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So many believe they can combat baccarat with a 'system', in other words a simplistic plan of attack compiled from a multitude of combinations.  Some players believe a certain wager or two, or perhaps three.  Such as play the 'cut' after a natural wins or play the 'cut' after every single 3 or 4 repeats on either side, etc.  Other players will read a book or gain 'secret info' from another player as to how their 'system' of a few preconceived pre-selected and scheduled wagers should prevail the highest majority of the times.  Usually the latter is support by undocumented, non-certified and non-audited evidence of statistics derived from 10,000--100,000 or 1,000,000 shoes, seems to be the most popular numbers. 

Okay, all fine and yes--any and all 'system' can and will win at times.  They have to.  As anything and everything will happen in baccarat.  The problem is and the biggest problem happens to be be scheduling.  What the 'systems' authors have done, is merely pick a series of events that happen frequently and add their twists and non-documented statistics and sample shoes, then sell it with the promise of making easy money the new and correct way no one ever thought about or discovered.  Problem is, no one knows when those events will happen or continue the same way that, no one knows how long a run will be or not be or how many 1's and 2's there will be, etc., etc.  There is no difference.  The trick in baccarat is wagering anything and everything and attacking it from every side-direction and event the shoe produces or not produces.  Easy?  No.  Possible?  Yes.  Frame-of-Mind is everything.  There are no set schedules for anything to happen.  Some believe continual wagering will allow them to prevail just for that very same reasoning.  Also, far fetched.  Looks great on paper, go play it.  After all, why argue and defend something you have not implemented and tried.  If it is successful, keep doing it.  Oh yes--then the 'systems' come out in book, pamphlet or seminar course forms.  My question is, why no audited and certificated documentation as to the results, the profits and the successes?  With the amount of profits the author made (always claims) hiring an auditing firm would actually be the 'proverbial drop in the bucket' compared to the profits that would flood into his bank account if it was actually true. 


What the game does produce in the way of results.
What the game can do in the way of results.
What the game will do in the way of results
What the game does not produce in the way of results.
What the game cannot do in the way of results.
What the game will not do n the way of results.

There are not 1 or 2 or 3 wagers that can be pre-selected, preconceived and scheduled to be wagered on all shoes that, will prevail the upper majority of the times, let alone win every time.  Doesn't matter how many wins you are after each time you play, 1 or 3 or 6 or even 10.  Doesn't matter the amount of money (unit size) you are playing with.  A simple fact, fewer are always easier to win, the same as in any game, casino or not.  The same as speeding down the highway, much easier to get away with speeding for 1/4 mile everyday then it is 10 miles or 40 miles or 100 miles.  Simple, no different. 

Please think and be familiar with what the game can, does and will or cannot or does not or will not produce, rather than what you have to have it produce for your scheduled wager to win.  There is a difference and a huge difference at that.



Good Information from a Knowledgeable Source:


The Truth about Betting Systems

Not only do betting systems fail to beat casino games with a house advantage, they can't even dent it. Roulette balls and dice simply have no memory. Every spin in roulette and every toss in craps is independent of all past events. In the short run you can fool yourself into thinking a betting system works, by risking a lot to win a little. However, in the long run no betting system can withstand the test of time. The longer you play, the ratio of money lost to money bet will get closer to the expectation for that game.

In the many years that run this site I have received thousands of e-mails from believers in betting systems. Their faith surpasses religious levels. However, in all things, the more ridiculous a belief is the more tenaciously it tends to be held. Gamblers have been looking for a betting system that works for hundreds of years, and yet the casinos are still standing.

