coolest Numbers in 300 Spins in Double-Zero Roulette

The next table shows the probability of each count of the four collest numbers in 300 spins of double-zero roulette.

Count of the Coolest Four Numbers in 300 Spins on a Double-Zero Wheel

Observations	Probability Least Frequent	Probability Second Least Frequent	Probability Third Least Frequent	Probability Fourth Least Frequent
0	0.012679	0.000063	0.000000	0.000000
1	0.098030	0.005175	0.000135	0.000002
2	0.315884	0.088509	0.012041	0.001006
3	0.416254	0.420491	0.205303	0.063065
4	0.150220	0.432638	0.595139	0.522489
5	0.006924	0.052945	0.185505	0.401903
6	0.000008	0.000180	0.001878	0.011534
Total	1.000000	1.000000	1.000000	1.000000

The next table shows the mean, median, and mode for the count of the first, second, third, and fourth coolest numbers in the 300-spin simulations of double-zero roulette.

Summary of the count of the Four Least Frequent Numbers on a Double-Zero Wheel

Order	Mean	Median	Mode
Least	2.61	3	3
Second Least	3.44	3	4
Third Least	3.96	4	4
Fourth Least	4.36	4	4

Count of the Hottest Numbers in 300 Spins of Single-Zero Roulette

In 300 spins, the average number of wins on a single-zero wheel for any number is 300/37=8.11. The next table shows the probability of each count of the four coolest numbers in 300 spins of double-zero roulette. For example, the probability the third most frequent number happens 15 times is 0.015727.

Count of the Hottest Four Numbers in 300 Spins on a Single-Zero Wheel

Observations	Probability Most Frequent	Probability Second Most Frequent	Probability Third Most Frequent	Probability Fourth Most Frequent
25 or More	0.000034	0.000000	0.000000	0.000000
24	0.000078	0.000000	0.000000	0.000000
23	0.000245	0.000000	0.000000	0.000000
22	0.000728	0.000000	0.000000	0.000000
21	0.002069	0.000002	0.000000	0.000000
20	0.005570	0.000018	0.000000	0.000000
19	0.014191	0.000135	0.000000	0.000000
18	0.033833	0.000905	0.000008	0.000000
17	0.074235	0.005202	0.000125	0.000001
16	0.144490	0.025286	0.001624	0.000050
15	0.232429	0.097046	0.015727	0.001286
14	0.269735	0.259360	0.101259	0.021054
13	0.177216	0.382432	0.347102	0.175177
12	0.043266	0.208137	0.429715	0.508292
11	0.001879	0.021373	0.102979	0.283088
10	0.000003	0.000103	0.001461	0.011049
9	0.000000	0.000000	0.000000	0.000002
Total	1.000000	1.000000	1.000000	1.000000

The next table shows the mean, median, and mode for the count of the first, second, third, and fourth hottest numbers in millions of 300-spin simulations of double-zero roulette.

Summary — Count of the Four Hottest Numbers — Double-Zero Wheel

Order	Mean	Median	Mode
First	14.74	15	14
Second	13.30	13	13
Third	12.50	12	12
Fourth	11.92	12	12

Count of the Coolest Numbers in 300 Spins in Single-Zero Roulette

The next table shows the probability of each count of the four coolest numbers in 300 spins of double-zero roulette. For example, the probability the third coolest numbers will be observed five times is 0.287435.

Count of the Coolest Four Numbers in 300 Spins on a Double-Zero Wheel

Observations	Probability Least Frequent	Probability Second Least Frequent	Probability Third Least Frequent	Probability Fourth Least Frequent
0	0.009926	0.000038	0.000000	0.000000
1	0.079654	0.003324	0.000068	0.000001
2	0.275226	0.062392	0.006791	0.000448
3	0.419384	0.350408	0.140173	0.034850
4	0.200196	0.484357	0.557907	0.406702
5	0.015563	0.098547	0.287435	0.521238
6	0.000050	0.000933	0.007626	0.036748
7	0.000000	0.000000	0.000001	0.000013
Total	1.000000	1.000000	1.000000	1.000000

The next table shows the mean, median, and mode for the count of the first, second, third, and fourth coolest numbers in the 300-spin simulations of single-zero roulette.

Summary of the count of the Four Least Frequent Numbers on a Single-Zero Wheel

Order	Mean	Median	Mode
Least	2.77	3	3
Second Least	3.62	4	4
Third Least	4.15	4	4
Fourth Least	4.56	5	5

The least I hope you have learned from this article is it is to be expected that certain numbers will come up more than others. To put it in other words, it is natural that some numbers will be 'hot' and some 'cool.' In fact, such differences from the mean are highly predictable. Unfortunately, for roulette players, we don't know which numbers will be 'hot,' just that some of them almost certainly will be. I would also like to emphasize, contrary to the Gambler's Fallacy, that on a fair roulette wheel that every number is equally likely every spin and it makes no difference what has happened in the past.

