Gambling Systems and the Pursuit of Easy Money
For centuries, the greatest minds in science, maths and engineering have used intuitive and mathematical analysis to examine the laws of probability especially when it comes to gambling systems, searching for ways to beat the odds.
Their ultimate goal: To develop foolproof gambling systems for winning at games of chance. This pursuit of easy money has led to some astounding strategies, from progressive betting and card counting to outright cheating.
Indeed, the study of Roulette once prompted Albert Einstein himself to claim, “You cannot beat the table unless you steal money from it.” Yet people do walk away from casinos with more money than they started with. It happens every day.
In fact, some players actually make a living at the world’s craps, blackjack, and roulette tables as professional gamblers. Is their success based entirely on luck? Are they involved in some form of fraud or criminal behaviour? Or have they learned a secret system, to which only a few are privy?
Gambling Systems and The Marvelous Mr. Martingale
Many still believe that the Martingale Betting System is the basis for winning steadily at even money games, including Pai Gow Poker, Baccarat, and Blackjack as well as Einstein’s unbeatable spinning wheel. But the magical powers of Martingale are more myth and legend than reality, starting with the system’s name.
In the latter part of the 18th century, the practice of “doubling up on a loss” became quite popular as a way of wagering. It somehow became associated with the proprietor of a British gambling house, Henry Martingale, although he did not invent the system, nor did he champion its use.
The Martingale System’s long-lived popularity derives from its simple premise and easy math. Just by doubling your wager until you win, all previous losses can be recovered and a profit obtained on a single bet.
At Roulette, for example, you might start out by placing one unit on black. If you lose, bet two units. If you lose again, bet four, and so on, until black eventually comes up—as you know it will at some point, unless the game is fixed.
In fact, a few calculations will show that there is exactly a 98.1% chance of winning once within six successive spins on a European or French wheel with a single zero.
To be able to endure a streak of six red numbers and zeroes, doubling up on black each time, you have to be ready to wager 1+2+4+8+16+32 = 63 units. That’s what it will take in order to obtain a profit of a single unit.
But the Roulette wheel has no memory of past events. The results of previous spins have no effect on future outcomes. It can miss hitting black seven times, or eight times, or nine, ten or more.
That’s where the risk lies in Martingale. And when the progression fails on six consecutive spins, as can be expected 1.9% of the time, the loss is the full 63 units wagered. In order to maintain a profit, you must win the progression at least 64 times before losing once.
Is that likely to happen? The numbers indicate otherwise. The progression should fail about once every 50 times (1.9%). Therefore, it is rather certain that you will lose money if you play Martingale exclusively over the long term, limiting yourself to six spins per progression.
The temptation, then, is to keep doubling up until you win. But there are several reasons why this approach will not work, not the least of which is that you would need unlimited resources to keep doubling for an indefinite number of spins.
Should you happen to lose eight times in a row, for example, your accumulated loss would be 255 units, and the system will require you to bet 256 units on the next spin of the wheel to cover it. That’s a total stake of 511 units, just to win one single unit—a truly terrible wager, especially when the odds against you are 19:37 or 51.35%.
And it only gets worse if you lose again. Most casinos have maximum betting limits, typically 200~500 times the minimum, which would cause the progression to collapse after eight or nine straight losses.
Unlimited doubling just doesn’t work, so the trick is to win a bit quickly and then shift strategies or tables before the odds catch up to you.
At most Roulette tables, the ball is dropped about once every two minutes. To get 30 wins playing Martingale will take at least an hour, and probably longer. The chances of a five-spin, even-money losing streak occurring is 3.57% on a 37-slot European wheel.
Streaks of five winners or losers in a row can therefore be expected about once every couple of hours or so. So the best advice when playing Martingale is “Don’t overstay—quit while you are ahead.”
The Lucky Labouchere Gambling System
Convinced that Martingale was not the perfect gambling system, great minds set about modifying the basic strategy to recover losses and generate a profit without assuming high risk.
The result was a plethora of systems developed in the 18th and 19th centuries, many of which are still used with limited success to this day. One which deserves special attention is called Labouchere.
A British politician with a French-sounding name was writer, publisher and Victorian theater-owner Henry Du Pré Labouchere (1831~1912). He served in Parliament twice between 1865 and 1906.
