Gambling Systems: Scams vs. Strategies
How dangerous betting systems can bust your bankroll
By Basil Nestor

You’ll love this. It’s one of the cool tricks of the universe. In any series of bets that pay 1:1, if you double up after losing a bet (1, 2, 4, 8, and so forth), then one win anywhere in the series wipes out all previous losses. Plus it nets one unit, the value of the base bet.

For instance, consider this sequence: lose-lose-win. The results are -1, -2, and +4. The net profit is 1. Pretty nifty, huh? It works with any pattern of losses and wins. Any pattern!

The system is called the martingale. But before you rush out to try it in a casino, you should read the rest of this article because the martingale can be very dangerous. Ditto for other gambling systems when they are used improperly.

Keep in mind that a gambling system is technically synonymous with a gambling strategy. But in the jargon of the casino world, the word “system” implies a strategy that doesn’t work. This is somewhat unfair because the martingale does work. It just doesn’t work as some people might hope that it would. We’ll explain why in just a bit.

The martingale is a type of system called a “progression.” It is a method of raising and lowering bets based on previous results. Positive progressions raise bets after wins. Negative progressions (such as the martingale) raise bets after losses. There are also mixed systems that combine these two approaches, and systems that don’t change the size of bets, but instead focus on when to bet, or on what to bet.

It’s All about Decisions
Red or black? Hit or stand? Raise or fold? Gambling is all about decisions. Some of those decisions, such as hitting or standing in blackjack, are easy to measure mathematically. You simply make a few calculations (or read a strategy book), and the resulting numbers tell you which choice is most profitable in the long run.

But in some situations, such as when playing roulette, the best choice isn’t so obvious. For example, a bet on red in roulette is statistically no better than a bet on black. Indeed, almost every bet on the roulette table is equally disadvantageous. For every roulette bet that pays 1:1, the casino has 5.26% edge.

This is where gambling systems become useful and alluring, if not profitable. How can you erase the casino’s edge? It cannot be done with a betting scheme unless there is some sort of bias in the game, or you have special knowledge.

Nevertheless, gambling systems are enticing because they give the appearance of erasing the casino’s advantage. But this can be dangerous because it encourages players to increase bets in disadvantageous situations, which is exactly the wrong way to gamble.

Here is how the problem occurs. It is obvious that in any particular number of decisions, let’s say six red-or-black roulette spins, that three wins and three losses would be about average, and six consecutive losses would be unlikely. In fact, six consecutive roulette losses on a 1:1 bet will occur only about 2% of the time. So how do you bet for the side favoring 98%, against six consecutive losses? If you could make that bet, would it erase the casino’s advantage? It certainly seems as if it would. And that brings us to…

The Martingale
Nobody knows who invented the martingale, but the first person to write about it was Giacomo Girolamo Casanova. He was a famous lothario who gambled and slept his way across Europe in the eighteenth century. We know about his exploits because he meticulously recorded everything in his autobiography, The Story of My Life.

Casanova used the martingale in 1754 to win (and later lose) a small fortune. He wrote:

“M.M. [my lover] asked me to take some money, go to her casino, and play in financial partnership with her. I did so. I took all the gold I found and played the martingale, doubling my stakes continuously, and I won every day during the remainder of the Carnival. I was fortunate enough never to lose the sixth card. If I had lost it, I should have been without money to play, for I had two thousand sequins on that card.”

Casanova was playing faro, but the martingale can be used with any game that has 1:1 payoffs. You can see how the system works in the adjacent table.

Unfortunately, the martingale doesn’t erase the risk of losing. It only squeezes the risk into a tiny but powerful possibility. A 2% chance of hitting the wall doesn’t sound like a lot, but it will happen eventually. And what will be the result?

Let’s say you have exactly average luck when using the martingale, and you take it to six steps while playing roulette. You will win one bet 98 times and you will lose 63 bets twice. The net is -28. In other words, the martingale is doomed to fail against games that have a casino edge. And that is exactly what happened to Casanova. It took a few months, but eventually he tells us:

“I still played on the martingale, but with such bad luck that I was soon left without a sequin. As I shared my property with M.M., I was obliged to tell her of my losses, and it was at her request that I sold all her diamonds, losing what I got for them; she had now only five hundred sequins by her. There was no more talk of her escaping from the convent, for we had nothing to live on! I still gamed, but for small stakes, waiting for the slow return of good luck.”

But what if you extend the martingale to eight steps, or ten, or twenty? At some point, you surely will get a win. Right? Nobody loses twenty consecutive times.

Alas, yes. Some people do. The odds of losing twenty consecutive roulette bets are 1 in 375,899. It seems unlikely, but eventually it happens. More accurately, it would happen if a casino were to allow you to make a humongous bet of $524,288. In the real world, table limits prevent large progressions.

A Closed-End Progression
In all fairness, there is nothing “wrong” with using the martingale. Essentially, it’s a contract bet. In a seven-step martingale, a player risks $1,270 against a casino’s $10 that seven consecutive losses won’t occur.

The bet will win $10 about 99% of the time when the game is roulette, blackjack, baccarat, or craps.

The danger in using a negative progression is that a player won’t be prepared for that one-percent catastrophe of losing $1,270. But if a person chooses to play a closed-end progression, and he sets an absolute limit to the number of steps, then the martingale loses most of its menace.