Finally, it should not be interpreted that we give an endorsement to the 888 Casino, which we linked to earlier. I am very bothered by this rule in their rule 6.2.B. Before getting to that, let me preface with a quote from rule 6.1, which I'm fine with.

'If we reasonably determine that you are engaging in or have engaged in fraudulent or unlawful activity or conducted any prohibited transaction (including money laundering) under the laws of any jurisdiction that applies to you (examples of which are set out at section 6.2 below), any such act will be considered as a material breach of this User Agreement by you. In such case we may close your account and terminate the User Agreement in accordance with section 14 below and we are under no obligation to refund to you any deposits, winnings or funds in your account.' -- Rule 6.1

Let's go further now:

The following are some examples of 'fraudulent or unlawful activity' -- Rule 6.2

Next, here is one of many examples listed as rule 6.2.B

'Unfair Betting Techniques: Utilising any recognised betting techniques to circumvent the standard house edge in our games, which includes but is not limited to martingale betting strategies, card counting as well as low risk betting in roulette such as betting on red/black in equal amounts.' -- Rule 6.2.B

Let me make it perfectly clear that all betting systems, including the Martingale, not only can't circumvent the house edge, they can't even dent it. It is very mathematically ignorant on the part of the casino to fear any betting system. Why would any player trust this casino when the casino can seize all their money under the reason that the player was using a betting system? Any form of betting could be called a betting system, including flat betting. Casino 888 normally has a pretty good reputation, so I'm surprised they would lower themselves to this kind of rogue rule.

Written by: Michael Shackleford

By Ion Saliu,
Founder of Gambling Science, Spin Doctor in Roulette Mathematics

I. An Act of Napster-Like Piracy Makes the Super Roulette Strategy Freeware
II. Mathematical Roulette Systems Based on the Fundamental Formula of Gambling (FFG)

• A. Mathematics of Super Roulette Strategy
• B. Roulette Systems: Probability = 2/3
• C. Roulette Systems: Probability = 1/2
• D. Roulette Systems to Avoid

III. Roulette Software, Actual Casino Spins to Analyze and Test Systems
IV. Roulette, Gambling Resources, Software, Systems, Strategies

I. An Act of Napster-Like Piracy Makes the Super Roulette Strategy Free

The definitive version offered in 1999; first capture by the WayBack Machine (web.archive.org) on December 12, 2005.

• I was shocked to learn (2005) that a licensed roulette strategy I sold in 2000 became freely available as the music at Napster in the past. At least one guy collected over 300 roulette systems and made them available to everybody.
• I discovered three of my roulette systems. The first one, Handy, was formerly named Handy-Brandy. It is now known as the Free Winning Roulette System #1.
• The Licensed roulette system and Limited are one and the same. It is that old roulette strategy I sold in 2000 to a limited number of people. Many of them did not deserve my generosity. I suspect, most of them were casino moles and/or disgruntled gambling authors who sell fraudulent roulette systems.
• I decided to make the formerly licensed roulette strategy available as freeware. It is an act of justice. The pirates already possess my systems illegally. Let also honest people get to know, and certainly use, my super roulette strategy. My act is an equalizer. If the roulette winners with my systems want to be generous, in addition to being fair, I won't mind!

Most of the gambling roulette systems I saw pile up to nothing more than junk. Very few strategies have some value by just touching mathematics. Surprise, surprise — I saw also Powerplay Roulette on the list! Remember the gambler named Chip who caused some disruption at this Web site? 'Chip Casher' said that Power Play Roulette System sold for some $5,000 (five thousand US dollars!)

• If PowerPlay Roulette System sells for $5000, then my Super Roulette Strategy must be worth at least $50,000!
• If Don Young's Roulette System sells for $10,000, then my Super Roulette Strategy must be worth at least $100,000!
• If Intrinseca Ludica Roulette System sells for $10,000, then my Super Roulette Strategy must be worth at least $100,000!
• If Epocal Storm Roulette Strategy costs gamblers $40,000, then my Super Roulette Systems must be worth one million dollars ($1, 000,000)!
• Actually, if any roulette system/strategy/method sells for just $100, then my Super Roulette Systems must be worth at least $100,000!

No exaggeration! Let them take me to court, if they wish or dare — I'd make the same statements and produce compelling evidence! Better still, I suggest you take my statements to the bank! By the way, I licensed my Super Roulette Strategy for only $100 back in the year of grace 2000! No wonder (some of) the gambling suckers I sold my super systems to reacted cutthroat-like against me. They wanted me to STOP licensing my roulette systems!