His personal roulette gambling system was based upon the work of 18th century French mathematician Jean Le Rond d’Alembert, who had developed a betting progression of his own.
The Labouchere gambling system is quite elegant in its simplicity. You set up your bets as a series of predetermined numbers and then cross them off in pairs each time you win. For this reason, Labouchere is also known as the “cancellation system.”
Each time you lose, you add the value of your loss to the end of the series. Because wins cancel out numbers from the series twice as fast as losses add them, if you can win at least 34 percent of the time, you should be able to come out ahead over time.
For example, suppose your goal is to win ten units in profit. You structure your ten units as a series, such as (a) 1+2+3+4 or (b) 2+2+2+2+2 or (c) 5+2+3. The order of the numbers doesn’t matter, nor does how many numbers are in your series, just as long as their total is your profit objective.
The amount that you wager will always be equal to the sum of the first and last numbers in your series. For series (a), this would be 1+4 or five units. For series (b), it would be 2+2 or four units. For series (c), it would be 5+3 or eight units.
Supposing you are playing Roulette and decide to bet on black, whenever black comes up a winner, cross off the two numbers that you bet. For series (a), you would now have 2+3 remaining.
For series (b), you have 2+2+2. For series (c) the only number remaining would be 2. Your next bet will be the sum of the first and last of the remaining numbers: five units for (a), four units for (b), or the remaining two units for (c).
If you lose, add the value of the loss to the end of the series. For series (a), this would become 2+3+5. For series (b), it would 2+2+2+4. For series (c), it would be 2+2. The next bet you make would be 2+5 or seven units for series (a); 2+4 or six units for series (b), and 2+2 or four units for series (c).
Continue playing in this manner, crossing off two numbers each time you win and adding on the value of your loss whenever you lose. In time, you will cross off all the numbers in your series and finish with a profit of ten units.
Any time you get down to just one number remaining in your series, just bet that amount, and then cross it off if you win or add it on again to the series if you lose.
Labouchere is an improvement on Martingale, in that there is no need to risk large wagers at poor odds to recoup your losses. But Labouchere still has one major drawback.
As you eliminate the original small numbers, a sequence of losses can quickly add some rather large numbers to the end of your series. The series might easily end up looking like 10+15+21, requiring you to bet 31 units on the next spin.
In the event that this happens, you have some options besides continuing the progression. You can start betting just one number instead of the sum of two numbers, looking for a short winning streak to cancel out what remains.
Alternatively, you can break the larger numbers down into series of smaller numbers, such as (1+2+3+4)+(4+5+6)+(6+7+8), as if you were starting over with a new objective.
The Best Gambling Systems?
Martingale and Labouchere are solid short-term strategies that every successful gambler should be aware of. But these are by no means the only progressive betting systems in a professional’s tool kit. Played in moderation, the following schemes can also yield consistent profits.
Paroli (Anti-Martingale) – The goal is to win a series of three or four consecutive bets, yielding a net profit of 7~15 units. Begin by wagering one unit on an even-money proposition, such as the outside bets on Roulette: red, black, even, odd, small (1~18) or large (19~36).
Following a win, double the bet on the next play by letting the winnings ride. Continue playing in this manner until completing a sequence of three or four wins in a row. Upon a loss, restart the progression at one unit. Like the Martingale system, the objective is to gain enough profit from short winning streaks to cover any losses that may occur.
But unlike the Martingale system, this does not require a large bankroll, and it can be extremely profitable if you get on a winning streak. The trade off is that you are giving up small wins to accumulate larger ones.
d’Alembert – The goal is to win a single unit in profit. Begin by betting one unit on an even-money proposition, such as the outside bets on Roulette: red, black, even, odd, small (1~18) or large (19~36). Following a loss, increase the wager by one unit.
Following a win, reduce the wager by one unit. Continue playing in this manner until the required bet is zero. You will have won a single unit in profit. Then, begin the progression again.
This strategy relies upon the “Law of Equilibrium,” making use of the odds that even-money outcomes will, over the long term, be very close to 50-50.
Contra d’Alembert – This is the opposite of the d’Alembert system. Instead of requiring you to increase your wager when you lose and decrease it when you win, the Contra d’Alembert system instructs you to increase your wager by one unit when you win and return to your initial one-unit wager when you lose.
