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Hot Numbers in Roulette  Myths and Facts
Introduction
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 649 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 article by Frank Scoblete entitled . In that article, Scoblete recommends taking a count of each outcome for 3,700 spins in singlezero roulette and 3,800 spins in doublezero 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 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 30yearold handmedown 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 singlezero 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 DoubleZero 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 3800spin simulations.
Count of the Hottest Number in 3,800 Spins on DoubleZero 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 SingleZero Roulette
The results are very similar with 3,700 spins tracked on a singlezero wheel. Following is a summary of the results.
Count of the Hottest Number in 3,700 Spins on SingleZero 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 singlezero roulette is 130 or more is 0.072044.
Summary of the Count of the Hottest Number in 3,700 Spins of SingleZero Roulette and 3,800 spins of DoubleZero 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 DoubleZero 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 doublezero wheel at the Venetian.
In 300 spins, the average number of wins on a doublezero 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 300spin 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 doublezero 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 DoubleZero 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 300spin simulations of doublezero roulette.
Summary of the Count of the Four Most Frequent Numbers in 300 Spins of DoubleZero 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 DoubleZero Roulette
The next table shows the probability of each count of the four collest numbers in 300 spins of doublezero roulette.
Count of the Coolest Four Numbers in 300 Spins on a DoubleZero 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 300spin simulations of doublezero roulette.
Summary of the count of the Four Least Frequent Numbers on a DoubleZero 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 SingleZero Roulette
In 300 spins, the average number of wins on a singlezero 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 doublezero 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 SingleZero 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 300spin simulations of doublezero roulette.
Summary — Count of the Four Hottest Numbers — DoubleZero 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 SingleZero Roulette
The next table shows the probability of each count of the four coolest numbers in 300 spins of doublezero 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 DoubleZero 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 300spin simulations of singlezero roulette.
Summary of the count of the Four Least Frequent Numbers on a SingleZero 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 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