# Martingale System

The Martingale System is a staking plan and probably one of the most famous – although infamous is probably a more apt description – betting systems in the world. Believed to have been formulated in the 18th (or possibly 19th) century in France, the Martingale is, in theory, the holy grail of gambling systems: a way to beat the house and deliver a guaranteed profit.

Here we take a closer look at the Martingale System, covering how it works, or doesn’t as the case may be, as well as looking at the reasons it is so popular, what games it is used for and, ultimately, why it is almost certainly best left well alone.

## History of the Martingale System

The simplicity of the Martingale System means that it is still being “discovered” today by casino and sports betting fans who think they have hit upon a fool proof system. However, as we have said, it has actually been around for at least 170 years and quite probably well over 200.

We cannot know exactly when it was first formulated but as there are literary references to roulette from as early as 1758 and more definitely and definitively 1801 (but set in 1796), it is safe to say that roulette as we now know it has been played since at least the late 18th century. Given how simple and in a sense obvious the Martingale System is, it seems reasonable to believe it would have followed soon after.

That said, Martingale was not actually devised with roulette in mind so there is a strong probability that it may predate that. Initially it was intended as a staking and betting system to be used on a game that was as simple as the system itself, the toss of a coin. Martingale dictates that after any winning toss the player maintains their initial base stake, for example £1, whilst after any losing toss they double their stake for the following toss.

The system was quickly picked up on and became very popular in roulette circles in the casinos of Paris at the turn of the 19th century. Roulette and the Martingale System have changed little in the intervening years and despite its many obvious flaws, the system has continued to attract attention. Some players genuinely believe it can work whilst some disingenuous “experts” will even try and cash in on the system via books and websites offering to reveal “the secret the casinos don’t want you to know” or some other such nonsense.

## What is the Martingale System?

The Martingale System, as said, is a staking plan which requires the player to double their stake following a losing bet. If we imagine friends tossing a £2 coin, with the initial toss worth £2, if the player using the Martingale system loses the first toss, the second is then for £4. However, if they win the first toss they pocket the £2 and toss again for the same £2 stake. Should they lose the first and the second toss, the third stake then becomes £8, with the value continuing to double after any loss but always returning to the base £2 stake following any win.

Using this system, any win, when it comes, will always leave the player in profit by the value of their original staking unit. For example, in our example above, a player may lose £2, then £4, then £8, then £16 before tossing for £32. When they win, that £32 spin leaves the £2 to the good (£32 minus (£2+£4+£8+£16) = £2).

So far it’s very easy to see why the Martingale System is easy to be seduced by. It’s simple to understand, very easy to use and, on the face of it, is backed by the very sound-seeming logic that no matter how many times in a row you lose, when you do eventually win, you will always immediately return to a position of profit.

Martingale is one of a number of related systems that are “negative progression staking plans”. The negative aspect of that is the losing of the bet, whilst the progression is the increasing of the stake. In other words, it is a system where the stake increases following a losing bet.

Negative progression staking plans have at their heart the idea that if producing a profit is the aim, it makes sense to bet more the further away you are from that aim. This is not a wholly illogical concept given that in just about all casino games and most sports bets the advantage is with the casino or bookmaker. As such, mathematically speaking, the longer you play, the more likely you are to lose.

This means that betting larger amounts when you are losing is a good way to try and recover your losses as you will need fewer strokes of luck to achieve your aim. However, negative betting systems have several general problems, whilst the Martingale System has some major flaws of its own (of which more later).

In terms of problems with negative progression staking plans in general, whilst it is true that they can be the quickest route to profit, the reverse of that is also true and they can also be a very quick way to large losses. Related to this, they also call upon the gambler to stake more at the time when their bank is lowest, betting an ever increasing proportion of their total bankroll.

We will go on to explain in greater detail why the Martingale System is to be avoided but first let us look at the different games it can be used to play.