Here is a long list of roulette systems saved for future reference. I can't believe how much fraud there is! I am suspicious and say it again: Only the casinos would be so fiercely aggressive and sell roulette and gambling strategies priced from US $5000 (five thousand) to US $40000 (forty thousand)! No individual gambling system developer would be thus fearless and dare to sell such outrageously priced casino gambling systems! It could turn deadly for him! Read this page:

• An inventory of free and outrageously pricedroulette systems.

II-A. Mathematics of Super Roulette StrategyMathematical Roulette Systems: Super Roulette Strategy version 3.0
(C) Copyright 1999-2000 Ion Saliu. All rights reserved

(as it first appeared on paper).

• The roulette systems in this collection are based on The Fundamental Formula of Gambling (FFG). The FFG is presented in detail on my Web page Gambling Formula: Degree of Certainty, Probability, Mathematics, Chance. You can download the page and print it. Although you do not need to memorize it, FFG can help you a great deal in better understanding these systems. The Formula, if understood well, can make clearer that probability events (or random events, or gambling) actually follow precise rules.
• The infamous gambler's fallacy is, in itself, a mathematical absurdity. In a nutshell, the fallacious fallacy warns that the losing streaks can be indefinite while the winning streaks are non-existent. My probability software Streaks undeniably probes that all streaks, win or loss, follow mathematical formulas. There is bias to the left (L) or bias to the right (W), but at the end of the day every streak occurred according to theory of probability.

A) The probability p for a single zero roulette game is: p = 1/37 = 0.027.
We apply the Fundamental Formula of Gambling to one value of DC (degree of certainty): 66.6% (or 2/3, 2 out of 3 cases). For DC = 66.6%: N = 40.4 (rounded up to 41 spins). There is a 66.6% (2 in 3) chance that each roulette number will repeat after 41 spins. Equivalently, there is a 66.6% chance that the next spin will be a number that also appeared within the last 41 spins.

B) The probability p for a double zero roulette game is: p = 1/38 = 0.026.
We apply the Fundamental Formula of Gambling to one value of DC (degree of certainty): 66.6% (or 2/3). For DC = 66.6%: N = 41.5 (rounded up to 42 spins or 41 for single-zero wheels). There is a 66.6% (2 in 3) chance that each roulette number will repeat after 42 spins. Equivalently, there is a 66.6% chance that the next spin will be a number that also appeared within the last 42 spins.

The accompanying roulette program SuperRoulette simulates spins for the double-zero roulette game in order to cover the worst-case scenario. We'll use now only the final part of the report. After a very large number of spin simulations, the 42-spin value confirmed FFG. Also importantly, even smaller number of roulette spins confirm FFG for a DC = 66.6%. Let's use the Fundamental Formula of Gambling with confidence. That's what formulas are for.

We'll use this number (42) in correlation with limited-steps Martingales (bets based on a Martingale progression). Basically, Martingale represents a gambling betting method. It doubles up the previous bet until the last step of the betting. For example, a 4-step Martingale using a one-unit bet follows this path: 1 unit; 2 units; 4 units; 8 units (step 4, end of betting). Don't worry about using a Martingale: the Formula makes Martingale a closed betting gambling system (a system with a limited number of steps).

• What you need is a notebook and a pencil. Write down the last roulette spins, from the oldest one available to the most recent spin. Do not start playing until you have at least 42 spins on your piece of paper. I prefer a small notebook with 20 rule lines. Multiples of 10 or 20 make it easy to count quickly the number of roulette spins. Use the roulette report that follows as the template (rows and columns).

The win/loss WL streaks report was generated by the gambling software Super Roulette, available to all registered members of this Web site.

The column Last 26 Roulette Spins reflects a DC (Degree of Certainty — see FFG, Fundamental Formula of Gambling) of 50% (it is 25 for single-zero casino roulette wheels). In half the situations, the next roulette number would have also appeared in the previous 26 spins. I decided not to use a betting system based on a DC = 50%. The losing streak can reach sometimes 10-13 spins in a row. Also, the losing/winning streaks are far more irregular. Instead, I chose to base my gambling betting systems on DC = 66% since the winning/losing streaks are a whole lot more manageable.

SYSTEM 1: Applies to Report Column Last 42 Roulette Spins.
The degree of certainty is 66.6% that the next spin will be a number that also appeared within the last 42 spins. In most cases, there are 25-26 numbers to play, since some numbers are repeats. The advantage of this system: the losing streaks (L or -) are far shorter, more regular, and less frequent.
From the opposite viewpoint, the winning streaks (W or +) are far longer, more regular, and more frequent. We can play a more efficient and safer Martingale.

