## Martingale Gambling

The Martingale Strategy is a tantalising betting system, for good reason, and in a vacuum, it works to a tee. Its mathematical principles are sound as can be, and the strategy is logical and sensical enough that make them easily applicable to many casino games. The Martingale strategy is one of the most well-known methods in sports betting. While the pitfalls are clear for all to see, there could be some potential uses thanks to the math involved. Read on to find out what bettors can learn from the Martingale strategy.

The Martingale Betting System was developed in 18th century France. It was actually part of a group of betting methods that were classified as “martingale.” Today, Martingale refers to a relatively simple sports betting.

## Table Of Contents

**Why is the Martingale betting system such a popular strategy?****What can go wrong with using the Martingale system?****Have you heard of the anti-Martingale system?****Should you use the Martingale system?**

The **Martingale system** is one of the most commonly used betting strategies for traditional Casino table games, as well as sports betting.

The Martingale betting system is one that many people have latched onto due to its simplicity and an assumption that no-one can possibly lose all of the time.

**But does it really work? Or is it just another betting fallacy? **

Read on to discover all there is to know about one of the oldest betting systems in the book.

## How did the Martingale system come about and how does it work?

This particular betting strategy dates all the way back to the 18th century. The system is named after a man named **John Henry Martindale**, a proprietor of multiple gambling properties in the UK back in the day.

Although the title of the betting strategy is ever so slightly different from his surname, it was inspired by his belief in the system.

**He would encourage his customers to use it in his Casinos**, who would believe him when he said that many of his high-roller players had won vast sums of money at the tables.

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The Martingale system quickly became **a go-to approach for recreational punters** as it was a straightforward and seemingly rational strategy.

There were no algorithms or equations to remember, they simply had to remember the following:

- Double your next bet after a loss
- Continue doubling your next bet after a loss until a win is achieved
- Restart the cycle again

For example, if you were to place an initial bet of $10 on black on the Roulette wheel and the ball landed on a red number, you would wager $20 on the next bet. Casino play for real money.

If you were to lose that bet, you would wager $40 on the following bet and so on, until you win a bet.

It is an approach that has proven particularly popular with those fascinated in Roulette strategies and Blackjack strategies.

Games that offer a perceived coinflip outcome on winning and losing i.e. *those with the tightest house edge*.

However, there are several pitfalls to be mindful of too, as we'll explain later below.

## The pros of the Martingale strategy

- If you continue to double your bet after every loss, you are certain to win back the amount you lose – and improve your net winnings in the short term.
- Speaking of short-term betting, Martingale betting works best if you're thinking of playing for a short timeframe rather than a long session.
- The Martingale strategy can help beginners quickly recover losses whilst learning to play a new Casino game.

## The cons of the Martingale betting system

- You'll need a large betting bankroll to be able to handle a run of losing bets, as this system depletes your bank far quicker than most other strategies.
- It's not tailored for long-term players – the longer you play, the more chance there is of the Casino's house edge eating into your bankroll.
- It's possible the Martingale system will be affected by caps on the maximum bet at any given table. If you experience a lengthy losing streak, you may not be able to sufficiently increase your bet above the maximum bet to retrieve your losses.

### Should you use the Martingale system?

If you're testing out new Casino table games like online Roulette and online Blackjack for the first time, the Martingale system could be a dangerous option for you.

If you don't have a sufficient bankroll or you just don't want to risk to lose your money, **have a look at this gaming website.**

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Alternatively, you might wish to consider the anti-Martingale betting system:

- Half the next bet after every losing money bet
- Double the next bet after every winning bet

You could try this out on some of the table games at the same site with a 50-50 percent split of the bankroll.

This allows you to see whether the anti-Martingale strategy can help you capitalize on 'hot' winning streaks better than the regular Martingale.

## Martingale betting FAQs

To conclude this guide to the Martingale betting system, let's go through some of the questions our readers sent us on *Facebook* and *Twitter*.

### What is wrong with the Martingale Roulette strategy?

If you encounter a losing streak on the Roulette or Blackjack table, you can lose your betting bankroll alarmingly quickly.

You might think that it's impossible to lose ten times in a row when betting on red. The statistics show that there is a 784/1 chance of losing ten bets in a row for betting on a colour on a European Roulette table.

If your starting bet is $10, you could expect – statistically – to win £7,840 before encountering said losing streak.

However, this losing streak would wipe out your profits, costing you $10,230 in the process. It just goes to show why Martingale strategy is very much a short-term option and not for the long run.

### Does the Martingale strategy always work in Blackjack? Why?

As we've already touched upon, the Martingale strategy works best for Casino games that offer 50/50 'coinflip' situations.