Gambler's Fallacy

The biggest gambling myth is that an event that has not happened recently becomes overdue and more likely to occur. This is known as the "gambler's fallacy." Thousands of gamblers have devised betting systems that attempt to exploit the gambler's fallacy by betting the opposite way of recent outcomes. For example, waiting for three reds in roulette and then betting on black. Hucksters sell "guaranteed" get-rich-quick betting systems that are ultimately based on the gambler's fallacy. None of them work. If you don't believe me here is what some other sources say on the topic:

A common gamblers' fallacy called "the doctrine of the maturity of the chances" (or "Monte Carlo fallacy") falsely assumes that each play in a game of chance is not independent of the others and that a series of outcomes of one sort should be balanced in the short run by other possibilities. A number of "systems" have been invented by gamblers based largely on this fallacy; casino operators are happy to encourage the use of such systems and to exploit any gambler's neglect of the strict rules of probability and independent plays. — Encyclopedia Britannica (look under "gambling")

No betting system can convert a subfair game into a profitable enterprise... — Probability and Measure (second edition, page 94) by Patrick Billingsley

The number of 'guaranteed' betting systems, the proliferation of myths and fallacies concerning such systems, and the countless people believing, propagating, venerating, protecting, and swearing by such systems are legion. Betting systems constitute one of the oldest delusions of gambling history. Betting systems votaries are spiritually akin to the proponents of perpetual motion machines, butting their heads against the second law of thermodynamics. — The Theory of Gambling and Statistical Logic (page 53) by Richard A. Epstein

Vegas Click also has a good expose of the gambler's fallacy.

The Martingale

Every week I receive two or three emails asking me about the betting system by which a player doubles his/her bet after a loss. This system is generally played with an even money game such as the red/black bet in roulette or the pass/don't pass bet in craps and is known as the Martingale. The idea is that by doubling your bet after a loss, you would always win enough to cover all past losses plus one unit. For example if a player starts at $1 and loses four bets in a row, winning on the fifth, he will have lost $1+$2+$4+$8 = $15 on the four losing bets and won $16 on the fifth bet. The losses were covered and he had a profit of $1. The problem is that it is easier than you think to lose several bets in a row and run out of betting money after you've doubled it all away.

In order to prove this point I created a program that simulated two systems, the Martingale and flat betting, and applied each by betting on the pass line in craps (which has a 49.29% probability of winning). The Martingale bettor would always start with a $1 bet and start the session with $255 which is enough to cover 8 losses in a row. The flat bettor would bet $1 every time. The Martingale player would play for 100 bets, or until he couldn't cover the amount of a bet. In that case he would stop playing and leave with the money he had left. In the event his 100th bet was a loss, he would keep betting until he either won a bet or couldn't cover the next bet. The person flat betting would play 100 bets every time. I repeated this experiment for 1,000,000 sessions for both systems and tabulated the results. The graph below shows the results:



As you can see, the flat bettor has a bell curve with a peak at a loss of $1, and never strays very far from that peak. Usually the Martingale bettor would show a profit represented by the bell curve on the far right, peaking at $51; however, on the far left we see those times when he couldn't cover a bet and walked away with a substantial loss. That happened for 19.65% of the sessions. Many believers in the Martingale mistakenly believe that the many wins will more than cover the few losses.

In this experiment the average session loss for the flat bettor was $1.12, but was $4.20 for the Martingale bettor. In both cases the ratio of money lost to money won was very close to 7/495, which is the house edge on the pass line bet in craps. This is not coincidental. No matter what system is used in the long run, this ratio will always approach the house edge. To prove this point consider the Martingale player on the pass line in craps who only desires to win $1, starts with a bet of $1, and has a bankroll of $2,047 to cover as many as 10 consecutive losses. The table below shows all possible outcomes with each probability, expected bet, and return.


The expected bet is the product of the total bet and the probability. Likewise, the expected return is the product of the total return and the probability. The last row shows this Martingale bettor to have had an average total bet of 11.81172639 and an average loss of 0.16703451. Dividing the average loss by the average bet yields .01414141. We now divide 7 by 495 (the house edge on the pass line) and we again get 0.01414141! This shows that the Martingale is neither better nor worse than flat betting when measured by the ratio of expected loss to expected bet. All betting systems are equal to flat betting when compared this way, as they should be. In other words, all betting systems are equally worthless.