D’Alembert
This is an ingenious system in which the gambler increases the bet by one unit after every loss and decreases by one unit after every win. It works quite well on a choppy table, and it’s mathematically guaranteed to produce a winning session when the wins and losses are nearly equal. Unfortunately, there’s no mathematic rule that says losing streaks eventually must be cancelled by winning streaks, especially since the house has a frequency advantage in most games. In blackjack the casino wins about 53% of hands. In craps on the pass line it’s about 51%.

D’Alembert is named after Jean Le Rond d’Alembert, an eighteenth-century French mathematician who was good at math, but bad at making accurate physical observations. For example, d’Alembert correctly understood that when flipping a coin twice, the frequency of seeing heads is 0, 1, or 2. But he incorrectly assigned an equal probability to each outcome (33.3%). Of course, there is actually a 50% chance of seeing heads once, and a 50% chance of seeing heads twice or zero times. Oops!

Positive Progressions
The idea behind positive progressions is that you should bet more when you’re winning and less when you’re losing. It sounds logical. Unfortunately, it’s difficult to say when someone is “winning.” We can only accurately say when someone “has won.” Thus positive progressions work well in some situations, but not so well in others.

The adjacent chart shows a side-by-side example of flat-betting compared to a positive progression. In the example we have two players, Sid System and Fred Flatbet. Sid uses a 1-2-3-4-5 positive progression; he increases his bet by one unit after every win, and then falls back to a single unit (the first level of the progression) after a loss.

The system does very well on streaks, but notice how it loses money on a choppy table. Fred Flatbet doesn’t do nearly as well during the hot streak, but he doesn’t lose when the cards, dice, or wheel go choppy. Keep in mind that this particular sequence has a streak at the beginning that happens to favor Sid, but it’s just as likely for the table to produce a long choppy sequence more favorable to Fred.

Here are some other popular positive progressions: 1-1-2-3-4-5, 2-1-2-3-5-8, 2-1-1-2-3-4, 2-1-2-3-4-5, 2-2-3-3-4-5.

All of the above progressions solve the problem of an extremely choppy table, and in fact, the sequences that begin with 2-1 will actually win one unit after every two decisions when the table goes choppy. Unfortunately, they’re all vulnerable to other patterns such as two wins and two losses. There is no such thing as a perfect progression. Every system has a weakness somewhere.

Scam Systems
The web page says, “Make money at roulette on a consistent basis! This powerful playing method derives its strength from the maturity of chances. Learn how to divide the table layout to greatly increase your win probability. Teaches how to construct a basic progression that virtually assures a quick and profitable session. Unconditionally guaranteed!”

Another advertisement promises, “Gambling will be like going to the bank for a withdrawal.”

If only it were true. These systems usually are progressions combined with convoluted tactics for choosing bets. Many are bald-faced scams, while a few are sold by hopeful entrepreneurs who have deluded themselves into believing that they’ve found a magic method for winning. Here is an example of a betting system for roulette:

Bet two units on a group of twelve and three units on an opposite 1:1 payoff. A way to do that would be $10 on 1-12 and $15 on high numbers. This combined wager pushes the risk into only eight numbers, 13-18, 0 and 00. A win either way pays a net of $5. A loss costs the bettor $25. Losses occur 21% percent of the time, on average about one in five spins. Wins occur the other four times, so five spins will usually cost a net of $5. Of course you could easily win ten consecutive times and be ahead $50. Or you could get a run of 15, 17, and zero. That would cost you $75.

Note that the system does lower the frequency of losses, but it doesn’t change the casino’s advantage.

There are many other imaginative schemes, including a venerable progression known as Oscar’s Grind which has you increase bets by one unit after each win but you don’t decrease after losses until you net at least one unit of profit from the betting series. If your first bet is a win, then that completes the series, and the next wager is one unit.

Interesting, yes? But it’s a useless tactic. Flipping a coin to choose the size of your bet would be equally effective.

What Makes a Strategy Work?
The problem with all of these systems is that bets are placed, increased, or decreased for reasons that have nothing to with a change in the probability of winning. Cards, reels, dice, and wheels are inanimate objects. They have no memory. So past results do not necessarily predict the future. Losing five times in a row tells you nothing about what will happen on the sixth trial.

Compare that to proven optimal strategies such as blackjack basic strategy, hold ‘em poker strategy, Caribbean Stud strategy, craps optimal strategy, and so forth. An optimal strategy will raise bets when the probability of winning goes up, and lower bets or stop them when winning becomes less likely. What a concept!

Let’s say you’re playing blackjack, you’re dealt 9 and 2, and the dealer has a 6. Congratulations! You have an advantage. Raising the bet by doubling in that situation makes perfect sense. Ditto for when you have a pair or better playing Caribbean Stud, or when you get pocket aces in hold ‘em. You have a better chance of winning, so you put more money on the table. A good gambling strategy is based on the current situation rather than what happened in the past.

If you’re playing a game in which the edge never changes, such as roulette or baccarat, then there is no harm in using a betting system, but only if you intend to risk the money anyway. In that situation, it doesn’t matter how you size the bets, the long-term net effect of using a system is zero.

A betting scheme like the martingale or a positive progression simply magnifies good luck at the expense of mediocre luck. How lucky will you be? Flip a coin.
Basil Nestor is author of The Unofficial Guide to Casino Gambling, The Smarter Bet Guide to Blackjack, and other comprehensive gambling guides. Got a question? Visit SmarterBet.com and drop him a line.