First, we need to keep a good record of the spins. We (you, if you will) need to make the record accurate and easy to read. AFTER the spin # 42, write down + or W if the number was a repeat from the last 42 spins; or - or L if the roulette number was not a repeat from the last 42 spins. Also, keep writing the numbers drawn. You'll write two rows such as:
16,11,16,15,20,36,28,32,19,28,13,24,2,16,23,31,10,19,27,8,26,27, 00,19,16,12,36,18,9,8,30,6,14,17,25,12,8,3,17,18,10,13, 7,14,2,19,7,24,32,2,25,11,13,29,17,25,25,14,26......... (1st row!)
-- keep a few empty lines for more spins ---
-++++++++-+-+++++ (2nd row)

The bar after #13 marks the start of the betting for System 2. The first number drawn after you marked the start of the betting is 7. It does not appear among the previous 42 spins, so you write a - in the streak column. I prefer +/- rather than W/L because I can visualize easier the winning/losing streaks. The next operation is to write another bar after 16. It will make it easier to figure out the current 42-number roulette block. In this example, it will be between 11 (the number following 16) and 7.

The next number drawn was 14, which appeared also in the previous 42 spins. Write a + in the streak column. Write another bar after 11. The new 42-number block will span between 11 and the 14 just drawn.

So, you always write down the very last number drawn and move the marking bar one number to the right. This way, you don't have to count the previous 42 spins. Place your chips on the numbers between the two bars marking the latest 42-number block. Of course, some numbers are repeats, so you only need to play each number once. In most cases, you'll only play 26 unique roulette numbers (sometimes 24, sometimes 27).

II-B. Roulette Systems Based on p = 2/3 (close to 66.6%)

S1.1: Applies to Report Column: Last 42.
It is very rare that there are more than two consecutive groups of LL or longer than 2L. Therefore, at the end of the 2nd LL or longer streak we'll bet 1 unit on all the numbers drawn in the last 42 spins (24-27 numbers to cover).

In most cases, we'll win right away. If not, we wait for the next LL or longer streak. We'll use a power-3 Martingale: 1-3-9-27 etc. When the LL streak ends, we'll bet 3 units on all the numbers drawn in the last 42 spins. It may be even less frequent to encounter another LL or longer streak. If it occurs, we may regret if we didn't continue the Martingale with a 9-unit bet!

S1.2: Applies to Report Column: Last 42.
In reverse, we can bet on W groups longer or equal to two (WW, WWW, WWWW, etc.) Now, we wait for two consecutive groups of single W.At the next W (after an L) we bet that it'll be another W. In most cases, we'll win right away. If not, we'll bet 3 units at another W after an L.

°° The safer variations on the last two roulette betting methods. We can wait for three single W groups and bet directly $10 or $20 at the very next W after an L. There is no such an occurrence in the report above. It might occur, albeit rarely. We can wait for three LL groups (2L or longer) and bet directly $10 or $20 at the very next L after a W. There is no such an occurrence in the report above.

Variations

* You can also bet directly $10 (or 2 units) after the second L in an LL roulette sequence.

Last Second Roulette Rules

° Or, we can bet directly $20 (or 4 units) after the third L in an LLL sequence.

What would the cost amount to? $10 x 26 numbers = $260.
The winning: $36 x 10 = $360.
Profit: $100.

Based on the Fundamental Formula of Gambling, these are the streaks for a probability p=0.666. The degree of certainty DC is 95% that the losing streaks will be no longer than 3 (LLL). The degree of certainty DC is 99% that the losing streak will not be longer than 4 consecutive losses (LLLL).

The chance of coming across 3 consecutive LLL groups is :
5% (0.05) to the power of 3 = 0.000125 (1.25 in 1000).
The chance of coming across 3 consecutive LLLL groups is :
1% (0.01) to the power of 3 = 0.000001 (0.001 in 1000).

The 66.6% probability offers a tremendous advantage over probabilities around 50%. First and foremost, the losing streaks are definitely shorter. There is a 99.9% degree of certainty that the losing streak will be no longer than 6 when p=66.6%. That can make possible to use an intelligent Martingale after a second or (more safely) third loss in a row (LL or LLL). In 999 out of 1000 roulette spins, the L streak will go no longer than 6. Therefore, a Martingale will go no longer than 4 or 5 steps. That is perfectly manageable within the minimum/maximum ratios at the roulette tables.

Secondly, the winning (W) streaks are definitely longer than the losing (L) streaks. It is very rare that two groups of single W will not be followed by W streaks longer than two (WW, WWW etc.). We can reverse the Martingale technique presented above. After the second single W (such as LWLLWL) we'll start another 4 or 5-step Martingale.