Here is another experiment I conducted earlier which proves the same thing as the experiment above. This one is played against roulette testing three different systems. Player 1 flat bet a $1 each time. He was not using a betting system. Player 2 started a series of trials with a bet of $1 and increased his wager by $1 after every winning bet. A lost bet would constitute the end of a series and the next bet would be $1. Player 3 also started a series of bets with a bet of $1 but used a doubling strategy in that after a losing bet of $x he would bet $2x (the Martingale). A winning bet would constitute the end of a series and the next bet would be $1. To make it realistic I put a maximum bet on player 3 of $200. Below are the results of that experiment:
Player 1

    Total amount wagered = $1,000,000,000
    Average wager = $1.00
    Total loss = $52,667,912
    Expected loss = $52,631,579
    Ratio of loss to money wagered = 0.052668


Player 2

    Total amount wagered = $1,899,943,349
    Average wager = $1.90
    Total loss = $100,056,549
    Expected loss = $99,997,018
    Ratio of loss to money wagered = 0.052663

Player 3

    Total amount wagered = $5,744,751,450
    Average wager = $5.74
    Total loss = $302,679,372
    Expected loss = $302,355,340
    Ratio of loss to money wagered = 0.052688

As you can see the ratio of money lost to money wagered is always close to the normal house advantage of 1/19 ≈ 0.052632. In conclusion, varying of bet size depending on recent past wins or losses makes no difference in the long run outcome and is no different than always betting the same.

A Third Experiment

"An Old Timer's Guide to Beating the Craps Table" was a betting system that makes big promises about turning the craps tables into your own personal cash register. I offered to test his system for free. Here are the results.
The Cancellation Betting System

Despite all my warnings about betting systems, readers continually ask me to suggest one. To satisfy those who enjoy playing systems I have done a full explanation and analysis of the cancellation betting system.

Don't Waste Your Money

The Internet is full of people selling betting systems with promises of beating the casino at games of luck. Those who sell these systems are the present day equivalent of the 19th century snake oil salesmen. Under no circumstances should you waste one penny on any gambling system. Every time one has been put to a computer simulation it failed and showed the same ratio of losses to money bet as flat betting. If you ask a system salesman about this you likely will get a reply such as, "In real life nobody plays millions of trials in the casino." You're likely to also hear that his/her system works in real life, but not when used against a computer simulation. It is interesting that professionals use computers to model real life problems in just about every field of study, yet when it comes to betting systems computer analysis becomes "worthless and unreliable," as the salesman of one system put it. In any event, such an excuse misses the point; the computer runs billions of trials simply to prove that a system is unsound. If it won't work on a computer, it won't work in the casino.

Gambling systems have been around for as long as gambling has. No system has ever been proven to work. From an inside source, I know that system salesmen go from selling one kind of system to another. It is a dirty business by which they steal ideas from each other, and are always attempting to rehash old systems as something new.

System salesmen usually promise ridiculous advantages. For example, even with just a 1% advantage on an even money bet, it would not be difficult to parlay $100 into $1,000,000 by betting in proportion to bankroll. I was asked to prove this claim so I wrote a computer simulation based on the toss of a biased coin, with a 50.5% chance of winning. At all times the player bet 1% of his bankroll, rounded down to the nearest dollar. However, if a winning bet would put the player over $1,000,000 then he only bet as much as he needed to get to exactly $1,000,000. In addition, I ran simulations with a 2% advantage and for a starting bankroll of $1,000. Following are the results of all four tests.

