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Top 10 Roulette Systems
By Henry Tamburin
Casino players have devised more systems for beating roulette than any other casino game. I believe the reason is because the game is played at a leisurely pace so it allows plenty of time to make bets between spins. System players will use this down time to analyze the data from past results and have enough time to figure out and make the next bet before the ball drops into a pocket.
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The sheer number of roulette systems is staggering. In an attempt to get a handle on this I decided to select the ten most popular systems that fall into one of the following three categories of roulette systems.

Progressive Betting Systems
Most of these systems have been around for a hundred years. Their characteristic is that the amount of your next bet is determined by what happened on previous bets. 
Betting Zones
Some of these systems involve covering contiguous sections of the wheel so that no matter where the ball lands in the covered section you are assured a win. The other is to bet on specific numbers around the wheel so that no matter where the ball lands you have a chance of winning. 
Predictive Systems
There are two popular predictive systems; one is geared to exploit flaws in the equipment and the other to detect flaws in the roulette dealer. The bias wheel system is based on the theory that some wheels may contain a mechanical flaw that contributes to a nonrandom distribution of winning numbers. The dealer signature system is based on the fact that some roulette dealers get into a rhythm or groove when they spin the wheel and launch the ball such that they consciously or unconsciously can place the ball in a given section of the wheel. The latter dealer trait is known as a dealer’s signature and systems have been developed to try to find and exploit these dealers. 
Let’s begin by examining the popular betting systems for roulette.

System #1. Martingale
This is the granddaddy of all roulette betting systems. In fact, the Martingale system is probably the oldest betting system ever devised to beat the casinos. It is also the system most used by novice roulette players who give it a try on the evenmoney bets on odd/even or red/black.

The Martingale is a doubleupafteryoulose progressive betting system, which simply means you double the size of your next bet whenever the previous bet lost. It is based on the assumption that if you keep doubling your bet after every loss, you will eventually win and recoup your losses plus end up with a 1 unit profit.

For example if you wagered $5 on red and a black number wins, you would lose the $5 wagered and your next bet is doubled or $10. If a black number won again, you would bet $20. At this point in the progression you are down $15 ($5 + $10). If you win the third bet you win $20 which is enough to cover the $15 lost on the previous two spins plus a profit of $5.

The allure of the Martingale betting system is that theoretically the wager has to win at some point since the chance of hitting a black number 5, 6 or even 7 consecutive times is pretty slim (see chart below). In fact you’ve got about a 99% chance of hitting a red number after 6 consecutive black numbers have won. This is what the system sellers promote (“99 percent chance of winning – a sure fire winning system”).


The reality of the Martingale is this – you will win frequently using it but in the long run you will be a loser. Here’s why.

Suppose we are ready to wager step 5 in our progression. We have 96% chance of winning the progression through step 5 and 4% chance of losing. The 96% of the time that we win the progression, we net a measly $5 which over 32 cycles of the progression gives an average win of $5 x 32 x 96% = $154. So far so good. But take a look at how much money on average we stand to lose the 4% of the time our progression fails. It’s $155 (cumulative losses through 5 steps) x 32 x 4% = $198. Yikes! Even though we have a 96% chance of winning the 5 step progression we end up losing $154$198 = $44 more money. The reason of course is the amount you win 96% of the time does not offset the amount you will lose 4% of the time.

But let’s suppose you want to give the Martingale a try anyway and you’ve got a hefty bankroll to back you up (see chart below). You begin your betting progression on black with a $5 starting bet and darn if it’s not your lucky day. Right from the get go you lose on the first spin, then the second, right up to the 7th spin. Already you are down $635 but the odds of red hitting on the 8th spin are in your favor and when it does you’ll win back the $635 plus an extra $5 profit to boot. As you start to plunk down $640 wager (8th wager in the progression) for the privilege of winning a paltry $5 (got the nerve to do this?), you hear a voice from the other side of the table say, “Sorry Sir, but the maximum bet on the outside numbers is $500”.

So even if you had the stomach and bankroll to play a Martingale progression until you won, the casinos won’t let you. That’s why there are maximum betting limits on each table. A $5 table usually has a $500 maximum bet so a Martingale progression would be stopped after step number #7. Therefore you won’t be allowed to make a bet that would give you the one unit profit for the progression.

