Electronic Roulette Wheel
Answer 1 of 24: All, I am heading to Vegas next week and want to find out which casinos have Electronic Roulette. I am talking about the one with a REAL roulette wheel but no dealers. The machine spins the ball every 30 - 45 seconds or so. I think IGT makes this. Of course it can and anyway why gamble on roulette when you are destined to lose anyway. Work out the probability and with a zero and very often a double zero only a dim brain would play for anything other than amusement and to lose money.
For as long as gamblers have wagered money on games of chance and skill, the temptation to cheat has loomed.
Unwilling to let fate decide, casino cheaters use creative and unscrupulous tricks to gain an unfair edge over the house.
Among the earliest methods employed by poker cheats, the gunslinging poker games of the Old West era saw cheats wield aces up their sleeves. These days, cheaters who plague poker can be found in both brick and mortar card rooms and online sites, colluding or dumping chips to team up on unsuspecting opponents.
Cheating in modern casinos predominantly afflicts the skill-based games like poker and blackjack, but you’d be surprised by how prevalent the crime has become in roulette and other games of chance. You wouldn’t think a simple wheel-spinning affair like roulette would be subject to cheating because players don’t really have any influence on the gameplay.
Nonetheless, cheats can be found anywhere real money is being wagered, and the roulette table is no exception. Even with the ever-present “eye in the sky” watching their every move, and eagle-eyed croupiers (dealers), pit bosses, and other staff members trained to detect malfeasance, roulette cheaters just can’t help themselves.
The allure of making easy money without incurring risk certainly makes sense, but trying to cheat the casino while playing roulette is a fool’s errand. Don’t take my word for it though, just ask the long lineup of convicted roulette criminals who tried the five ways to cheat at roulette listed below.
1 – Past Posting or Late Betting to Increase Wagers on Known Winners
Every roulette player knows the feeling well…
When you nail the number perfectly and watch the croupier stack the 35 to 1 payout, wishing you would’ve bet $10 instead of $1, the experience can be bittersweet to say the least. Beating long odds for a big payout is always cause for celebration, but when you only bet a few bucks, it can be easy to kick yourself for not putting more out there.
Some roulette cheaters aren’t content with their minimal payouts, so they resort to a tactic popularly referred to as “past posting.” Also known as “late betting,” the concept of past posting is quite basic on the surface. You add chips to your bet once you know it’s a winner.
When the croupier watches the wheel to find out where the ball landed, it will take them a split second to scan the spaces, find the ball, and turn their eyes back to the table before calling the number. In that split second, past posting artists use sleight of hand tricks to secretly add significant sums to their winning bet.
Let’s say you sprinkled various bets between $5 and $40 on several single-number spaces, using combinations of both the red $5 and green $25 chips. You have the number 17 covered with one $5 chip, but when you see the ball nestle into the 17 space, you instantly dart your hand out and cap the $5 bet with a $25 chip. The croupier never notices your trickery, and just like that, you’ve turned a $175 payout (35 to 1) on $5 into a whopping $1,050.
Why You Shouldn’t Try Past Posting
While potentially lucrative when undetected, past posting is inherently dangerous based on the moving parts in play.
A professional croupier is trained to scan and memorize the bets in play when they wave for final wagers, so they might notice your small chips suddenly transforming into big ones. While you’re watching the croupier, a nearby pit boss outside of your peripheral vision might see you make the switch. And up above, high-resolution cameras are recording every move you make.
Add it all up, and past posting just isn’t worth the risk involved, a fact Charbel Tannous and Constandi Lubbat can attest to. In 2011, while playing roulette at L’Auberge du Lac Casino Resort in Louisiana, the pair were caught red-handed past posting for big money.
After authorities used surveillance footage to confirm that over $175,000 was stolen via the roulette scheme, Tannous and Lubbat were charged with felony cheating and swindling over $1,500 and criminal conspiracy.
Tannous was eventually convicted and sentenced to 37 months in federal prison for organizing the roulette racket. This is a harsh punishment US Attorney Stephanie Finley made clear will be the norm for casino cheats:
“We are very pleased with the court’s decision to give this defendant a significant prison term. The casino and the citizens were victims in this case. A portion of the profits from the casino goes to the State of Louisiana and the Calcasieu Parish School Board.
We will continue to partner with our local, state, and federal law enforcement partners to prosecute crimes of this nature and seek the maximum amount of prison time available.”
2 – Partnering With a Croupier to Produce Fake Winners
If you read the previously linked reporting, you know Tannous and Lubbat didn’t work alone.
By conspiring with two croupiers working at the casino, these cheats made sure their past posting antics would never be reported.
That approach certainly makes sense on an objective level, too. By doubling down on the scam, colluding to ensure their cheating is allowed by the people running the table, conspirators don’t leave anything to chance. Having an “inside man” on the team only makes cheating at roulette that much easier, as a corrupt croupier can allow their partner to inflate winning bets or pull back chips on losers.
Why You Shouldn’t Partner With a Dealer
In 2016, a casino pit boss at the Horseshoe Casino in Council Bluffs, Iowa, decided to go rogue. He enlisted a croupier to do the dirty deed, and a third partner to act the part of lucky player. Past posting provided the bulk of the team’s $20,000 in ill-gotten gains, but like almost all roulette cheats before them, these three were eventually caught on camera and arrested.