$100 Bankroll, 1% Advantage

    Bets won = 7,182,811,698 (50.4999%)
    Bets lost = 7,040,599,544 (49.5001%)
    Player achieved $1,000,000 first = 79,438 (83.019%)
    Player went bust first = 16,249 (16.981%)
    Average number of bets to reach $1,000,000 = 174,972 (364.5 days at 8 hours per day, 60 bets per hour)


$100 Bankroll, 2% Advantage

    Bets won = 7,027,117,205 (51.0000%)
    Bets lost = 6,751,539,769 (49.0000%)
    Player achieved $1,000,000 first = 215,702 (98.099%)
    Player went bust first = 4,180 (1.901%)
    Average number of bets to reach $1,000,000 = 63,775 (132.9 days at 8 hours per day, 60 bets per hour)

$1,000 Bankroll, 1% Advantage

    Bets won = 5,213,026,190 (50.4999%)
    Bets lost = 5,109,817,544 (49.5001%)
    Player achieved $1,000,000 first = 74,818 (99.0285%)
    Player went bust first = 734 (0.9715%)
    Average number of bets to reach $1,000,000 = 137,208 (285.8 days at 8 hours per day, 60 bets per hour)


$1,000 Bankroll, 2% Advantage

    Bets won = 6,332,837,070 (50.9996%)
    Bets lost = 6,084,596,671 (49.0004%)
    Player achieved $1,000,000 first = 267,445 (99.9996%)
    Player went bust first = 1 (0.0004%)
    Average number of bets to reach $1,000,000 = 46,428 (96.7 days at 8 hours per day, 60 bets per hour)

These simulations prove that with just a small advantage of as little as 1% and a bankroll of as little as $100 you can grind your way to a million dollars through the gambling equivalent of compound interest. Yet you never hear of this actually happening. Could it be that these gambling systems don't work after all?!

Here are some examples of system salesmen who try to take advantage of the mathematically challenged. There are hundreds of sites like these on the Internet, and this list is just a sampling. Frequently these sites vanish in the middle of the night, or suddenly direct traffic to a porn site. Please do let me know if any of these links don't work or take you to other than the intended place.

    Ultimate Craps System
    Gambler's Bookcase
    Let's Talk Winning
    Power Craps
    Goldmine Roulette


Also be warned that there are many others out there selling get rich quick gambling schemes that claim they are not betting systems. These sites usually throw out lots of fancy physics words like "chaos" and "fractals," but display no evidence they know what these words mean. In the past I have listed some such sites above but got angry letters claiming I shouldn't criticize what I don't understand. Personally I feel that every method claiming an easy way to beat the casinos is a scam, and I don't need to understand whatever the secret is. However, to be totally fair, I'll only list betting systems above since those have been mathematically debunked by computer simulations. If anyone did find a true easy way to beat the casinos, why aren't they getting rich doing it?

(They are not getting rich with their own system and the standard, 99.9% given response by the expert systems author, which is: "I rather help my fellow man get revenge on the casino by writing and publishing this book than getting rich myself, the book will give me a comfortable living and satisfaction eventually".)

The Wizard of Odds Challenge

For about six years, from 1999 to 2005, I offered $20,000 to anyone with a betting system that could show a profit over a one billion hand computer simulation. Here you can find the rules of the challenge. However, in all this time I only had one serious taker and hundreds of people wasting my time, pretending to be interested but never following through. So in January 2005, I took down the offer.

My webmaster, Michael Bluejay, now offers essentially the same challenge on his own site, VegasClick.com. If you accept his challenge, and win, I will be happy to state as such on the front page of this site, for proving the experts wrong.

A Fourth Experiment


On October 19, 2004, Daniel Rainsong accepted my challenge. Mr. Rainsong was so confident he would win he doubled the stakes to my $40,000 against his $4,000. Although the rules of the challenge are based on craps or roulette I allowed this challenge to be based on blackjack rules with a house edge of only 0.26%. Can a betting system beat a game with a house edge this small and a 1,028 bet spread? Visit my Rainsong Challenge page for all the details.

Please, Don't Write


I no longer respond to e-mails that suggest a player can beat a negative expectation game over the long run with a betting system. Such e-mail is deleted on sight. I have said all I have to say on the topic here and in my Gambling FAQ.

