7. Systems and Strategies
Betting systems fall into the broad categories of betting the same after each decision, known as flat betting, raising wagers after wins, called positive progressions, and raising money after losses, named negative progressions.
There are also systems which have characteristics of one or more of these types, such as the Maximum Advantage Roulette Betting System which we will encounter in a few more chapters. Many of the classical betting systems were developed for roulette in the eighteenth and nineteenth centuries, but they can be used for other games with even-money wagers such as craps, LIVE baccarat and LIVE blackjack. Although none of these systems in its pure form is a winning system, it is worthwhile to study the efforts of our ancestors as these betting systems are the grandparents of every modern betting system.
Martingale is one of the oldest betting systems using a negative progression. The origin of the name is in dispute. Many gambling writers believe it is a bastardization of the name "Martindale" and that it was named after Henry Martindale, an English casino owner in the 1700s who is reputed to urge losing punters to "double 'em up" with their wagers.
If you are looking for a system that wins a majority of the time, you need look no further than Martingale. If you use it, the odds are in your favor that on a given night you will be a winner. This system is very simple. You will use a betting series where each bet in the series is twice as large as the preceding one, as with 1, 2, 4, 8, 16, 32. So long as you win a bet, you will continue to bet at the lowest level, e.g. wager 1. If you lose a bet, you will move up to the next wager, doubling the amount of the previous wager.
Use of the system ensures that whenever your wager eventually wins, you will win the amount of the original wager, in this instance 1.
One of my gambling friends once told me about an amazing system he had developed for craps. He had gone to Las Vegas on two consecutive trips and returned a winner. He was wagering only on don't pass at casino craps using a betting series starting with a $1 bet and doubling his bet after each loss. He was certain that his risk of loss was very small and planned to continue to use the system. He was reluctant to share the system with me but he finally confessed that he was using the following betting series, increasing his wager one level following a loss: 1 2 4 8 16 32 64 128 256. He correctly pointed out that he would have to lose nine times in a row to lose the betting series, and he just didn't think that this was possible.
I pointed out to him that there was a very real possibility that he could lose nine decisions in a row; in fact, this would happen once about every 500 pass line - don't pass decisions. With craps decisions averaging fifty to sixty per hour, a loss of all nine wagers could happen once every eight to ten hours. I asked him to consider whether he was winning enough to sustain a loss of $511.00 (the total amount he was risking) in order to win the sum of $1. This must have impressed him as I don't think he ever used this system again (or at least he didn't tell me about losing with it).
Here's a demonstration of how this system would work in a coin flipping contest. You are betting that the next coin toss will be heads. You have a 50-50 chance of winning any given bet. Should you lose a bet, or two bets, or three bets, just keep doubling your wager until you win one bet. Here's the beauty of this strategy.
You only have to win one bet to be a winner! Here's how you could use the Martingale System in the coin-tossing contest:
The above sequence of four tails in a row had a one in 16 chance of occurring. The odds of you winning here are 15:1 in your favor!
This seems like a pretty safe bet, doesn't it? You'd only hit a losing streak of four straight losses once in every 16 times you played.
That's the best part about using the Martingale System.
A coin toss is a "fair" game where neither the roulette casino nor the house has an edge. Here are the odds against various runs of a given bet (heads or tails) coming up in a fair (50-50) game:
However, with roulette there are no true "even-money" bets. There are several bets that pay even-money, but the true odds are not 50 - 50 as in the coin toss. Let's take a look at "even-money" bets on both zero and double zero wheels.
On a double-zero wheel an "even-money" bet wins 18 times but loses 20 times. On a single-zero wheel this wager wins 18 times but loses 19 times. Thus your odds of winning on a double-zero wheel are not 1 to 2 as with a coin toss, but 1 to 2.11. Since the house pays off a dollar for a win rather than $1.11, it keeps 11 cents for itself as the house edge or casino "vig." This gives the casino a 5.26% edge over "even-money" bets in the long-run.
On a single-zero wheel, the odds are 2.0556 (rounded up to 2.056) which works out to be a 2.70 percent house edge for long-term play.
The table below shows the odds against consecutive hits of evenmoney bets on each type of roulette wheel.
The Martingale system would be just about unbeatable if you could continue to double your wagers until you finally won a bet.
Modern casinos are very aware of Martingale, and they know that the easiest way to thwart the system is to narrow the spread between maximum and minimum bets allowed. In other words, the minimum wager must be high enough and the maximum wager low enough that no more than eight or nine doublings can occur. If you find a table with a low minimum, such as $1 and a high maximum, such as $3,000, you may wish to try using a Martingale system against the table.