David Dales, a special agent with the Iowa Division of Criminal Investigation (IDCI), issued a statement explaining how the scam was set up:
“There was a dealer that was doing some active cheating mechanism on the roulette table at Horseshoe Casino. And there was a patron he was consistently cheating for. The allegations are they were past posting – adding chips to the winning numbers – doing other activities that gave them illegal winnings at a table game.”
The offenders were charged with four felonies, including ongoing criminal conduct, first-degree theft, conspiracy, and cheating at gambling. They faced significant jail time and hefty fines.
3 – “Coloring up” Small Chips for Higher Denominations off the Table Before Cashing Out
An especially clever way roulette players can cheat the game involves the old bait and switch.
To make the “color up” scheme work, two players working in tandem start by sitting at different tables. In roulette, cash is turned into specially designed chips that are only good at the table. To avoid confusion between different players betting, everyone gets a different color chip in the denomination of their choosing.
A color up team moves from table to table, one buying in for the minimum $1 chips, and the other going bigger with a $25 or $100 denomination. When they both receive the same color chips, they’re always at a different table and only six or seven colors are in play so this will inevitably occur, the trap is sprung.
The low stakes player pockets a handful of chips on the sly, then heads off to take a quick bathroom break. With no surveillance cameras to worry about, they wait for their partner to hit the head as well, then they deliver a handful of chips when nobody’s around.
Flush with new chips in the same color as those at the big stakes table, the second player proceeds to play a spin or two with minimal action before requesting a color up and cash out.
When cheaters turn 10 of the $1 chips into an equivalent amount of $25 chips, they’ve instantly “earned” $240 in profit without incurring an ounce of risk. And if a $1 to $100 exchange rate is in play, the color up scam produces a massive $990 profit margin.
Why You Shouldn’t Color up Chips
Between 2012 and 2013, a highly organized team of color up cheaters based in New York toured the country targeting small commercial and tribal casinos. Their run came to an end in Ohio, after the team struck at four casinos and stole thousands of dollars, only for 13 members to find themselves behind bars when it was all said and done.
Karen Huey, director of enforcement for the Ohio Casino Control Commission (OCCC), told local media outlets that the Buckeye State was not alone:
“This is a very organized group of about 70 people. They travel the country. They’ve been identified in 18 states running this scam.”
The roulette cheating team wound up facing 29 felony counts and the possibility of lengthy prison sentences. According to Lucas County Prosecutor’s Office Special Units Division Chief John Weglian, casino criminals will never receive leniency.
“One of the principle purposes of these casinos is to provide revenue to the State of Ohio so the laws that the legislature has passed cover casino violations will be enforced strictly by the Attorney General’s office and this office. We will enforce the laws of the state.”
4 – Using Hidden Lasers to Measure Ball Speed Before Betting Concludes
These last two are so absurd that they hardly merit mention, but based on their scientific innovations alone, they made the cut.
Back in the 1970s, a physicist at the Santa Fe Institute in New Mexico named Norman Packard postulated that laser beams could be used to measure crucial roulette variables. By using a laser and a computer to chart the ball and wheel speed, Packard succeeded in predicting which quadrant of the wheel the ball would land in.
Here’s how he described the gambit in an interview with New Scientist:
“In the best circumstances, we could predict the quadrant correctly. Even saying which half of the wheel is extremely powerful because the payoff is so good. We definitely got to the point where we were winning money, but we didn’t continue long enough to make large amounts.”
Why You Shouldn’t Use Technology to Cheat
Obviously, pulling out a laser pointer and hiding a computer on your person is impractical in the modern casino setting. Maybe the laser cheat works in a laboratory, or even an old-school gambling hall before cameras became prevalent, but this is a method of cheating at roulette that would never fly nowadays.
5 – Directing the Ball to Certain Spaces by Generating a Magnetic Field
Using a laser pointer and a computer isn’t the most discreet way to cheat at roulette. So, how about a magnetic roulette ball to improve your odds?
In the early 2000s, a team of Austrian roulette cheats found a way to activate magnetic fields that drew the ball to certain numbers based on where the player stood. While the team didn’t win on every single spin, the use of a remote-controlled ball helped them improve their chances of winning.
Why You Shouldn’t Use Magnets
Unfortunately for this team of conmen, the croupier eventually found the ball stuck to his cufflink. The jig was up, forcing the cheaters to abandon their winnings and run away in shame. Today, some casinos use magnetic field sensors to prevent this from happening.
Conclusion
Folks who feel the need to cheat at roulette represent the bottom of the barrel when it comes to casino gambling. Desperate and down on their luck, yet unwilling to simply learn a skill game and play it well, roulette cheats refuse to accept reality. And as the five entries above should show you, the run of free money always ends at some point, leaving prison, probation, and a ruined reputation as the roulette cheater’s only legacy.
Please enable JavaScript to view the comments powered by Disqus.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 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
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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.
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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
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'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
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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.
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Written by: Michael Shackleford