If you really want to discuss the topic, then I invite you not to do so at my forum at Wizard of Vegas, but instead one where you will be among like-minded people, like the the forum at John Patrick's site.
External Links


Betting Systems and the House Edge, an article by Ph.D. mathematician Eliot Jacobson debunking betting systems.

Betting Systems, an article by Michael Bluejay of VegasClick.

German translation of this article.

Debunking the "No Risk Don't Come" betting system.

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(An excellent piece to read, there is something for anyone interested in the subjects of gambling, baccarat, blackjack, systems, winning and losing, (bagels and lox too for those from NYC)--(only kidding---lighten up!!!)


BETTING SYSTEMS AND THE HOUSE EDGE

By Eliot Jacobson

Eliot Jacobson has a Ph.D. in Mathematics from the University of Arizona. He was Professor of Mathematics from 1983 to 1998 at Ohio University, and currently holds a teaching position in the Department of Computer Science at the University of California, Santa Barbara. Jacobson recently published his first book on blackjack ("The Blackjack Zone," Blue Point Books, 2005) and it is available in the BJI store. To read a review of Jacobson's book that appeared in issue #61 of BJI, click here.



There is no mystery to the success of casinos. People place wagers on games that have a built in house edge. The players win or lose the individual bets, but that's of no concern to the management. The only concern is that players continue pumping wagers through the system. In this case, the large variance of individual bets evens out and the house earns according to the following basic equation:

Earnings = (Total Wagers) x (House Edge)

A progression betting system is based on the belief that this equation is wrong. It is an attempt to defy the laws of economics and mathematics by placing wagers according to a fixed pattern in an attempt to change the house edge.

A progression betting pattern is one that bases the current wager on the previous amount wagered and the result of the previous hand. Many authors write books about these systems, claiming they will win if combined with stop-loss and money management methods. Because of their simplicity, many people try them at the tables. Most lose. Some win.

Those who see individuals win using betting systems may come to regard these systems as an advantage method. Moreover, the arguments in favor of betting systems appear logical. But it is important to understand that it is the large variance of the games that lures most customers. Of course players will win. There are always winners. There have to be winners. But others players will lose. In the end, the losses will more than compensate for the wins so that the final result represents the house edge.

On the other hand, the "authors" and "experts" who extol betting systems usually blame the losers for their losses. They claim the losers are not disciplined or don't fully understand the system (which essentially means that the loser is not able to foretell the future perfectly). They point to the myriad of winners (there are always winners, that's a given). They claim that the computer simulations that show their systems are fraudulent don't model the "real world." They invent fancy theories involving chaos and fractals and never fully explain them. They post defensive messages on Internet bulletin boards, using terms like "math boyz" and "flaw." They hire publicists who send out press releases. They gain media exposure. And worst of all, they gain credibility among the gaming public.

But betting systems do not give the player an advantage over the casino. Fallacious arguments, anecdotal accounts, and slick book covers cannot overcome the physical laws of the universe.

Wagering Law. A betting system can not change the house edge; players using these systems as a whole lose at exactly the predicted rate.

However, progression betting systems do change the way in which losses occur. To understand the appeal of these systems, we will look at two of them in detail.

The first progression we will consider is called the "Martingale system." This is the most common progression used by blackjack players. In it, a player starts with a basic unit bet (say $10). If he loses a wager, he then doubles his wager for the next bet. He continues doubling each wager until he wins. After a win, his wager returns to its original value of $10. On a push, the wager stays the same. By always leaving on a win, the player ensures himself a winning session.

This seems to be a sure thing. For example, if the sequence is lose, lose, win (LLW) then the player will bet $10, $20, $40. He lost the $10 and $20 bets for a net loss of $30, but he won $40 for an overall gain of $10. For a longer sequence, consider

LLWLWLLWWLLLLLLLLLLW

It is easy to figure out the profit for the player: it is his minimum bet times the total number of wins in the sequence, in this case $10 ´ 5 wins = $50.