You could use the following series of wagers: 1 2 4 8 16 32 64 128 256 512 1,024 2,048. With 12 bets in the series, you would be an odds-on favorite to win any weekend gambling contest involving even-money wagers. However, you might want to consider one thing. If you try this, sooner or later you will lose bet number 11, for $1,024. You will now have lost $2,047 and will be called on to bet $2,048 in order to win the grand sum of $1. Are you willing to risk it? If you win, you will be up exactly one buck for your efforts. However, if you lose your last wager of $2,048, you will have lost $4,095 in the gaming contest. While the risk of loss is low, it will happen at some time if you continue to wager this way, and there is no guarantee that it won't happen during your first casino excursion using this system.
A story is told in The Sealed Book of Roulette (remember this was copyrighted in 1924) that Arnold Rothschild once said to M. Blanc, manager of the casino in Monte Carlo:
"Take off your maximum and I will play against you as long as you like."
Rothschild knew that without a maximum bet he could use the Martingale system and eventually beat the house. Unfortunately, you are not likely to encounter a casino without a maximum bet.
Martingale in its purest form is too risky for the amount of reward offered. Nearly every gambling expert likes to cite Martingale as an example of a losing system and then jump into a gloating mode and proclaim that all betting systems are losers. However, a Martingale system can be used with very good results if it is used on a spot basis. Assume that you are wagering on an even-money game and that you have lost the last four consecutive wagers. Usually, a three-stage Martingale against this trend continuing for three more decisions will be quite profitable and the reward will be reasonable as compared to the amount risked.
A five-stage Martingale progression can be used when it is used against a betting pattern which is less likely to occur than would normally be expected.
One criticism of Martingale is that too much is risked as compared to the potential return. For example, in the first Martingale series shown, you would have had to wager $256 in order to win a net $1.
With Grand Martingale, additional chips are added to each increased wager, so that when a win finally occurs, the amount won will be greater than just the amount of the first wager. A typical Grand Martingale series is: 1 3 7 15 31 63 127 255 511. Martingale in all forms risks a lot to win a little. When the losses come, they will wipe out hours of profits. Another twist to using a Martingale series is to play Martingale in reverse called an "Anti-Martingale" betting series. With this system, winning wagers will be pressed (doubled). Whenever you encounter a long winning streak this system can produce phenomenal profits. Assume we use the following Anti-Martingale series: 5 10 20 40 80. With five consecutive wins, we will $155, while our total risk is only the amount of our first wager, $5. The high-risk reward ratio is a major reason raising your wagers after wins is recommended by many gaming experts. However, as we saw two chapters back, this type of system wins very infrequently, and the many small losses overwhelm most gains, so that over 90% of all games will end with a loss.
This system was first "discovered" by Henry Labouchere, an English gambler who traveled the world playing it until he died in 1912. His discovery was actually created in the eighteenth century by a French mathematician, named the Marquis de Cordorct.
With Labouchere, also known as the Cancellation System, the player sets up a series of numbers which will add up to the profit he will make if he wins this betting series. If he picks 1 2 3 as his series, his expected profit for winning this series is 1 + 2 + 3 = 6.
Like the variations of Martingale, this series is used with evenmoney bets.
To start the series, a player will wager the sum of the two outside numbers, in this case 4 (1 + 3 = 4). If he wins this wager, he will cancel the two outside numbers by scratching them out, and wager the sum of the next two outside numbers. In this simple series, only the single number of 2 is left, so the player would wager 2.
If he also wins this wager, he will have won the series, having won 4 on the first round and 2 for the second wager, for a total of 6, the total of all bets in the series.
Any time the player loses a wager, he will add the amount lost to the series and continue to wager the sum of the two outside wagers.
Let's assume the player lost the first bet of 4. He would add this wager to the series, which would now become: 1 2 3 4. His next wager would be for 5, the sum of the two outside wagers. We will assume that this bet wins. Having won the bet, our players cancels the outside numbers of 1 and 4 leaving the series as: 2 3. He next wagers the sum of these two numbers, betting 5. If this wager wins the series is completed. If he loses this wager, the losing bet of 5 will be added to the series and he will continue the series.
The principal appeal of this system is that it appears to be a two for one proposition in that each win cancels two numbers while a loss only adds one number to the series. However, this isn't the case, as the player is not paid two to one on winning bets.
In testing this system, I have had bets escalate to wagers of hundreds of dollars all too frequently. This is probably the most insidious of the old time roulette systems. It is said to have been responsible for more suicides on the French Riviera than any other system. Part of the problem with this system is that the small stream of steady wins tends to lull the player into believing that the system can't lose. Unfortunately, a long enough losing streak will occur that the wagers called for will either be larger than the player's bankroll or will exceed the house limits and not be allowed. In either case, the series will be over with the end result that the player suffers a substantial loss.