The goal here is to win as much as possible during any series of positive outcomes, while limiting losses on negative ones. The winnings you take in excess of the amount required to make the next bet should offset any losses.
For example, if you win four bets in a row and lose the fifth, you would have two units after the first win and wager them both and four units on the second win and wager three, while pocketing one. Your third win would bring in six units, of which you bet four and pocket two.
On the fourth win, you receive eight units, pocket three and bet five which you would lose on the fifth play. You have pocketed six units and risked only your initial one, a profit of five units.
The system does, however, have a down side. Although losses are limited during losing streaks, it can take a lot of winning streaks to recoup them.
Fibonacci – The goal, once again, is to win one unit in profit. The amount to be wagered is always the sum of the preceding two losses. You begin by betting a single unit on an even-money area of the table. Following a loss, bet one unit again.
Upon another loss, increase the bet to two units (1+1). After a third loss, bet three units (1+2), etc. Following a win, cross off the last two numbers in the sequence. Continue playing in this manner until all of the numbers have been crossed off.
The strategy is to cancel numbers twice as fast as you add them. Eventually, all of the numbers in the series will be crossed off, yielding a profit of one unit. Then, start the progression again.
Gambling Systems That Work
Professional gamblers are different from amateurs in many respects. Their success, however, is based less on knowing gambling systems or odds than it is on treating gambling as a business. Although most of them enjoy what they do, they do not mix work with pleasure.
They never drink alcohol or allow themselves to be distracted when they play. They may develop certain instincts over time, but for the most part they base their decisions on logic and past experience, not feelings.
They set specific objectives and limits and they stick to them. So if you are seeking a winning strategy for any form of wagering, take a tip from the pros and incorporate the following four “business” features into your gambling activities.
1. Create Your Bankroll. This may sound like something only for wealthy players, but if you want to win with any consistency, it is necessary to know how much you have available to play with, no matter what level of wagering you are involved in.
In simplest terms, a “bankroll” is the total amount of cash you are willing to wager for an entire “season” of betting. In race or sports betting, the seasons are fairly well defined. For casino table wagers, it might be based upon a calendar month, a quarter or a year.
How much you budget for your bankroll will depend on the maximum you can afford to lose. This should be a separate category within your personal budget, just like salary, rent or utilities, and maintained separately from other expenses and income.
You might want to think of it as your “business capital.” Professionals always know exactly how much they have available and what percentage of it they can risk on any given bet. The bankroll can be expected to increase or decrease as you win or lose. It is not a static amount.
2. Maintain Your Records. Most amateurs have no idea how much they wagered last year, how much they won or lost, what games returned the greatest return on investment and which ones sucked their bankroll dry.
Record keeping is ultimately the only way you will ever know how much success you have at gambling. All you need is a notebook to keep track of your gambling sessions, or you may want to set up a spreadsheet on your computer.
A simple record book requires information in six columns: (1) the date you played, (2) a description of what you bet on, (3) the place where you bet, (4) the amount won or lost, (5) the running total of your bankroll, and (6) a space for any notes, such as the odds for races or sports bets or the length of time at the tables or slots.
There is certainly much more data you can add, but be sure you keep accurate records of at least the first five.
3. Do Your Research. Study statistics and trends, read books and articles, and watch other players. Become detail oriented. If you are into sports betting, be aware of weather conditions, injury lists, coaching changes…anything at all that could impact the outcome of a match.
Professionals are always looking for ways to “up their game.” Even the world’s best athletes have coaches and trainers to help them excel. You need to develop a habit of learning more and more about your game. A healthy curiosity and an insatiable passion for your game will serve you well.
4. Manage Your Money. The biggest mistake that most casual gamblers make is mismanaging their funds. When they win, they blow their profits in celebration or trying to stretch their luck too far.
When they lose, they go to the ATM for fresh funds and start betting bigger to get back to even. Professionals know that risk can be minimised and the possibility of winning maximised by playing steadily, wagering over the long-term and not being overly concerned about short-term gains or losses.
They accept the fact that some sessions will lose, but they also know that enough sessions will win to keep their bankrolls growing. The key is to always quit while you are ahead or before you exceed your session’s allotted limit.
Gambling Systems and Turning the Odds Around
There may be no “magic bullet” for winning consistently, no foolproof gambling systems for wagering that always works. However, there is plenty of evidence to support the theory that the more information you have about a game and the more skilled you are in applying it, the more likely you will be to able to turn the odds in your favour.