Bet # Amount Cumulative Losses
1 $5 $5
2 $10 $15
3 $20 $35
4 $40 $75
5 $80 $155
6 $160 $315
7 $320 $635
8 $640 $1,250 
Often the Martingale progression is used for sleepers or numbers that haven’t come up after many spins. Players will watch the wheel, record the numbers that win, and then if certain numbers or colors or columns haven’t won in a while they jump in and start betting using a Martingale progression. The flaw in betting on sleepers is that past results has no bearing on future results. The chance of red hitting on any spin is 18/38 regardless if red numbers have been ‘sleeping’ for the past 5, 10, or even hundred spins. The bottom line is the Martingale betting progression doesn’t work in the long run and the more that you bet using it, the more you will lose.
System #2. Grand Martingale
Not satisfied with just a 1 unit profit for the progression, you’ll often see players use the Grand Martingale, which calls for a doubling of your last bet plus adding one more unit. For example if you bet $5 on red or black and the bet losses the player’s next bet would be $15 ($10 + $5 = $15). Here’s what the betting progression looks like through 5 steps.

Bet # Amount Cumulative Losses
1 $5 $5
2 $15 $20
3 $35 $55
4 $75 $130
5 $155 $285After 5 steps of the progression you’d wind up winning on average $292 and losing $368 for a net average loss of $76, which is a lot more than the average $44 lost for the traditional Martingale. Enough said?
System #3. Laboucher or Cancellation System
This betting system requires a pencil and pad (which the casinos will gladly provide you free of charge). It begins by selecting a sequence of numbers of any length, say 12345 (you can pick any sequence of numbers you wish). Each of the numbers in the sequence represents a unit of betting and the sum of the numbers (in our case 1+2+3+4+5 = 15 units) is the win goal.

Here’s how the cancellation system works. The player makes his first bet the sum of the first and last numbers in the sequence, in our example 6 units (1+5). Two events can occur. He can either win the 6unit bet or lose it.

If the bet is lost, the amount of the bet is added to the end of the sequence of numbers so that your new sequence looks like this: 123456. Your next bet would be the sum of the first and last numbers in the new sequence, which would be 7 units.

If instead the initial 6 unit bet wins, the player crosses off the first and last numbers in his sequence to arrive at the new sequence X234X and his next bet would be 6 units (2+4).

Mechanically the system is pretty straightforward. Each time you win a bet you cross off the first and last numbers of your sequence and each time you lose a bet you add the amount lost to the end of your sequence of numbers. Your next bet is always the sum of the first and last uncancelled numbers.

The goal of the system is to cancel out all the numbers in the sequence. If the player is successful in doing this, he will win the sum of the original sequence of numbers (in the above example 15 units = 1+2+3+4+5). What the system sellers will tout is that the system shrinks by two numbers when you win and grows only by one number when you lose. Of course what they don’t tell you is that the number you add at the end of your sequence is greater then the sum of the two numbers you cancel!

The problem with the cancellation system should become apparent. With a few losses, the sequence gets bigger and the losses will increase. The bets won’t quickly hit the house betting limit like the Martingale but neither does a single winning bet end the session. Like all other betting progressions, over the long run you will lose money with the cancellation system.
System #4. d’Alembert
This betting system is based on the assumption that if Bet A wins more than Bet B, then Bet A is less likely to win again and bet B is more likely to win. In practice the system has you decreasing your bet by one unit following a win (since it is less likely to win again) and increasing your bet by one unit following a loss (since you are more likely to win).

Some hucksters even have the gall to base this system on the “Law of Equilibrium”. The problem, however, is that the little ole wheel doesn’t know it’s suppose to balance things out. The wheel has no memory and it doesn’t know or even care whether the last spin was red or black, odd or even, or high or low. The chance of hitting red for example on any spin is 18 over 38 or 47% regardless whether the previous 5, 10 or even thousand spins were red. To put it simple, the results of previous spins have no effect whatsoever on the likely outcome of the next spin. The wheel, the ball, and the numbers have no memory whatsoever and every spin is an independent, random event. Period.

