# Chapter Two: Why Systems Fail

## Naïve versus Sophisticated Roulette

What do I mean by "naïve" roulette? If you are a serious player, then no doubt you have played long enough to watch the average player come up to the table and steadily lose money by betting a collection of birthdays, Michael Jordan's uniform number, and other favorite numbers. You know full well that whether such players come out ahead or down is entirely a matter of luck.

"Naïve" roulette is when players do not play the game with any sort of Roulette strategy or awareness of the probabilities involved with the game. From time to time a naïve player may make some money, but they are virtually guaranteed to lose money in the long run. Why? For a combination of reasons that I will summarize by the labels the House Advantage and the Variance Demon.

A word of warning: This chapter upsets many of my roulette-playing friends because the obstacles to winning at roulette seem so huge. Do not despair. I would not bother to share these obstacles with you if I did not have a set of solutions to offer. So do not skip this part! Understanding these notions will help you a good deal when it comes to using the strategies that Roulette 2000 has to offer. After all, the goal here is to increase your sophistication in the game of roulette.

As I mentioned earlier, LIVE casinos make their money because of the built-in advantage the casino has from the "vig" - the house "take" of each bet. In roulette the house advantage is very large: 5.26%. They get this advantage by paying the player less than the true odds of a bet. For example, an outside bet on red or black pays even money as if the odds were an even 50/50. But the odds are not 50%. Because of the 0 and 00, the odds in any given spin of red or black hitting are actually 47.37%. So if you bet one unit (where 1 unit can be anywhere from 25 cents on up to \$100) on red every time, at best you will win only 47.37% of the time and end up losing 52.63% of the time, for a net loss of 5.26%. Similarly, with inside bets the true odds are 38 to 1 (36 numbers plus 0/00), but you get back 36. The difference is, again, 5.26% in the casino's favor. Most of the time this edge is all the casino needs to make money. To be sure, some players walk away winners, but many more walk away losers. On average the house can be confident that it will clear at least a profit of 5.26%.

A note about single zero wheels: Obviously the odds are slightly better on a single zero wheel because the house edge is less; about 2.7%. Let me take this opportunity to say that many players put themselves at a disadvantage by not playing on single zero wheels when they get the chance. There are plenty of single zero wheels available in Las Vegas, Atlantic City, and even in some riverboat casinos. However, most of these wheels require the player to bet a minimum of \$25 per spin. So it is understandable that you may not want to play on a single zero table unless you have a large enough bankroll.

The difference between true odds and the casino's payoff is, by itself, no guarantee that the house will come out ahead. As I will explain below, there are some systems that could produce consistent winning except for one other house advantage: Table limits. By keeping the range between the minimum and maximum bets under control, the casino assures itself that some progressive systems will run into the limits before they beat the house.

## The Variance Demon

What is variance? To answer I have to get into statistics a bit, but bear with me. The concepts are not all that difficult and you will understand the game a good deal better by mastering them. At the very least, skip to the end of this section to see just how long it can take for certain bets to come in that appear to be "due." Under-standing the extreme limits of variance can literally save you a fortune.

Let's say you have 10,000 spins of a roulette wheel. If the results were distributed in a perfectly random pattern, each of the 38 numbers would appear n/38 times, or 100,000/38 = 2632. However, even with a perfectly unbiased wheel or a very good computer program to generate random numbers, there is variation from a "perfect" distribution. Some numbers will appear more than 2632 times and some will appear less.

You can test this idea by flipping a coin 100 times. I can virtually guarantee you that it will not come up heads and tails exactly 50 times each. In fact, if you flipped a coin 100 times a day for 30 days, most or maybe even all of those days you would not get exactly 50 heads and 50 tails. In the theoretical long run, we assume that you will get an average of a 50/50 split. But on any given day your "score" of heads or tails will vary from 50%, and your cumulative average will probably not be precisely 50%. Some days the mix might be 51 to 49, other days it might be more like 70 to 30.