This is the thinking that drives race and sports handicapping. It is also the basis for at least two approaches to table games that put power in the hands of the player.
The first of these, as applied to Roulette, is called “clocking.” The clocker will study a Roulette wheel, often for hours, trying to discern any flaws in the way the ball falls into the pockets of the spinning wheel. The idea is that mechanical devices are subject to wear and tear.
If the wheel is not perfectly balanced or a fret is bent, then certain numbers may come up with higher frequency than others.
This approach was first put to successful use in 1873 by British engineer Joseph Jagger in Monte Carlo. He reportedly won £65,000 (equivalent to £3.25 million today) by monitoring and finding a biased wheel in the Beaux-Arts Casino.
To find this wheel, Jagger employed six clerks and had them record the results of every spin on all the wheels at the casino for six days. He then wagered on nine of the numbers that occurred more frequently than the others (7, 8, 9, 17, 18, 19, 22, 28 and 29). Eventually, the casino management caught on and repaired the wheel.
As recently as the 1990s, another clocker was able to win over one million Euros at the Casino de Madrid. Gonzalo Garcia-Pelayo used a computer to discover biased Roulette wheels there.
The casino took him to court, claiming he had cheated, but the court found he had done nothing wrong. Garcia-Pelayo kept his winnings, and clocking was declared to be legitimate gaming research.
The minimum number of spins required to clock a wheel and identify any bias pattern is about 200. At an average of 30+ spins an hour, you need to observe every spin of a wheel for no less than six hours.
Supposing you could find such a wheel, the house’s built-in advantage of 2.7% might be reduced to zero or even tipped in your favor, as in Jagger’s case, to 4.6% or more.
At that rate, you would need to place about £1.3 million in wagers over time to recreate the British engineer’s success. Even if you wagered £1,000 on each spin, it would take more than 40 hours of play to reach that level.
Wary of clockers, modern casinos use oscilloscopes to monitor the balance of their Roulette wheels. The chances of you finding a biased wheel before they do are therefore quite slim.
And even if you could, it is likely that the wheel would be taken out of play long before you made a small fortune off your hard-earned knowledge.
Counting Cards at Blackjack
The second approach applies to Blackjack, and it is known as “card counting.” Unlike Roulette and Craps, Blackjack has a built-in bias, in that the removal of cards from the deck as hands are played has a significant influence on the odds of other cards being dealt.
An observant player who knows what cards remain can bet accordingly, wagering small amounts when the cards favour the house and large amounts when the odds are with the player.
In his 1961 book “Beat the Dealer,” Dr. Edward O. Thorp detailed the optimum way to play Blackjack—the so-called Basic Strategy. Card counters combine this strategy with another called the Plus Minus Strategy to determine how much to wager.
In the simplest version of card counting, revealed low cards (2, 3, 4, 5, and 6) are each given a value of +1. Each high card (10, Jack, Queen, King and Ace) that appears is counted as -1. The other cards in the deck (7, 8, and 9) have no value.
Small cards removed from the deck have been shown to give the player an advantage, so the count becomes positive. Large cards removed favour the house, and the count turns negative.
A card counter will bet big into a deck rich with high cards. When playing with a single deck, you should bet just one unit if the count is +1 or less, and two units if it is +2 or more.
For multiple decks, adjust the procedure accordingly to +4 or lower and +5 or higher for four decks, and +6 or lower and +7 or higher for six decks, etc.
When the hands are played, you will also want to adjust your play—drawing, doubling down and splitting—based upon how rich or poor the deck is. For example, when the count is negative, and the deck has a lot of small cards, you might choose not to double down on a nine facing a dealer’s 2 through 6.
Some card counters also track of fives. Others track Aces separately. It really depends on how good your memory is. The more you can remember, the better you can play. But no matter what approach to card counting you take, you will find that it is not as easy as it might seem.
Card counting demands unwavering concentration, excellent recall, and flawless mastery of basic play. And since Blackjack is essentially an even-money game, the winnings stack up slowly, often requiring hours at the table to reach a predetermined profit objective.
Like clocking a Roulette wheel, card counting is certainly not cheating, nor is it illegal. It is nothing more than a strategy that reduces the house edge and guides the player’s decisions.