## What Games and Bets Can Martingale Be Used For?

Obviously in theory the idea of doubling your stake after any loss can be applied to any casino game or any bet of any description. However, in order for Martingale to work as has been described above, the odds for a win must be evens, as only this will lead to a profit of the original staking unit following a win.

In essence Martingale works best, in as much as it works at all, on a game with a payout of even money and a chance of success of that bet as close to 50% as possible. This means that the even money shots on a roulette wheel – odds/evens, high/low and red/black – as well as blackjack, certain craps and baccarat bets and any sports wager where the odds are evens are the best suited to use of the Martingale System.

Odds of just less than even money can still be used up to a point as this can still return an overall profit by doubling the stake. For example, if we assume you place the bets on a casino game or outcome, or sports bet, with odds of 4/5 (1.80 in decimal odds, as opposed to 2.0), a doubling of the stake after the first bet would work as such:

- Bet £10 and win - £8 profit
- Bet £10 and lose - £10 down (not including the first wager)
- Bet £20 and win - £16 profit so £6 up overall

However, if we take a run where the first three bets are lost, the first at £10, second at £20 and third at £40, the next bet, of £80, will only deliver a profit of £64 based on the odds of 4/5. At this stage the rolling debt will be £70 (£10+£20+£40) and therefore Martingale will fall down.

Equally, just as odds of less than evens can be used, the probability of the bet winning need not, in theory, be 50%. However, we shall consider this issue, essentially the value inherent within the bet and the house edge, and how they relate to Martingale, in greater depth in the following sections.

## Practical Problems with the Martingale System

As we see it there are two distinct but related problems with the Martingale System and these can be called the practical problem and the mathematical problem. Let us deal first with the practical issue as that is easier to understand and should in itself be enough to turn you off the Martingale System for good.

For this example, let us assume we are talking about a simple roulette bet on black on every spin, at a standard UK/European roulette wheel with just a single zero. This wager pays out at odds of 1/1, otherwise called evens or even money. There are 18 black numbers, with 18 red and the zero, giving you an 18 in 37 chance of success. That equates to a 48.65% chance of winning which is more or less as close to a 50% chance as you are going to get in the casino.

Now, as we have discussed, the compelling case for using Martingale is the truism that no matter how many losses you suffer in a row, by doubling your stake you are 100% guaranteed to return to profit with just one win. That is mathematically true and true in casino theory but what about in practice, in the real world, in a real casino, either online or offline but using real money – your money?

**Running Out of Money**

Let’s imagine you load up your favourite online casino and settle in for a session of roulette using this amazing new system you’ve just heard about that means you can’t lose! You use the system and results follow a fairly typical pattern of reds and blacks, perhaps there is the odd streak of consecutive blacks to start with and you pocket a few wins. Then a streak of five reds has you betting 32 times your standard stake unit.

So, if we assume you started out betting £10 per spin, five consecutive losses now means your next bet is now £320. Quite a substantial bet to win just £10 but, nonetheless, the next spin lands in 20, black, and you once more win another £10. Things are going nicely and you decide to call it a day with a tidy profit of £60.

Thinking your days of the office commute, nine to five drudgery and unavoidable chats with Stacy from marketing about the weather and cute pugs are soon to be a thing of the past, the very next day you hit the online casino again.

Once more things are going swimmingly but after an hour or so, in which time you’ve made £30 after a few longish losing sequences were only reversed by betting large amounts, you hit a REALLY bad run. You had decided that more than eight reds, or more accurately, eight non-blacks, in a row just couldn’t happen. If you’re being truthful, this was more of a practical decision than one based on a sound knowledge of probability and eight losing spins was essentially all that your bank would allow for.

After eight losing spins the required stake based on a £10 starting point is £2560. At this stage you are already £2550 down and so your £5,000 bank can no longer double up the stake. You decide to try and get your money back and bet the remaining £2,450 on black, knowing that a win won’t leave you up but you’ll only be £100 down. You were £60 up yesterday and a further £30 to the good before this UNBELIEVABLE run of reds and zeroes and so all you need now is any of the 18 blacks to drop in and you’ll only be £10 down.