We should also expect (high expectation, indeed) that W streaks of 4 or longer are common. Therefore, if we do not see such W streaks in the last 3-4 W streaks, we should bet they will occur soon. If there is a W/L string such as WWLWLLWLWWLLW I can bet there will be another W, and another one.

* The disadvantage of the roulette systems based on p=2/3: the use of a power-3 Martingale: 1-3-9-27-81.
The Roulette Systems based on p=1/2 applies a power-2 Martingale: 1-2-4-8-16...

These roulette systems are a variation of SYSTEM 1, based on the 66.6% degree of certainty. At the same time, they are a reply to the fictitious roulette 'system' presented in the James Bond novels and films. No doubt, the author of the James Bond novels, Ian Fleming is a person with a strong interest in roulette. He noticed what I presented above: the winning streaks tend to be longer than one (WW or longer) for degrees of certainty above 50%.

Fleming, however, has no clue on the mathematical foundations of such occurrences. James Bond plays 1-12 AND 13-24, betting large amounts of money. Since it is fiction, James Bond always wins at the roulette table! Now, if any person in this world will walk to a roulette table and place bets on 1-12 AND 13-24, he/she will win a 2-to-1 payoff 65% of the times at French roulette (64% playing American roulette).

In other words, if you would play this way at any roulette table three times in a row, you will win a 2-to-1 payoff two times (not necessarily twice in a row). You will also lose once, roughly. That's a far cry from the 100% winning insinuated by Fleming in his book Casino Royale.

You should never, ever play in that manner at the roulette table! You should enter the game at favorable moments, as presented in SYSTEM 1. When such favorable moments occur, get ready to use a limited-step Martingale (no longer than 4 or 5 steps). The betting sequences are 1-3-9-27 etc. This is determined by the 2-to-1 payoff when playing 12 roulette number groups (douzaine in French).

When using this betting plan, you are only allowed to place bets on numbers 1 to 36. You are not allowed to include 0 (or 0 and 00) in the groups of numbers you bet on. The 36 numbers can be divided into three groups: A (1-12 and 13-24); B (1-12 and 25-36); C (13-24 and 25-36). Each of the three groups (A, B, or C) has an equal probability: p = 64% (in the American roulette) or p = 65% (in the French roulette). The two probabilities are very close to the degrees of certainty we used as the foundation of SYSTEM 1 (66.6%). Consequently, we will encounter virtually the same composition of the W and L streaks.

SYSTEMS 1.3, 1.4, 1.5 do not require a long tracking session at the roulette table. The table will show the last 20 spins, so you can start betting immediately. You can choose to play only one of the three double-douzaine groups: A, B, or C. Or, you can play two of the groups, or all three groups. It is best, however, to keep track of all three groups. Only one of the three double-douzaine groups will have a stronger advantage over shorter tracking sessions.

We apply the same betting principles presented in SYSTEM 1. The structures of the W+/L- streaks are very close to the W+/L- strings encountered in SYSTEM 1. Keep in mind this mathematical rule. When the probability p is significantly above 50% (10%+ above 1/2), most of the winning streaks (W+) are two in length or longer (WW, WWW, WWWW, etc). On the other hand, most of the losing streaks (L-) are singles (LWWLWLWWWLLWLW...). When betting, we know that only rarely will we encounter:

° More than three consecutive groups of LL or longer (LLL, LLLL ...). Using the +/- notation and a real report generated by SuperRoulette, a W/L streak looks like this: ++-+++--+--+++--++-+
You can see three consecutive groups of LL (--). The very next L group was single (-), ending the L streak longer than or equal to 2.

° More than three consecutive groups of single W+. Using the +/- notation and a real report generated by Super-Roulette special program, a W/L streak looks like this: --+++++----+-+---+++
You can see two consecutive groups of single W+. The very next W group was longer than 2, ending the single W+ streak.

Based on the two probability facts, we can devise two betting methods. They are similar to the methods described in SYSTEM 1.

S234.1: We check to see which of the groups A, B, C has two or more consecutive groups of LL or longer. At the end of two consecutive groups of LLW or longer (LLLW, LLLLW, etc.) we place one unit bet on a douzaine and another unit bet on the other douzaine of the A, or B, or C group. Let's look at a practical example. Group A has had the following streak: ++-+++--+--+++--++-+, or using the W/L notation: WWLWWWLLWLLWWWLLWWLW

You can notice three consecutive LLW groups. The second group is LLWWW; then an L (or -) follows. You start betting right there, after the first L. You know that there is a high probability to get a single L. In this example (a real case, though), you lost your roulette bet. The first L was followed by another one.