However, because it really does help the player win to such a great degree, casinos keep a close eye out for signs of card counters and often exclude them from their Blackjack tables.
As private businesses, they have the right to prohibit anyone from playing, so if you do choose to count cards, it is a good idea not to stay too long or win too much at one table or casino.
Real Casino Cheats
As you have seen, winning consistently as a gambler requires a lot of patience, knowledge and hard work—perhaps too much for those who are only interested in getting rich quickly.
Not surprisingly, some elect to take faster and easier pathways to wealth, ones that involve bending rules or breaking laws. Indeed, given the current recession, the incidence of cheating at casinos has been on the rise, as evidenced by the 400+ arrests made in Nevada in 2009 for casino and gambling related crimes versus fewer than 300 the previous year.
To the chagrin of law enforcement and the gaming industry, even though the role of organised crime in casinos has virtually disappeared, individual cheats have emerged as the biggest threat to the gaming industry.
And the people who have the greatest opportunity to cheat at the gaming tables are the casinos’ own employees. Dealers are in direct contact with the cards, dice and Roulette equipment. They also handle the chips and cash.
Although players may worry about being cheated by dealers, such occurrences are really quite rare. The house already has an advantage built into every game.
There is no incentive for employees to cheat players. Instead, if they are dishonest, the dealers are more likely to be stealing from the house, so you can be sure that legitimate casinos keep a close eye on their employees for cheating.
In August 2009, for example, four casino supervisors at the Planet Hollywood casino in Las Vegas were caught falsifying poker room payouts. Their records showed that players had won jackpots that didn’t exist. Instead, the white-collar criminal quartet had pocketed the “winnings.”
Then, in September, a craps dealer at the River Palms casino in Laughlin, Nevada was found stealing $1,000 chips. He had cut a hole in the bottom of his pocket so that the chips would drop down through his pants leg and into his shoe.
And in October, the manager of a small company that supplies slot machines to Nevada gas stations and grocery stores was taken into custody on charges of embezzlement.
Staffing cutbacks, pay reductions, decreases in benefits, low morale, lack of job security…all of these may be contributing factors to the rise in thefts by casino employees.
According to Willy Allison, a casino security consultant recently interviewed by the Las Vegas Sun newspaper, “You’ve got staff on the floor whose tips have dropped 40 percent, they’re having trouble paying their mortgages and they don’t know whether they’ll have a job tomorrow.
You have opportunity, motivation and rationalisation. People who were honest before the recession aren’t now, now that their children are starving.”
In many cases, casino workers collude with players to defraud the casino. A slot technician may rig a machine to payout more frequently for a secret partner. A card dealer might mark cards, deal from the bottom of the deck, or slip chips to an associate posing as a player.
One ticket writer at the Caesars Palace sports book was apprehended for taking chips used to pay for wagers and passing them off to an accomplice who then cashed them at the cashier’s cage. Sometimes the temptation to steal from the boss is just too much.
Old School Cheats
Short of pulling out a gun and actually robbing the cashier, most forms of cheating by players at casinos fall into two broad categories: old school and techno.
Surveillance staff are quite familiar with both of these, but for your own protection it is a good idea for you to be aware of them as well, especially those that relate to your own money, such as chip theft and hand cheats.
Coin Cheats – Taping a string to a coin was a clever way to trick slot machines back in their early days. Called the “Yo-Yo,” it could be used to add credits by simply pulling the coin up and down through the slot mechanism.
Modern cheats have used “shaved coins” that trigger a credit and are then discharged, or foreign coins of little value that can substitute for higher denomination domestic coins. “Slugs” of worthless metal have been used, too.
More recently, slot chutes and optical coin readers have been designed to prevent such fraud, and the newest machines are paperless, making old school coin cheats a practice of the past.
Counterfeiting – This includes the use of counterfeit slot tokens, as well as paper currency, which are usually caught by the money handling mechanisms of slots and the watchful eyes of cashiers and dealers trained to spot fakes.
The most sophisticated counterfeit money used by casino cheats is designed to outwit the various checks and balances of the bill validators used by slot machines. The bogus bills are not discovered until the casino empties the machine and counts the money.
Chip Theft – This is one of the most common forms of old school cheating in casinos, often occurring at the Craps tables. While everyone’s attention is focused on the action, the cheater will reach over and steal a chip or two from your tray on the railing or else grab your chips directly from the table after the dealer has paid out all winning bets.