This system can also be played in reverse, known as Reverse Labouchere. With Reverse Labby, as many punters call it, the amount of each win is added to the series, and the two outside numbers are canceled whenever a loss occurs. Each wager is still the sum of the two outside numbers. This system produces many small losses in exchange for an occasional win over 1,000 times the amount at risk.
Use of this approach is recounted in Norman Leigh's fascinating account of his successful effort to beat the casino in Monte Carlo by playing Labouchere in reverse (Thirteen Against the Bank, William Morrow & Co., 1976). Norman Leigh theorized that the reason so many players lose with Labouchere is that they run into the house limits or lose their playing capital and are unable to recoup losses. Since the bank has almost unlimited capital in comparison to the players, the bank can out wait most player assaults, knowing that either the house betting limit or the player's own limited financial resources will bring about the player's demise.
In using the reverse betting strategy, Leigh reasoned that this approach would most closely resemble the bank's approach to most other players. He would wait out the small losses until a large win occurred. Leigh spent months recruiting and training a team to play against the casino. His trials in pulling off this coup make for fascinating reading. I believe that one of the reasons he was eventually able to beat the casino in Monte Carlo was that his starting wagers were fairly low and the house maximums large in comparison. Consequently, he was able to keep his losses fairly low while his team played on, waiting for the monster win.
It is doubtful that this system could be used successfully now, as the spread between minimum and maximum wagers are not large enough in most casinos. The losses realized while waiting for the large win would be enormous, with the house limits on maximum wagers limiting the systems' ability to ultimately recoup the losses.
This system was invented by a French mathematician, based on the assumption of equilibrium in gaming contests. Jean Le Rond d'Alembert reasoned that since winning and losing bets must eventually equal one another, a system of adding one chip after each losing bet and subtracting a chip after a winning bet would ultimately result in a win as winning wagers would always be greater than losing ones.
It is not unusual to win only ten of the first thirty wagers in an even-money betting contest. With d'Alembert's system, the player will wager higher and higher amounts until he eventually runs into our old nemesis, the house limit.
The d'Alembert betting system can be fairly successful if it is modified to include no more than nine or ten bets in a series of wagers, so that potential losses are limited. An additional modification to improve the system is to space the bets so that the win of two consecutive wagers will offset prior losses. A series which accomplishes this is 1 2 3 4 7 11 18. With this series, a player would drop back to the lowest bet after winning two consecutive wagers, such as 7 and 4. This system can be fairly successful if used by two partners betting the opposite in roulette, craps or baccarat.
The betting system incorporated for even-money wagers in the Maximum Advantage Roulette Strategy uses a highly modified type of d'Alembert. As you will see, in a modified form, coupled with a special bet selection strategy, the system can become a very stable and predictable performer.
Like Reverse Labouchere, the idea behind Contra-d'Alembert is to reduce the amount risked while allowing profitable runs to rise to great heights. With this strategy we will increase our wager one level after a win and reduce it one level following a loss. The only positive aspect to the strategy is that when you hit a prolonged losing streak the size of your wagers is quickly reduced.
In this respect this system can help protect your bankroll. However, the upside of using any system requiring increasing your wager following wins is limited. Trends of long, uninterrupted winning streaks are fairly rare in gaming and a system relying on piling up win after consecutive win is not going to win very often.
Here's an example. Your first bet is for one unit. You win and move up to betting two units. With another win, you wager three units and have a loss. You have won two out of three bets and have absolutely nothing to show for it. All of your profit evaporated with that single loss.
If you could always pick your spots, this system would have merit.
Of course, if pigs could fly . . . well, you get the idea. It is just about impossible to know in advance when a three-wager consecutive win might occur so that you could jump in with a Contra-d'Alembert. Like so many systems, this one sounds good on paper, but is difficult to squeeze profits out of in real world gaming.
This is another of the old time roulette systems that can be adapted to any game offering even-money bets. With Ascot, winning wagers are increased one unit at a time in a predetermined series of wagers while losing bets are lowered one step using the same betting series. An Ascot betting series can be from seven to eleven numbers. A typical series is: 2 3 5 8 13 20 30. The player's first wager would be a middle number such as 8. If this wager wins, the next wager would be 13. If this wager also won, the succeeding wager would be for 20, and so on, with each win followed by an increase of one level in the betting series. The series would end with the win of the last bet in the series. For a win, that would be a win of 30. A losing series would be terminated with the loss of the lowest bet of 2.
The greatest problem with Ascot is that alternating wins and losses at the higher levels of wagers will destroy the profit potential of the series. This can be a serious flaw in any system calling for a large reduction in the amount wagered following a loss.