When everything is said and done, the d’Alembert like it’s cousins the Martingale and Laboucher will give you a fair number of winning sessions where you win a small amount of money and a few sessions where you will lose a lot more money. Over the long run it will not alter the casino’s 5.26% edge.
System #5. Oscars Grind
This is a popular upasyouwin betting system. It first appeared in Allan Wilson’s classic book, The Casino Gambler’s Guide. With Oscar’s Grind, you bet the same amount following a loss and increase your bet by one unit following a win. As the system progresses, the caveat is that you never bet more then what you need to recoup prior losses plus a oneunit profit.

For example, suppose a player bets on red and winds up with following sequence of wins and loses over 8 spins: LLLWWLW. The chart below summarizes the bets he would make after each spin (same bet following a loss and increase 1 unit following a win). Note that bets #6 and #8 were made at 1 unit so that if it won, you would recoup prior losses and achieve the 1 unit profit goal. This is in fact what happened when bet #8 won.

Bet # Amount Result Net
1 1 unit L 1 unit
2 1 unit L 2 units
3 1 unit L 3 units
4 1 unit W 2 units
5 2 unit W 0
6 1 unit L 1 unit
7 1 unit W 0
8 1 unit W +1 unit 
For the most part, all betting progressions and cancellation systems can be fun to play and will give you many winning sessions where you will win a small amount of money. However, over time your losses will eclipse your winnings and you will end up losing 5.26% of all the money you bet (sound familiar?).

System #6. The Paroli
The Paroli betting system is designed to take advantage of hot streaks, which could occur when you play roulette. Like the Shotwell system it features an upasyouwin betting progression but a much more aggressive one. 
One of the more popular Paroli systems is the “Paroli of Three” which involves an aggressive betting progression with the goal of winning three bets on any even payoff wager (odd/even, red/black, high/low).

You begin by making an initial one unit bet and as long as you are losing you continue to bet 1 unit. As soon as you win a bet, you make your second bet double the initial bet plus one more unit ($15 or three units). If the next bet wins you double and add 1 unit and make the third bet $35 (7 units). If you win the third bet you lock up your $55 profit ($5+$15+$35) and begin the next progression at 1 unit.

There are two basic problems with the Paroli. From a practical standpoint if you have an alternative series of WLWL etc. you will be taken to the cleaners. More importantly, you never know when a streak is about to begin (or for that matter end). Over the long term, you will lose 5.26% of all the money you bet.
System #7. Shotwell System
This system first appeared in print in 1978 (Gambling Times Magazine). It has remained a popular system because its strategy is to cover specific numbers that are evenly spaced around the wheel so no matter where the ball lands you’ve got a shot at winning.
If you make one of the six number combo bets and associated four straight up bets in the chart below, you would have 10 numbers covered with a total outlay of 5 units. For example if you placed one chip on the 6 number combo 1 through 6 and one chip each straight up on the numbers 20, 26, 8, and 10, no matter where the ball lands it will be no more than 3 pockets away from or on one of your numbers. As the system sellers claim, “You’ve got a 1 in 4 shot at winning”.
The problem with the Shotwell as with all other combination betting systems in roulette is that over time the money you win when your numbers hit will not compensate for the money you lose when your numbers don’t hit. It’s another fun system but in the long run it will not alter the casino’s 5.26% edge.

Six Number Bet Straight Up Bets
1 through 6 20, 26, 8,10
4 through 9 13, 14, 15, 10
10 through 15 16, 17, 18, 28
13 through 18 11, 12, 27, 28
19 through 24 1, 2, 4, 26
28 through 33 00, 22, 24, 35
31 though 36 0, 00, 29, 30 
System #8. The Red System
This popular betting system tries to take advantage of the fact that the third column of the layout contains 8 red numbers and only four black numbers.

You make only two bets  $5 on the third column and a $10 insurance bet on the black numbers. The possible outcomes are:

If a red number in the third column hits, you win $10 for your $5 bet in the third column and lose $10 on your bet on black therefore you break even.

If a black number in the third column hits, you will win $10 on the column bet and $10 on the bet on black for an overall win of $20.

If a red number hits in the first or second column, you will lose both bets for a $15 loss.

If a black number in the first or second column hits you lose your $5 bet on the column but win $10 on the bet on black for a net gain of $5.