How can there be anything wrong with this logic? Just leave on a win and the player walks away with profit in his pocket every time.

However, for many reasons, the player can't always leave on a win. For example, in the previous sequence, the player was actually down $10,190 on the wager before the final win. Very few people can sustain this type of loss and keep on playing. The player placed a wager of $10,240 on the last bet in an effort to win $10. The situation of losing 10 hands in a row is not rare. It occurs about once every 1,540 hands (or 15 hours of play). A series of 10 consecutive losses is almost a certainty on any prolonged trip to Las Vegas. What if the sequence of losses was 15 hands? Then the player will need to wager $327,680. At blackjack, a sequence of 15 losses in a row occurs on average about once in every 100 hours of play. What if he needed to split and double down? What if he lost that hand?

One final comment is appropriate about table limits. Table limits are not in place to defeat the Martingale betting system. It is a losing system. Table limits are in place to protect the casino's bank from the effects of a single large wager, where collusion might be involved. These limits also help separate the premium players from the pack. Nevertheless, most table limits allow at most seven or eight Martingale double-ups.

The result of a Martingale system is that most players will come away a small winner most of the time because they did not endure a long string of losing wagers. But, on those rare times the player cannot walk away a winner, his losses will be huge.

A system where wagers are raised after a losing bet is called a "negative progression." The hook of this type of betting system is the frequency of winning sessions. Almost every session, the player will be able to leave on a win and therefore bank a small win. The sinker is that some rare losing sessions can be catastrophic for the player. The player most fears a long series of losses. In the long run, the wins and losses add up to the house edge. The player cannot overcome the "Wagering Law."

The other type of betting system that many players use is a "positive progression system," also known as pyramiding your profit, a bet parlay, or letting it ride. Players often think of their winnings as house money, and are willing to gamble more freely with this money in an effort to win even more. In this type of betting system, the player is willing to accept many frequent small losses in an attempt to bank a single huge win. The player needs less capital (since he is not chasing loses), so the downside risk is smaller for each session and the upside potential is huge.

For example, a common progression among blackjack players is to "almost" double up after a win. The player will wager a base amount, say $10 on a blackjack hand. After a single win, he will wager $15 (he doubles his $10 bet, and then removes $5 to add to his "winnings" pile). After two wins, WW, he will wager $25 (he doubles the $15 bet, and then brings $5 back to his "winnings" pile). After three wins in a row, WWW, his wager is $45 = $25 + $25 - $5. If he loses this bet, he then brings his bet back to $10 and starts again.

A typical sequence of ten wagers might look something like WWLLWLLLWW. Our player won bets of $10, $15, $10, $10, and $15. He lost bets of $25, $10, $15, $10, $10. His net for this sequence is a loss of $10. He endured a small loss while looking for a big win.

What is the player hoping for? How about WWWWWWWWWW, followed by leaving? In this case the player has made and won wagers of $10, $15, $25, $45, $85, $165, $325, $645, $1,285, and $2,565. And as far as he is concerned, it is all house money. He has hit the jackpot, winning $5,165 on his $10 initial wager. He leaves the table with the applause of those around him. He is humbly asked to share his wise and mysterious winning ways. He writes a book about his system and the lore of this one magical evening helps him sell a million copies. Don't buy this book!

The hook of a positive progression betting system is the lure of the big win. The player is hoping for that rare but life changing event that will forever prove the power of the system: a long series of wins. The sinker is that the big winning sessions are very rare. The usual outcome of an evening's play is a small loss. The effect to the player is very much like a slot machine and the mathematics are the same as well. In the long run, the wins and losses add up to the house edge. The player cannot overcome the "Wagering Law."

Betting systems are not a tool of advantage players and will not help you beat blackjack; they are used by naïve gamblers who have been sold a bill of goods about an easy "winning" system. The house edge is not just another number; it's The Law.