Unfortunately the ball lands in red 1. It bounced out of black 33 when you were sure it’s motion had stopped but red 1 it is and there goes your £5k balance.

This highlights the first practical issue we have: for Martingale to work, you would need to have unlimited funds. Even aside from the fact that the notion of betting potentially millions of pounds to win just £10 is crazy, the fact is that not even the richest man alive has an infinite bank balance. As such, when a long run of losing bets happens, most people will go bust and mathematically, as we shall later learn, they will, on average, lose more than all the previous small wins they accumulated.

**Running Out of Time**

As well as infinite cash, the Martingale System also requires that players – be they betting on roulette in a casino, blackjack online or over 2.5 goals at football – have an infinite amount of time at their disposal. Time is unlikely to be a factor for most people, with cash almost certain to be the bigger issue. However, casinos close, people have jobs and lives to lead and the fact is that if all other conditions were met and you were playing indefinitely, in theory, some form of time restraint would ultimately stop you from being able to place the next wager.

**Hitting the House Limit**

The third and final practical issue is more likely to impact you than running out of time and unless you are among the mega rich, less likely to affect you than running out of money. In theory, betting at a casino or on sports you could always return another day and place your next doubled up wager. Other than dying, time is, perhaps, not a factor we need worry about (although just imagine dying on a run of 36 consecutive losses!).

However, reaching the house limit, be that a maximum stake at blackjack, roulette or whatever sport you are betting on, is a very real and definite issue, especially for those who have a huge bankroll.

If we imagine again a player staking money on black at European roulette but this time we imagine a wealthier player whose starting stake is £100. Again, they have lots of single £100 wins and this may even go on for days, weeks or even, if they are lucky, months. They may build a very healthy profit in the thousands or perhaps tens of thousands of pounds.

Eventually though, their time will come and a long sequences of losses will hit them. They don’t consider this a problem as they have millions in the bank and feel they can always just double up no matter what.

However, starting at £100, a run of 14 straight losses will require a stake of more than £1.6m. Ignoring the fact that this is to win just £100, even the mega rich will struggle to find an elite casino prepared to accept a wager of well over £1m. Even if the person making the bets is prepared to take on a bet that would leave them £3,276,700 down, the simple fact is that all casinos and sports betting operators have a house limit over which they will not accept bets.

As such, anyone deciding to use the Martingale System should at least be aware that unless they are very lucky they will encounter one of the three problems we have discussed. That’s right, very lucky. You may think that the opposite is true and that only the very *unlucky* will fall foul of Martingale, with extraordinary or even impossible bad luck needed to suffer a run of 14 (or more or less) consecutive losses whilst making a bet with an almost 50% chance of winning. However, this is not the case, as the maths will show.

## Mathematical Problems with Martingale

When it comes to what we are labelling the mathematical issues with Martingale, there are two further sub-issues. The first is a misunderstanding of probability and the second is the simple yet undeniable fact of the house edge in roulette and as with many of the issues we are making, once more these are inter-related.

The house edge is the casino’s advantage over the player and this exists in all casino games. In theory, the punter could gain an edge over the bookie in sports betting, where they consider (and are correct) that the bookie has offered odds that are too big on a given outcome. However, we’ll stick to the casino and explain how the house edge scuppers Martingale.

The simple fact of the matter is that whatever you stake and whatever you bet on, the house edge always remains the same when playing roulette. Other casino games can vary slightly, although in all of them the best the player can achieve is the minimum possible house edge, as opposed to actually overturning it and creating an advantage for themselves.

Any decent discussion of staking plans should note that there is no way for a staking plan to turn a bad bet into a good one. A staking plan can control your balance, try to limit losses or maximise wins but ultimately it cannot make a disadvantageous wager with a negative expectation into a value bet with a positive expectation.