The L streak ended with WW. Another L follows. You start betting again after that first L. The probability is even higher now for L to be single (that is, it will be followed by W). Bet now 3 units on the first roulette douzaine of the group and 3 units on the other douzaine of the group. In this case, you won a 2-to-1 bet. You won 3 x 3 units = 9 units. Your cost was 3 units + 3 units = 6 units. The net gain is 3 units. But you lost the previous bet: 1 unit + 1 unit = 2 units. Deducting 2 units from the gain above, your final gain is 1 unit.

S234.2: We check to see which of the groups A, B, C has two or more consecutive streaks of single W.
At the end of two consecutive groups of WL we place one unit bet on a dozen and another unit bet on the other dozen of the A, or B, or C group.

Let's look at a practical example. Group A has had the following streak: --+++++----+-+---+++, or using the W/L notation: LLWWWWWLLLLWLWLLLWWW. You can notice two consecutive LWL groups (isolated W or +). The second group is LWLLL. Then a W (or +) follows. You start betting right there, after the first W. You know that there is a high probability to get a W longer than one (WW, WWW, etc.). In this example, you bet $10 + $10 (after that 1st W) that another W will follow. It actually did happen, so your payoff was $30 ($10 profit).

If it did not happen (as in case S234.1 above), you would continue with a double-up base-3 bet: $30 + $30 = $60. In by-far-most cases, you will win a $90 payoff. The profit would be:
$90 - $60 - $20 = $10.
Do not fear reality. If you lost again, you would continue with a double-up base-3 bet:
$90 + $90 = $180. In the most cases, you will win a $270 roulette payoff. The profit would be:
$270 - $180 - $60 - $20 = $10.
You can still lose another step and double-up within the roulette table maximum bet. Losing that many steps in this manner is so extremely rare, that it may take to play the roulette for many, many thousands of spins in a row.

•• The safer variations on the last two betting methods.
We can wait for three single W groups and bet directly $10 or $20 at the very next W after an L.
We can wait for three LL groups (2L or longer) and bet directly $10 or $20 at the very next L after a W.

Variations

* You can also bet directly $10 after the third L in an LLL sequence.
* Or, we can bet directly $20 after the fourth L in an LLLL sequence.

II-C. Roulette Systems Based on p = 1/2 (close to 50%)

We apply the Fundamental Formula of Gambling to a value of DC (degree of certainty): 50% (or 1/2).
For DC = 50% => 25 (rounded up to 26 spins). There is a 50% (1 in 2) chance that each roulette number will repeat after 26 spins. Equivalently, there is a 50% chance that the next spin will be a number that also appeared within the last 26 roulette spins.

I was reluctant to recommend roulette systems based on p=1/2. People may be tempted to use Martingales that a losing streak will end within 4 or 5 steps. Please do not do that: A losing streak can reach 13-15 spins at times, albeit rarely! Instead, I will show you a more intelligent type of betting. They are similar to the systems in category 1. They also use a power-2 Martingale: 1-2-4-8 since the payoff is 1-to-1.

S2.1: It is very rare that there are more than three consecutive groups of LL or longer than 2L.
Therefore, at the end of the 3rd LL or longer streak we'll bet 1 unit on all the roulette numbers drawn in the last 26 spins (17-20 numbers to cover, 18 in most cases). In most cases, we'll win right away. If not, we wait for the next LL or longer streak. We'll use a power-2 Martingale: 1-2-4-8 etc. When the LL streak ends, we'll bet 2 units on all the roulette numbers drawn in the last 26 spins. It may be even less frequent to encounter another LL or longer streak. If it occurs, we may regret if we didn't continue the Martingale with a 4-unit bet!

S2.2) In reverse, we can bet on W groups longer or equal to two (WW, WWW, WWWW, etc.) Now, we wait for three consecutive groups of single W. At the next W (after an L) we bet 2 that it'll be another W. In most cases, we'll win right away. If not, we'll bet 4 units at another W after an L.

°° The safer variations on the last two betting methods. We can wait for four single W groups and bet directly 4 units at the very next Win after a Loss. We can wait for four LL groups (2L or longer) and bet directly 4 units at the very next L after a W.

SYSTEMS 2.3, 2.4, 2.5 cover the even-money bets: Red/Black, Odd/Even, High/Low. They follow the same rules as S2.1 and S2.2.In this case, however, we do not track W/L, but B/r, o/E, H/l.

• Let's take the Black/Red bet. Write first the numbers drawn:

36 10 29 25 16 1 22 4 7 23 26 4 10 29 21 27 16 15 6 37 19 22 29 36 18 16 30 37 35 10 37 15 16.