The Fibonacci System
Fibonacci was a mathematician who discovered a series of numbers where the sum of each two numbers in the series equals the number which follows. A Fibonacci series with twelve levels of bets would look like: 1 2 3 5 8 13 21 34 55 89 144 233 for a total risked of $608.
This is a very low risk system for use with even-money bets at craps, roulette and baccarat. To use it, you will increase your bet one level following a loss. After any win, you drop your next wager one level. If you win two bets in a row, or win two out of three bets, you drop back to the first bet in the series.
This system was sold many years ago for $100 a copy with instructions to use it betting Don't Pass in craps. This is a good system for partners to use betting opposites. With roulette, for instance, one partner could bet red while the other wagered black.
With craps, one would wager on pass line and the other on Don't Pass. With baccarat, one partner would bet banker and the other on player hands.
Incidentally, there are a number of derivations of the Fibonacci series of numbers, including ratios of the numbers, which are regularly used in trading stocks and commodity future contracts.
This is indeed a versatile and powerful sequence of numbers.
A parlay or paroli is a positive progression method. In its simplest form, it consists of leaving a winning bet plus the winnings up for a second win. If you are betting $10 on an even-money bet and win $10, you parlay the wager by leaving $20 up for the next decision.
If this bet wins, you will have won $30 while only risking $10.
Probably the most attractive aspect of a successful parlay is that it wins three times as much as the amount risked. However, the probability of winning two bets in a row on even-money wagers is less than one in four. For this reason, one of the better ways to use a parlay is to combine it with a series of bets where the amount wagered is increased following a loss. For example, the following parlay progression could be used: 2 2 3 4 6 8 12 16. To use this series, you would normally start with the first wager in the series.
If this bet won, you would parlay it and next wager $4. If either the original wager or the parlay lost you would move up one level in the betting series. Any time a parlay bet is won, you will start the betting series over. If the series is lost, you may either start the series over or leave the table.
Setting up parlay progressions like the one above can be the basis for some of the best performing betting progressions in gambling.
To use such a series in blackjack, which requires additional money in order to handle pair splitting and doublings, requires adjustments to the series. One way to handle this is to modify basic strategy to reduce the number of splitting and doubling plays. However, this is not a wise way to play blackjack as these moves represent one of the player's strongest winning options. A better way to handle the program of developing a winning parlay progression for blackjack is to modify the progression so that it allows for splitting and doubling opportunities.
If you want to use a system with very little risk of loss, here's the one you want.
Oscar has a target of winning one unit at the end of any successful betting series. That's it. One unit. Here are the rules:
- Increase your bet by one unit after every win; provided that winning the wager won't result in a series gain larger than one unit.
- Never change the size of your bet following a loss.
Assume that your betting unit is $5 and you are betting don't pass. You find yourself fighting a hot streak and you have lost six bets in a row for a cumulative loss of $30. You continue to bet $5 since you never change the size of your wager following losses. You bet $5 again and win. Now, with one win and six losses, you are down a net $25. Following the win, you raise your bet one unit and wager $10. This wager also wins. You have reduced your net loss to $15. You raise your next wager one more unit to $15 and win. You are now even. Your final wager will revert to $5. Why?
Because of the rule limiting the size of a wager to one which will not result in a gain larger than one unit.
Your last bet of $5 wins. You now have a net win of $5, having lost six bets and won four.
Even this system can take you to high levels on occasion. If you find yourself in a situation where you have occasional wins followed by multiple losses, the size of your wagers will continue to grow. If this occurs, you will be forced to stop the series at some point and accept a loss rather than risking larger and larger amounts of money.
The Red System
This system originated in the 1960s. It is based on the fact that in the third column of the roulette layout there are eight red numbers and only four black numbers.
This system requires that you wager one unit on the third column and two units on the color black. With a $5 table minimum, this means $5 on the third column and $10 on the color black. If a red number in the third column hits, you win $10 for the column bet (it pays 2 to 1) and lose the $10 wager on black, for a breakeven decision. However, if a black number in the third column hits you will win $10 on the column wager and $10 on the black color bet, for a total 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 will lose the $5 column bet and win the $10 wager on black, for a net win of $5.
If a 0 or 00 shows you will lose both bets for a $15 loss. This system does not gain any real edge over the house and in using it, the casino will eventually beat the player. This system could be set up using a negative betting progression, but I would not recommend it.
The Black System
This system is much like the red system and is based on the fact that in the second column there are eight black numbers and only four red ones. Instead of betting on the third column and black, you will wager $5 on the second column and $10 on the color red. This is just the opposite of the Red System and offers no real advantage to the player.