In simple terms this means that the Martingale System is impotent in overcoming the house edge. However you bet and whatever you stake, in the long term the casino will always win the same amount from you, the amount that equates to the house edge.

If you were to use the Martingale System betting on an even money payout with a 50% chance of winning – such as the toss of a coin – you would see a similar pattern. This game has no house edge and neither player has an advantage over the other. As such, whether you used the Martingale or any other staking plan, in the long term you would break even.

There are complex mathematical ways to prove this fact and several simulations have been done covering millions and millions of roulette spins. Comparisons between level stakes betting, Martingale and other staking plans all show the same result in the long term and that is a win to the casino more or less exactly equal to the house edge.

These simulations are run literally millions of times covering a range of eventualities, such as the house limit or player bankroll covering eight, 10 or even 20 straight losses and profits being taken after a small number of spins right up to a hundred spins or more.

The point is that these variables are irrelevant as the only one that matters is the house edge. In the simulations there will be lots of small wins for the player but equally there will also be times where the whole balance is wiped out, even up to 20 straight losses! And crucially what we see is that the substantial losses outweigh the small regular wins by an amount that corresponds, as said, with the house edge of roulette.

This leads us nicely on to the final part of this article and congratulations if you’ve stuck it out this far! The fact is, when it comes to probability, most people have a very basic knowledge (if any at all). Many more sophisticated advocates of Martingale, those that are aware of the risks of suffering a big loss, will argue that the small wins will more than cover the losses.

This may indeed be true in the short term. As we saw in our examples above, the player can easily win and make a profit over a number of sessions using the Martingale System. If they are lucky and avoid a bad run, this could extend for months or even years or even a lifetime.

However, what the simulations and maths behind roulette undeniably prove is that *on average* any player playing roulette who uses Martingale will lose. Simulations show a percentage of players winning but they also show a large amount of players being entirely wiped out. In the long term, the reality is that most, if not all, players will lose. We say not all, but collectively, averaged out, all players will lose.

On an individual level this means the most likely scenario is that small wins will occur but eventually a single catastrophic loss will not only wipe them out, but leave the player in the red too.

This is because runs of unlikely sequences are not impossible, not unlikely but, in fact, 100% guaranteed. If you played Martingale long enough you would see a sequence of 100 consecutive reds. In fact, if you played long enough, you would see a sequence 100 consecutive zeroes!

Now, in order for such a sequence to occur you would have to play an unfeasibly large number of games but if we consider the sorts of runs that would ruin most players the stats become a lot more realistic.

If we look at a sequence of 10 consecutive losing bets based on any even money roulette wager, the reality is that this is a run that any player who uses Martingale or plays a lot of roulette will experience. The chance of losing 10 spins in a row is just under 0.1%, or more accurately a one in 784 likelihood.

Naturally enough, that seems quite improbable and indeed it is, if you were only playing 10 spins. However, anyone using the Martingale System will be playing hundreds of spins a day, if not more. In a series of just 200 spins, the average number of consecutive losses is seven, enough to bust most players. In fact, playing 1,000 spins the chances are you will suffer 10 consecutive losses.

The probability of such a sequence is significantly higher than 50% at this quantity of spins, meaning that if you spin 50 times an hour – which is quite conservative – and play Martingale four times a week, you will more than likely suffer a series of 10 straight losses within your first week of playing!

## Martingale Conclusion

The simple conclusion is that the Martingale System should be avoided unless you are fully aware of the high risks, the fact that it is guaranteed to lose in the long term and the fact that it certainly isn’t a fool proof betting system.

Equally, treat any attempts to sell you a system to “beat the house” with extreme caution, be they via a website or a book. Such systems are more than likely to be some form of Martingale variant and ultimately are certain to be scams. If something sounds too good to be true, it often is, and more importantly, why would someone with a casino-busting system be selling books to make their money?