By Henry Tamburin
When I was a youngster, I used to think it was unfair when teachers gave me homework. When I was a teenager and missed curfew, I thought it was very unfair when my mother “grounded” me. But asI grew older and wiser I realized a lot of things in this world ain’t fair including the games I play in casinos.

#DerrenBrown #RussianRoulette #RussianRouletteStuntAlong with his chosen contestant, Derren plays Russian Roulette live on live TV (Aired on 5 October 2003). In our Unfair Game of Interview Roulette, two artists have been randomly paired together to answer each other’s questions about the specs and rambles of their artistic life & practice. A classic game of roulette as none of the artist know to whom they address their questions beforehand. Unfair comparison -Main Story roulette was completed as level 67, inflating the Main story Roulette values by a full level.Completed a dungeon 1 level below my current level.

I know that the casinos must have some sort of an advantage over players in order to pay their bills and generate the capital they need to build those gambling palaces that we love to visit.But the casino’s advantage is unfortunately a big mystery to most players. It certainly was to me until I finally figured out how they win and why I lose. But nowadays most casino players don’tcare about casino advantages or unfair games. They are just satisfied with having fun and letting Lady Luck determine their fate. If that’s your modus operand when you gamble then stop readingthis article right now. However, if you're tired of being the patsy that always contributes your hard earned cash to the casinos' coiffers and wants to do something about it, then read on, forthere is a light at the end of the tunnel (or in your case cash in your pockets at the end of your casino visits).

Knowing a little about how the casinos create their unfair games to begin with is the first step you must take to become a smarter player. By smarter I mean learning which games and bets arehighly unfair and then avoiding them while at the same time learning how to turn an unfair game into a nearly fair game.

There are three different ways that a casino creates unfair games. One way is to create playing rules that favor the casino so that they win more decisions than the player. For example, atypical craps player that makes a total of 1,980 pass line bets stands to win 976 times while the casino stands to win 1,004 times. The casino rules for the pass line obviously favor the casinowinning more times than the player. This is what creates the unfair game. Pretty simple huh?

It’s the same concept as if I let you play a game in which I have a bowl containing 50 black white marbles and 50 black ones. You get to pick a marble at random and of you pick a white marbleyou win. What are the odds of picking white? Since there are equal number of white and black marbles, the odds are 50-50 and the game is fair. I shouldn’t quit my day job if I offered this gameto you. However, if I placed only 40 white and 50 black marbles in the bowl, it’s clear that this game now becomes unfair for you and I can tell my boss what he can do with this job.

Let’s look at a totally different way casinos create an unfair game. This is the most common way and it has to do with the amount the casinos pay players when they win a bet.

Suppose I flip a coin and if you lose you pay me a dollar and when you win I pay you 95 cents. Is this game fair? Even though the odds of winning is 50-50 the game is unfair becauseinstead of paying you $1 when you win, you get paid only 95 cents. You are short changed 50 cents every time you win. After 100 flips you would stand to win half of them at 95 cents winper flip. The other 50 coin flips you stand to lose $1 per flip. If you do the math, you would stand to lose $2.50 after the 100 coin flips. Quite an unfair game.

The same concept – known as paying less then true odds - is used by casinos when you win a bet at say roulette, the Big Six Wheel, most craps bets, video poker, and even the slots. For example,take the infamous bet on Any 7 (known as Big Red to the craps affieciendos). You plop your chips on Any 7 on the layout and if the next roll is a 7 you win. If it’s not you lose. Pretty easybet to make but also a very devastating one for your bankroll. The reason is because the casinos are giving you a reduced payoff. The odds of rolling the 7 is 30-to-6 or 5-to-1. The casinopayoff isn’t at the true odds of 5-to-1 but rather at the reduced odds of 4-to-1. Get it??

Another way to think about how the casino’s create their unfair game is to just remember they that really make their profits not from player losses but rather from the money that players win,because winnings are paid out at less then true odds. As Frank Scoblete puts it; “You have a partner when you win – the casino”.

The third relatively easy way that casino’s create an unfair game is by simply charging you a fee when you win a bet (what a novel idea). Going back to the bowl of marbles analogy, supposethere are an equal number of white and black marbles. If you lose a pick, you lose a dollar. If you win a pick I pay you a dollar but I charge you a 5% fee (that’s a nickel). I created anunfair game by charging a fee or commission every time you win a bet. That’s how I created the unfair game.

A winning bank bet in baccarat falls under the “you pay the commission when you win”. In fact if you bet on the bank hand you would win more times then the casino wins. For every 100 bankhand decisions that result in a win or loss, you stand to win on average about 51% of the time and the casino wins 49% of the time. The game is extremely fair for the player at this point– infact the player would wipe out a casino by winning 2% more times then the casino. Of course the casino isn’t stupid, they are after all in business to make money not give it away. So tocompensate for the edge a player has by winning more times then the the casino, they smartly impose a 5% commission every time you bet on the bank hand and it wins. I know it’s not fair butthat’s how the casinos do it.

What about playing the slots, the most popular game in a casino? How does the casino create the unfair slot machine? Trust me when I tell you that they don’t do it by having someone in abackroom throw a switch that prevents players from winning jackpots. In fact with slots it’s easy to create an unfair game. The casino just programs the slot computer to keep whateverpercentage that the casino feels like keeping by paying winning combinations at less then the true odds (sound familiar). Sure it’s a lot more complicated with the microchips now being used incasinos with virtual symbols on each reel. But the concept is the same. Pay less then the true odds and you’ve created an unfair game.

In casino jargon the difference between the true odds and the odds paid is called the casino’s advantage. This can be calculated for every game and bet in a casino including those bets in whichthe casino charges a commission or wins more decisions. By ranking the casino’s edge for every bet it’s easy to determine which games and bets are unfair and by how much. And now the caveat.You can become an instantly smarter player by promising to do this on your future casino trips

Don’t make any bet in a casino where the casino’s edge is greater than 1.5%.

Wow that didn’t hurt did it? It all boils down to this. We know the casino offers unfair games but we can control how much unfairness we are willing to let the casinos have. By making thefollowing recommended bets, you will, in essence, be letting the other guys pay the bulk of the casino overhead while you pay next to nothing. What this all boils down to is the following. Onlyplay the following casino games and only make the recommended bets listed.

Blackjack with perfect basic playing strategy

Video poker on full-pay machines with optimum playing strategy

Pass line and don’t pass in craps

Bank and player bet in baccarat (or mini-baccarat)

Pass line and don’t pass line with odds

Place bet on 6 and 8 craps

Slot machines which have a sign guaranteeing at least a 99% or higher payback.

What’s your reward for making only the above bets? For blackjack and video poker you’ll turn an unfair game into a nearly fair game (with the possibility of turning it into an unfair gamefor the casinos to boot). For the other recommended games and bets, you’ll still be playing an unfair game but not by much. Look at it this way - it’s your best gamble in a casino.

Henry Tamburin is the author of the best-selling book, Blackjack: Take The Money and Run, editor of the Blackjack Insider e-Newsletter, and Lead Instructor for the Golden Touch Blackjackcourse featuring Speed Count. For a FREE 3-month subscription to his blackjack newsletter with full membership privileges, visitwww.bjinsider.com/free. For details on the Golden Touch Blackjack course visitwww.goldentouchblackjack.comor call 866/WIN-BJ21. For a free copy of his casino gambling catalog featuring over 50 products call 888/353-3234 or visit the Internetstore atwww.smartgaming.com

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

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

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 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

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

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

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

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.

Unfair Roulette Games

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

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

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

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

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

Unfair Roulette Rules

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