Your cumulative average will move up and down each day. Once you have tracked your coin flips for enough days, you could calculate how much variation from 50% you have experienced.

In statistical terms such variation is called "variance." The cool thing about variance is that we can measure it. That is, we can measure how much each individual day's average varies from the expected mean of 50%. The amount of variation from the mean (in this case, 50%) is measured in units described as the "standard deviation."

Let's return to roulette. The amount of variation from the mean of 2632 can be calculated as a standard deviation. Let's say the standard deviation is 200. This means that each number appeared "on average" between 2432 and 2832 times.

One standard deviation above the mean would be +200 in this example (or 2832), while two standard deviations below the mean would be -400 or 2232. Now here is the cool part: Using standard deviation as a measure allows us to estimate the probability or chances of the occurrence of an actual score compared to what we expect the “normal” scores to be. We expect approximately 68% of all frequencies to fall between plus-or-minus one standard deviation of the mean. That is, only 32% of all scores will be outside of the range of 2432 to 2832. Moving further away from the absolute average of 2632, we expect a little over 95% of all scores to fall between plus-or-minus two standard deviations. This means that a score outside of the range of 2232 to 3032 has only a 5% chance of happening. When applied to the various betting options in LIVE roulette games, the concepts of variance and standard deviation explain how difficult the game is to beat. And later Roulette 2000 will explain how to utilize these notions against the game in order to defeat it.

Let me give an example of what I mean by the Variance Demon. Let us say that I am just learning about roulette and I quickly figure out that each number should hit on average once every 38 spins. I also happen to notice that the number 23 has not hit for 30 spins. "Wow!" I think to myself. If I bet on 23 for the next 8 spins or so, I ought to have a hit. Well, maybe yes, maybe no. The problem is that each number will hit on average once every 38 spins.

But the variance on the frequency of a single number is huge. The number might hit 4 times in the next 8 spins, or it might not hit for another 360 spins.

Even though a number disappearing for over 300 spins is unlikely, it does happen. When something like that happens, I often think of myself as falling victim to the Variance Demon. Now, even if you did not follow all the mathematical details, it is not difficult to understand the results: Numbers do not always hit when they are "due." The improbable happens.

I know many people who have lost a lot of money chasing a particular bet because they just cannot believe that "X" won't hit. Now "X" can be the red or black, or the first dozen or even a single number. Absolutely convinced that "X" must hit soon, people pour hundreds of dollars on a string of bets that wipes them out. If you are going to chase a particular number or set of numbers, you need to be aware of just how long you might have to chase them before you start the chase. Let me warn you now about the extreme limits of variance:

• Straight-up: To hit 1 number might take 1 spin or up to 360 spins.
• Split Bet: To hit one of 2 numbers might take 1 spin or up to 180 spins.
• Trio/Street: To hit one of 3 numbers might take 1 spin or up to 120 spins.
• Line Bet: To hit one of 6 numbers might take 1 spin or up to 60 spins.
• Dozen/Column: To hit one of 12 numbers might take 1 spin or up to 30 spins.

What about the even-money bets, like red/black, even/odd, 1-18/19-36? This means you are trying to hit one of 18 numbers, and it might take 1 spin or up to 20.

The lesson to learn here is that you cannot trust a vague intuition that a particular number or set of numbers is "overdue." You need to know just how long they can lay dormant, or "asleep," before they finally wake up.

## Why the Improbable Happens

Before I get potential players excited with various strategies, I need to issue a word of caution. Roulette is a game in which "the improbable" happens all the time. In fact, it is not as odd as it sounds to say the "improbable is probable" in roulette.

Allow me one example. Every experienced roulette player knows that streaks of 8 or 9 reds or blacks in a row happen regularly. If you have played long enough, you may have seen a streak of 14 or 15 in a row. The odds of a streak of 18 in a row are very slim indeed: .0000096. However, there is a sense in which this kind of unlikely event is happening all the time in roulette.