Next, write down what the roulette number represents: B for black, r for red and x for 0/00:

rBBrrrBBrrBBBBrrrBBxrBBrrrrxBBxBr.

Last Second Roulette Games

Bet 2 units after the 1st B in the 4th B group 2 or longer (it is BB after the 3rd r in the row above). We lost, because the BB streak did not end there. The next B (black at roulette) group of 2 Bs or longer meant we lost again; this time we lost 4 units. Another BB group follows and we bet 8 after the 1st B in the group; there is an x, then another B. We win this time. A safer variation is to wait for four consecutive BB or longer groups. They occur far more rarely, however.

We can do the same thing betting on r. You can notice there are 3 rr or longer groups (rrr, rr, rrr). They are followed by a single r (...BxrB...)

Last Second Roulette Movie

• As in System S1.2, we bet on the continuation of singles (single B, single r, etc.). Let's look at this Odd/Even streak:

oooEoExoEoEEEExoExoEoEEoEooE.

We bet 2 units after the 3rd single o. We lose. More single o groups followed and we used the following Martingale: 4 (loss) - 16 (loss) - 32 (loss) - 64 (WIN). 64 times $5 = $320, an acceptable maximum limit at most roulette tables. The roulette game in Garmisch-Partenkirchen, Germany has a maximum limit of DM 6000 for even-money bets (for a DM 5 minimum limit).

• Can you keep track of all the roulette betting systems presented here? It is difficult in the beginning, but not impossible to write down the roulette numbers in rows & columns. Practice in a real casino, at a real roulette table helps a great deal.
• First practice, then play roulette with real money. The advantage of keeping track of all betting systems: CHOICES. You have plenty of options to choose from in a short time. You don't need to track a large number of spins until one of the favorable situations will come up. It is very likely that you will find yourself in a betting situation right after writing down the first 15 numbers displayed at the roulette table (the marquee).
• A team of two players at the same roulette table is even more efficient.

II-D. Roulette Systems to Avoid

SA1: Straight-Up Bet on One Favorite Roulette Number Only the payoff is enticing in this case (35-to-1), but you are assured of losing at a rate of 5.26% of your total bets. The roulette software you get with this system (SuperRoulette) shows lengthy reports on each roulette number. The roulette wheel does not favor any number whatsoever. There is a discrepancy among numbers, but there is no strong bias towards a particular one -- unless the wheel is worn out.

Some roulette numbers hit more frequently than others within certain ranges of spins. Percentage-wise, the frequency differences are not mathematically significant. And nobody can accurately predict which number will be more frequent within the next range. The operative word here is SKIP. The SKIP represents the number of roulette spins a number waits between hits. The skip varies between 0 (zero, i.e. consecutive hits; it is also 1: number of spins back) to over 200.

These roulette skip values are absolutely in accordance with the Fundamental Formula of Gambling. It will be common occurrence that your favorite roulette number will skip over 100 spins at any given time (during your playing session). So, what's the big deal of winning $36 after you lost $100? How about waiting 200 roulette spins for your number to hit? It really happens! Also, it is very unwise to track 100, or 200 spins, given the $35 potential win!

Conclusion: I do not recommend you play a favorite roulette number.

SA2: Bet That the Next Roulette Number Will Be a Consecutive Hit

It certainly happens around 26 times in 1000 spins. Playing this way, we still lose 5.26% of our total bets. As you can notice in the SuperRoulette reports, sometimes it happens 35 times (or more!) to encounter consecutive hits in 1000 roulette spins! Indeed, there are these situations: You play on consecutive hits and win 30 times (or more) within 1000 roulette spins. You are a winner! But that doesn't happen all the time, first of all. Secondly, the profit is not that big. Keep in mind also that you can wait for a consecutive hit over 150 spins sometimes...

Conclusion: It's not worth the risk! You should use it only when you must play in order to keep your seat at the roulette table! You can improve the outcome somehow by skipping some spins.

SA3: Instead of betting on consecutive hits, you bet that the next number would have also hit in the last 0 to 9 roulette spins.

It is a combination of the two NON-betting methods presented above. In this case, the situation is more manageable, because the probability p is higher: p = 1/4 (approximately). You remember the rules above. If the probability p is significantly above 50%, there are more frequent winning streaks and shorter losing streaks. Conversely, if the probability p is significantly below 50%, the losing streaks are longer. In the case of p = 1/4, the losing streaks can reach over 30 roulette spins! It's dangerous to bet with the expectation that the next roulette number would have also hit in the last 0 (1) to 9 (10) spins.