Blackjack is (almost) one of those. In terms of table limit restrictions, some Casinos will only offer a minimum bet, with no maximum bet ceilings either, which gives Blackjack players a chance to chase their losses continuously – providing they have a bankroll that's substantial enough to handle losing streaks.

### Is the Martingale strategy legal on betting and Casino sites?

Yes, Martingale betting systems are permitted when you play Casino games online. There's no reason why it wouldn't be prohibited.

In the long term, the Casinos will always take money off players, but those prepared to practice Martingale for short-term bursts could succeed.

### Can a Martingale system work in Forex trading, too?

The Martingale is actually increasingly popular among Forex traders.

That's because, unlike stocks, the value of fiat currencies almost never fall to the bottom. When you trade forex, there is a 50% chance of your trade being profitable, and a 50% chance of your trade being a loss.

This makes Martingale strategy a possible forex trading system, however you'll still need deep pockets to handle losing runs, particularly if you make bad decisions regarding entry points into the forex markets.

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A **martingale** is any of a class of betting strategies that originated from and were popular in 18th-century France. The simplest of these strategies was designed for a game in which the gambler wins the stake if a coin comes up heads and loses if it comes up tails. The strategy had the gambler double the bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake.

Since a gambler will almost surely eventually flip heads, the martingale betting strategy is certain to make money for the gambler provided they have infinite wealth and there is no limit on money earned in a single bet. However, no gambler possess infinite wealth, and the exponential growth of the bets can bankrupt unlucky gamblers who chose to use the martingale, causing a catastrophic loss. Despite the fact that the gambler usually wins a small net reward, thus appearing to have a sound strategy, the gambler's expected value remains zero because the small probability that the gambler will suffer a catastrophic loss exactly balances with the expected gain. In a casino, the expected value is negative, due to the house's edge. Additionally, as the likelihood of a string of consecutive losses occurs more often than common intuition suggests, martingale strategies can bankrupt a gambler quickly.

The martingale strategy has also been applied to roulette, as the probability of hitting either red or black is close to 50%.

## Intuitive analysis[edit]

The fundamental reason why all martingale-type betting systems fail is that no amount of information about the results of past bets can be used to predict the results of a future bet with accuracy better than chance. In mathematical terminology, this corresponds to the assumption that the win-loss outcomes of each bet are independent and identically distributed random variables, an assumption which is valid in many realistic situations. It follows from this assumption that the expected value of a series of bets is equal to the sum, over all bets that could potentially occur in the series, of the expected value of a potential bet times the probability that the player will make that bet. In most casino games, the expected value of any individual bet is negative, so the sum of many negative numbers will also always be negative.

The martingale strategy fails even with unbounded stopping time, as long as there is a limit on earnings or on the bets (which is also true in practice).^{[1]} It is only with unbounded wealth, bets *and* time that it could be argued that the martingale becomes a winning strategy.

## Mathematical analysis[edit]

The impossibility of winning over the long run, given a limit of the size of bets or a limit in the size of one's bankroll or line of credit, is proven by the optional stopping theorem.^{[1]}

However, without these limits, the martingale betting strategy is certain to make money for the gambler because the chance of at least one coin flip coming up heads approaches one as the number of coin flips approaches infinity.

### Martingale Gambling Strategy

## Mathematical analysis of a single round[edit]

Let one round be defined as a sequence of consecutive losses followed by either a win, or bankruptcy of the gambler. After a win, the gambler 'resets' and is considered to have started a new round. A continuous sequence of martingale bets can thus be partitioned into a sequence of independent rounds. Following is an analysis of the expected value of one round.

Let *q* be the probability of losing (e.g. for American double-zero roulette, it is 20/38 for a bet on black or red). Let *B* be the amount of the initial bet. Let *n* be the finite number of bets the gambler can afford to lose.

The probability that the gambler will lose all *n* bets is *q*^{n}. When all bets lose, the total loss is

- $\sum _{i=1}^{n}B\cdot {2}^{i-1}=B({2}^{n}-1)$

The probability the gambler does not lose all *n* bets is 1 − *q*^{n}. In all other cases, the gambler wins the initial bet (*B*.) Thus, the expected profit per round is

- $(1-{q}^{n})\cdot B-{q}^{n}\cdot B({2}^{n}-1)=B(1-(2q{)}^{n})$

Whenever *q* > 1/2, the expression 1 − (2*q*)^{n} < 0 for all *n* > 0. Thus, for all games where a gambler is more likely to lose than to win any given bet, that gambler is expected to lose money, on average, each round. Increasing the size of wager for each round per the martingale system only serves to increase the average loss.