Finally if 0 or 00 hits you lose both bets for a loss of $15.

If you do the math through 38 spins you will discover that you will lose $30 for every $570 worth of bets. If you divide $30 by $570, low and behold you end up with the casino’s edge in roulette of 5.26%.

This result shouldn’t surprise you since each bet is independent in roulette and each bet has it’s own overall expectation of –5.26%. Combining different bets or making insurance bets will not alter the overall player’s negative expectation.
System #9. Betting on a Biased Wheel
The strategy is simple. If you can’t beat roulette with a betting system, you try to beat it by finding a wheel that has a bias due to some slight physical imperfection that causes some numbers to hit more frequently then probability dictates.

How do you detect if a bias exists? You have to track the winning numbers over a period of time to determine which numbers, if any, are hitting more frequently. Since casinos know that players like to track the winning numbers they try to help the systems player by installing devices that display the last 16 to 20 winning numbers. The strategy involves checking the numbers on the display and if you see any numbers that have hit more times then others start betting on that number.

These systems don’t work for several reasons. First numbers that have hit more frequently over a small sampling of 38 or even 100 spins could be just due to chance and not bias. How can you prove it? You must track the winning numbers over at least 4,000 spins, a task that can take many days to accomplish. And while you’re trying to manually record the winning numbers, most casinos nowadays can analyze the data on special computer software that will readily detect a bias long before you will. And if they detect a bias from their data or observed someone winning a large sum that has been tracking a particular wheel, they would quickly replace the wheel. Yes, a long time ago it was possible to beat the casino on a biased wheel, but nowadays it is much more difficult to do.

System #10. Dealer Signature
A veteran dealer’s job is monotonous and consciously, or unconsciously, they can spin the wheel and the ball with the same velocity every time. This consistency from one spin to the next is known as the dealer’s signature. Some players believe that a dealer’s signature is trackable and it works like this.

Once a player believes he has found a dealer signature he observes the dealer’s release point of the ball in relation to the wheel. He knows from observing the dealer’s signature, that the ball will always travel a specific number of revolutions before dropping into the wheel. The player is trying to predict in what zone the ball will land and bet according.

The key to this betting method is to find a dealer with a consistent pattern. If you observe a pattern, you only have a few seconds to calculate where the ball will drop and to make your bet. And unless you check the statistical results of many hundreds of spins by the same dealer you will never know if the results are due to just chance or in fact due to the dealer’s consistent pattern.

Although most dealers do not have a predictable signature there are probably a few veteran dealers that do and there is no harm in trying to locate them. The worse that could happen to you if the system fails is that you will due no worse then if you just blindly wagered on a few numbers.

Summary
There is no progressive or other betting strategy that will alter the casino’s edge in roulette on an unbiased wheel. Nevertheless, if you believe you’ve found a betting system that can’t lose in the long run, I encourage you to accept the challenge of my fellow gaming writer Michael Shackelford (aka The Wizard of Odds). For a small fee he will test the system over 100 million trials and if your betting system proves to make money, he will refund the fee and give you front page recognition on his web site for defying the laws of mathematics. (see www.thewizardofodds.com for complete details of the challenge).

The only way to theoretically gain the edge in roulette is to be able to predictably influence the outcome either through a biased wheel or dealer signature. Even though a few skilled players have done this in the past, nowadays it is much more difficult to detect and exploit wheel biases and dealer signatures. However, trying has no downside risk since the worse you will do is a negative expectation of –5.26%.

For the sake of completeness, let me mention one other system that has been developed to predict where the ball will drop. It involves timing the ball through one revolution, estimating the velocity of the ball and rotor, and using differential equations to predict the outcome (actually uses the laws of physics). Unfortunately, the system requires a computer to do the calculations, which is illegal to use in a casino, so the system isn’t practical.
If you want to learn more about roulette systems, I recommend the books by Christopher Pawlicki (Get The Edge at Roulette) and Frank Scoblete (Spin Roulette Gold). In addition you can keep up with new systems by checking out www.roulette.casino.com.
Consecutive Hits  Chance 
1  52% 
2  28% 
3  15% 
4  8% 
5  4% 
6  2% 
7  1% 