Think about it: Red or black is simply a random way of identifying 18 of the 38 numbers on a roulette wheel. In any given set of 18 spins, the most number of numbers that can be hit is 18. That means that in those 18 spins, over half of the numbers are not being hit--just like a situation when red hits 18 times without a single black number or 0/00 hitting. From a probability standpoint the two situations are identical--some random set of 18 number hitting 18 straight times. The odds of some set of 18 numbers hitting in a set of 18 spins is 100%, but the odds of any particular set of 18 numbers hitting in all 18 spins is less than 1 in 100,000. That is what I mean by the improbable is probable. Something weird is always happening on the roulette wheel. What we need to do is figure out how to spot those opportunities where the weird becomes reasonably predictable.

So how should we play? In the next two sections I want to explain the problems with "systematic" Flat and Progressive Betting. Then I'll teach you how to avoid these problems.

## Problems with Flat Betting

By "flat betting" I simply mean that a player bets on any given bet (inside or outside) at a constant rate. Typically, this is called one unit, where the unit can be anything from 25 cents to \$100. The precise bet does not really matter: It could be 5 of the player's favorite numbers on the inside, or some outside bet of even money or 2 to 1 odds.

It is possible to win money by flat betting, but not in the long run. If I went up to a table and bet \$5 on red each time for 100 spins, I might make a profit. You may say, but those bets only win 47.37% of the time! How can I win? The answer is "variance." In an analysis I did of an even money bet, I found that for my data set of 100,000 spins the standard deviation was 5.64%. This means that to the extent this sample is representative, about 68% of the time we can expect the average to range between 41.73% and 53.01% (one standard deviation); 95% of the time we can expect the range to be between 36.09% and 58.65% (two standard deviations). Because results vary, we seldom get exactly the expected average of 47.37%. Instead we might actually win a profit of 11 units. Or we could lose more than average. If we hit only 36% of the time in 100 spins, we would have lost 28 units.

In the long run, however, we can be fairly confident that we will have more losing sessions than winning ones with flat betting. The reason goes back to the house edge gained by not paying us the true odds. In theory the longer we play, the more the positive and negative variance will cancel each other out and we will get closer to the average, which for even money bets is 47.37%. Unfortunately, that means in the long run the house can count on getting its 5.26% profit. To make a long story short: The longer you play roulette with flat bets, the greater the chance that the odds will even themselves out and the house edge will become the determining factor. What we will need to do, then, is to talk about how to get in and out quickly, to play "strategically" rather than "systematically."

## Problems with Progressive Betting

OK, so if systematic flat betting fails why don't we systematically progress our bets? The classic example of a progressive betting strategy is the infamous Martingale strategy. This strategy is for the even money bets (red/black, even/odd, 1-18/19-36). One begins with a bet of one unit. If you lose, you next bet 2 units. You continue to double your bet until you have a winner. As a result, you are guaranteed to come out ahead one unit once you finally hit.

The problems of the Martingale strategy are shared by almost all other progressive betting strategies. The first problem is that it requires a large bankroll. To illustrate my point, I will focus on red/black even though the analysis would apply to any even money bet. Most streaks of red or black are fairly short, but if you have played for very long you have seen some long streaks. Let's take a streak of 15 as an outer extreme. If you are betting \$1 on red, to defeat a losing sequence where you encounter 15 black in a row you must bet 16 straight times as follows: \$1, \$2, \$4, \$8, \$16, \$32, \$64, \$128, \$256, \$512, \$1,024, \$2,048, \$4,096, \$8,192, \$16,384, \$32,768. Thus you need to have a bankroll of at least \$65,535.

Even if you have a large bankroll, you will get defeated by the next problem: table limits. Most tables have a minimum of \$5, in which case you can take the above numbers and multiply them times 5 (total bankroll now needed: \$327,675). However, tables also have maximums. On typical \$5 tables the maximum outside bet usually is \$1000 or \$2000 or at most \$5000. Even if you started with a \$1 bet, you would run into a table maximum before you won.