Suppose a gambler has a 63 unit gambling bankroll. The gambler might bet 1 unit on the first spin. On each loss, the bet is doubled. Thus, taking *k* as the number of preceding consecutive losses, the player will always bet 2^{k} units.

With a win on any given spin, the gambler will net 1 unit over the total amount wagered to that point. Once this win is achieved, the gambler restarts the system with a 1 unit bet.

With losses on all of the first six spins, the gambler loses a total of 63 units. This exhausts the bankroll and the martingale cannot be continued.

In this example, the probability of losing the entire bankroll and being unable to continue the martingale is equal to the probability of 6 consecutive losses: (10/19)^{6} = 2.1256%. The probability of winning is equal to 1 minus the probability of losing 6 times: 1 − (10/19)^{6} = 97.8744%.

The expected amount won is (1 × 0.978744) = 0.978744.

The expected amount lost is (63 × 0.021256)= 1.339118.

Thus, the total expected value for each application of the betting system is (0.978744 − 1.339118) = −0.360374 .

In a unique circumstance, this strategy can make sense. Suppose the gambler possesses exactly 63 units but desperately needs a total of 64. Assuming *q* > 1/2 (it is a real casino) and he may only place bets at even odds, his best strategy is **bold play**: at each spin, he should bet the smallest amount such that if he wins he reaches his target immediately, and if he doesn't have enough for this, he should simply bet everything. Eventually he either goes bust or reaches his target. This strategy gives him a probability of 97.8744% of achieving the goal of winning one unit vs. a 2.1256% chance of losing all 63 units, and that is the best probability possible in this circumstance.^{[2]} However, bold play is not always the optimal strategy for having the biggest possible chance to increase an initial capital to some desired higher amount. If the gambler can bet arbitrarily small amounts at arbitrarily long odds (but still with the same expected loss of 10/19 of the stake at each bet), and can only place one bet at each spin, then there are strategies with above 98% chance of attaining his goal, and these use very timid play unless the gambler is close to losing all his capital, in which case he does switch to extremely bold play.^{[3]}

## Alternative mathematical analysis[edit]

The previous analysis calculates *expected value*, but we can ask another question: what is the chance that one can play a casino game using the martingale strategy, and avoid the losing streak long enough to double one's bankroll.

As before, this depends on the likelihood of losing 6 roulette spins in a row assuming we are betting red/black or even/odd. Many gamblers believe that the chances of losing 6 in a row are remote, and that with a patient adherence to the strategy they will slowly increase their bankroll.

In reality, the odds of a streak of 6 losses in a row are much higher than many people intuitively believe. Psychological studies have shown that since people know that the odds of losing 6 times in a row out of 6 plays are low, they incorrectly assume that in a longer string of plays the odds are also very low. When people are asked to invent data representing 200 coin tosses, they often do not add streaks of more than 5 because they believe that these streaks are very unlikely.^{[4]} This intuitive belief is sometimes referred to as the representativeness heuristic.

## Anti-martingale[edit]

In a classic martingale betting style, gamblers increase bets after each loss in hopes that an eventual win will recover all previous losses. The anti-martingale approach, also known as the reverse martingale, instead increases bets after wins, while reducing them after a loss. The perception is that the gambler will benefit from a winning streak or a 'hot hand', while reducing losses while 'cold' or otherwise having a losing streak. As the single bets are independent from each other (and from the gambler's expectations), the concept of winning 'streaks' is merely an example of gambler's fallacy, and the anti-martingale strategy fails to make any money. If on the other hand, real-life stock returns are serially correlated (for instance due to economic cycles and delayed reaction to news of larger market participants), 'streaks' of wins or losses do happen more often and are longer than those under a purely random process, the anti-martingale strategy could theoretically apply and can be used in trading systems (as trend-following or 'doubling up'). (But see also dollar cost averaging.)

## See also[edit]

### Martingale Gambling

## References[edit]

- ^
^{a}^{b}Michael Mitzenmacher; Eli Upfal (2005),*Probability and computing: randomized algorithms and probabilistic analysis*, Cambridge University Press, p. 298, ISBN978-0-521-83540-4, archived from the original on October 13, 2015 **^**Lester E. Dubins; Leonard J. Savage (1965),*How to gamble if you must: inequalities for stochastic processes*, McGraw Hill**^**Larry Shepp (2006),*Bold play and the optimal policy for Vardi's casino, pp 150–156 in: Random Walk, Sequential Analysis and Related Topics*, World Scientific**^**Martin, Frank A. (February 2009). 'What were the Odds of Having Such a Terrible Streak at the Casino?'(PDF). WizardOfOdds.com. Retrieved 31 March 2012.