Tracking is easier than in the case above, but still difficult. There is a new element we can use in these situations, however: the median. Look at the SuperRoulette roulette software reports (the ROULETTE.REP file). The median for 1 to 10 hits is 2 or 3. In half or a little more than half the cases, the median will be 2. In other words, the next roulette number will be a repeat from the previous 10 spins in a little more than half the cases when this betting hits.

More explicitly: This type of betting hits around 250 in 1000 spins (1 in 4). In a little more than 125 roulette spins, the betting will hit within 3 spins from one another! If you think it is complicated, it probably is. Don't continue to read it, IF you don't understand it! Keeping track of this type of betting is complicated, too. So complicated, that I do not recommend you use this type of roulette betting! Nobody knows better than me how the Fundamental Formula of Gambling works (the configuration of W/L streaks). You should use it only when you must play in order to keep your seat at the casino table! Especially use it when it hit within the last 3 spins.

• A blackjack version of my streak gambling theory and strategy is presented on this page:
• Gambling Streaks, Betting Martingale Progressions.
• See how casinos reacted to my playing the Super Roulette Strategy in Atlantic City:Fearing Losses, Casinos Bar, Ban Winning Gamblers, Skilled Gambling Players.

III. Roulette Software, Actual Casino Spins to Analyze and Test Systems

You can run Super Roulette many, many times and get very similar results every time. This roulette program is a command prompt 32-bit application (runs under Win9x, 2000, XP, Vista, Windows 7, 8). It replaces the old 16-bit Roulette. Both applications are now identical (32-bit) to diffuse any confusion from my previous writings or software offerings. Read useful information regarding the command prompt, how to best use software in non-graphical mode (much faster than GUI software, especially in lotto).

Look at the main screen of SuperRoulette (also Roulette) casino gambling software.

You can also download here two files with actual roulette spins recorded at the Hamburg, Germany casino. The file HAMB00.DAT covers the period February 1-6, 2000. The other file, HAMB0106.WH1, covers the entire month of January 2006 (7990 real-life roulette spins… I can only assume real or correct or accurate… it's impossible to verify such data!) The data files are ASCII or simple text files. They look very much like the random output files generated by Super Roulette in random mode (Random0.DAT or Random00.DAT). The files contain roulette numbers (spins) only, one number per line. The casino actuals have also other data, such as frequency and various statistics. The files also have dashed lines (----) which probably represent casino dealer changes.

Last Second Roulette Game

HAMB0106.WH1 that I edited and saved represents the best recording format: Table by table. Do not mix the spins from different roulette wheels in the same file. Also, the most recent roulette spin always goes to the top of the file, while the oldest spin (casino result) goes to the bottom (bottom line). Each file line contains one roulette spin and ends with a carriage return (pressing Enter). Make sure you do not leave any blank lines: They are treated as roulette number 0 (zero). If your file is for double-zero roulette tables, be sure to type 37 instead of 00.

By the way, those files can be precious items! Most casinos do not want to offer real roulette spins. Hamburg Spielbank sometimes offers results (actual spins), sometimes doesn't. Another German casino does the same thing: Spielbank Wiesbaden. You can try casino links like these two (not in directly-clickable format, because they change addresses way too frequently):
spielbank-hamburg.de/spielsaal/permanenzen.php4)
spielbank-wiesbaden.de/DE/621/Permanenzen2.php

• Read an interesting statistical report:
• wheel bias, roulette number pairings.
• If there is roulette wheel bias, then each roulette number must be followed preponderantly by certain numbers.
• I recommend you also check out that piece of great probability software: Streaks. It undeniably proves that all streaks, win or loss, follow mathematical formulas, NOT the gambler's fallacy.

Read Ion Saliu's first book in print: Probability Theory, Live!
~ Founded on valuable mathematical discoveries with a wide range of scientific applications, including probability theory applied to roulette gambling, software, Roulette Strategies.

Roulette: Software, Content, Resources, Systems, Super Roulette Strategy

See a comprehensive directory of the pages and materials on the subject of roulette, software, systems, and the Super Strategy.

• BrightR: PowerfulRoulette Software, Systems.
  It bundles in a convenient system the most important pieces of roulette software, accompanied by a visual tutorial.
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• Probability, Odds to Win Roulettein Various Number of Spins: To Be Ahead and Quit.
• Roulette Wheel Slots, Sectors Systems, Software, Birthday Paradox.
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• The James Bond Roulette System, Strategyin the Taliban Desert.
• Roulette Systems, Threats from a Casino Chairman.
• Anti-gambler Advice: John Patrick, Casino Mole, Conspirator.
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• Casinos Intimidate Intelligent Gambling System Authors.
• Download the best software.
• Many roulette software programs, casino spins, gambling systems are nicely bundled in BrightR, available to all registered members who pay a one-time low fee to download ALL software titles, programs, updates, upgrades.

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