Unlike other casino table games, Craps requires players to take responsibility for removing chips and winnings; new players, in particular, often forget to do so.
Late Betting – Also known as “past posting” or “top hatting,” this form of old school cheating is the surreptitious placing of a bet after the outcome of an event has already been decided.
It often involves other players creating a distraction while the cheater sneaks a wager onto the winning spot at Roulette or Craps. Late bets are very hard to get past watchful dealers or the “eye in the sky” surveillance cameras that record every movement on the casino floor.
Hand Cheats – This form of old school cheating includes hiding or “palming” cards, swapping cards with another player, and stealing chips from the pot, all of which require some really quick hand techniques.
It also includes marking cards by creasing the corners or using fingernails to cut tiny slits into the edges. To prevent such cheats, most casinos do not allow players to handle the cards or chips for certain susceptible games.
Dice Cheats – A few old school cheats have learned how to throw dice to gain an advantage. They are known as “mechanics,” and the best of them can hold and throw dice to come up whatever numbers they want.
Others attempt to substitute “loaded” or unbalanced dice for the real ones. Craps dealers and pit bosses are always on the look out for such players. They watch for “whip shots” that send the dice spinning vertically without turning over. Each throw must hit the opposite end of the table to be considered a clean roll.
Also, the shooter can use only one hand to handle the dice. The stickman always offers five dice, so that if unbalanced ones were to enter the game, the chances of a shooter picking up two of them are diminished.
Techno Cheating
Slot machines are the number one target of gambling cheats. Only a few people watch over the vast numbers of these machines in a casino, many of which are virtually out of view, surrounded by so many other machines.
In the early 20th century, thieves would use a coat hanger to jam a machine’s payout mechanism. In one instance, a cheat was said to have stolen $200,000 from numerous slots by using this method before getting caught.
Magnetic devices that slow spinning reels, strobe lights that interfere with optical sensors, and electronic interference generators have all been used at one time or other in attempts to take money illegally from slots.
Tommy Glenn Carmichael, perhaps the world’s most infamous slot cheat, created a device he called the “monkey paw” to trip the payout switch in electronic slots. Carmichael said he could use the paw to add credits to a machine, too.
He also invented the Light Wand, which was used to blind a slot’s optical reader. But like so many clever technicians, he was eventually arrested. Today, having served his time, he is a security consultant to the casino industry.
To beat the Roulette wheel, cheats have developed hidden computers, laser tracking systems, magnetic-field generators and concealed cameras. In 2005, Hungarian gambler Laszlo Kovacs hid a small computer in his shoe.
Tapping the sole of it beneath the roulette table allowed him to determine wheel speed, ball velocity, and where the ball would land. Before getting caught, he managed to defraud casinos in Australia out of $200,000.
Perhaps the most recent trend in techno cheating is online. Programmers claim to have come up with software and “robots” that can hack the codes of a web site’s Roulette or Craps application and identify exactly what to bet and how much to wager.
In fact, most of these “bots” are simply math engines. You set the initial parameters and they apply standard betting progressions, such as Martingale or Labouchere, crunching numbers faster than you can and with absolute accuracy.
Many online casinos have prohibited the use of such applications, but the practice is difficult to monitor and stop. For now, the persons who are really making money off such software are the programmers.
And speaking of programming, perhaps the best example of a modern techno cheat is Ron Harris, a former computer programmer with the Nevada Gaming Control Board (NGCB).
He was able to use his position to insert special code into a device used by NGCB employees to check the proper functioning of slot machines. Once the device was connected, the code would be uploaded and the machine was ripe for cheating.
Harris had a team of players who would visit these machines and win pre-programmed jackpots. They managed to keep the scam up for four years before Harris was caught with an accomplice, winning a $100,000 Jackpot in Atlantic City.
The only reason cheaters are willing to risk the possibility of jail time is the overriding belief that they won’t get caught. Yet casino security has never been tighter or more high-tech. Anti-theft devices, surveillance systems, and forensic accounting techniques are in place.
Casino staff are better trained than ever to identify acts of fraud, larceny, and deceit, which also impacts the arrest statistics. So although there may be more cheating going on than ever before, more cheaters are also getting caught.