Now, admittedly my example is an extreme one. But the lesson still applies to less extreme cases. Because of the table minimum and maximum, a spin-by-spin strategy of doubling one's bets will encounter a losing sequence sooner or later that cannot be defeated.

Could it be worth it? Perhaps you have figured out that the odds of 6 reds or black in a row are about 2%. Why not take the wins and out weight the losses? Ah, if only we could! Let's say we have a \$1 table and a bankroll of about \$100. That means we can start with a \$1 bet and double it 5 times, so only a streak of 6 in a row will defeat us. How would we fare? Well, the good news is that on average we should win 98 times. 98 wins x \$1 = \$98.

The bad news is that our two losing sessions each cost us \$63 for a total of \$126. \$98 - \$126 = a loss of \$28.

Again, to shorten the story, the problem with almost all progressive betting schemes is either that they run into table limits that force losses, or the payoff rate multiplied by the win-rate suggest that you will end up losing money. For more examples of this, see the appendix where I offer statistical critiques of a number of different progressive betting strategies. To put it most simply, with almost all systems that require you to progress your bet, the problem is that only a few losses will wipe out your winnings plus most or all of your bankroll. Those systems that advertise even a 90% or 95% winning rate must be asked the simple question: How much do you win with each win (on average) and how much do you lose when you lose? I have yet to find a system that involves progressive betting that has solved this problem.

## The Gambler's Fallacy

A number of betting strategies try to avoid the problems I have identified with flat and progressive betting by trying to detect and follow the trends of a table. They admit that the Variance Demon will defeat conventional strategies, so they try to detect which way the variance is running and bet accordingly. Such strategies may hope to catch the wave of more reds than black, or catch the "hot numbers" that seem to be popping up at a greater-than-average rate.

This is where the difference between a "strategy" and a "system" become crucial. I suggest in the next chapter that "playing for repeats" is a perfectly acceptable short-term strategy. Streaks and repeats do happen. But to base a whole system on this notion is to commit what is known as the "Gambler's Fallacy." The Gambler's Fallacy refers to the belief that one can predict an upcoming spin based on a set of preceding spins. It is considered a fallacy because each spin is an independent event that cannot "cause" a future event to occur. The wheel does not know what color a number is, and it has no memory of what number just appeared.

Trends happen. But you cannot rely on them to continue. A trend where red is hitting 10% more than average could continue for another 50 spins or stop on the very next spin. The same is true for any other trend: they may continue, they may not. "Following the trend" is OK as a short-term strategy, but if you turn it into a system (as many systems do), it becomes an unreliable way to bet that will meet the same fate as flat betting or progressive betting as described above.

## Beware of Systems

It may seem odd in a book of roulette strategies to say "beware of systems" but I believe it is important for you to understand the difference between Roulette 2000 and "mechanical" systems. I have identified a set of obstacles to winning consistently at roulette. Before you ever purchase another system, you should ask how that system avoids the problems we've discussed.

• Is the system consistent with probability theory?
• If the system relies on flat betting, how does it beat the house edge?
• If the system relies on progressive betting, how does it beat table limits, bankroll requirements, and the Variance Demon?
• Does the system commit the Gambler's Fallacy?

If you have already purchased a system, I strongly encourage you to purchase a home computer roulette game and to try the system out extensively before ever risking your money at a casino. Do not just try it once or twice, but do a number of sessions and keep careful notes of your results. I recommend ideally 30 sessions of at least 100 spins each. That sounds like a lot, but it will go much faster at home than in a casino, and you could save yourself hundreds or thousands of dollars.

If you do not have a home computer or do not want to buy a roulette program, you can use the list of 10,000 spins included in the appendix of this book. Start any place and treat each number as a successive spin. The results will be virtually identical to a home program or a real casino with an unbiased wheel.

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