Some of the sports bettors are very diligent followers of certain money management strategies, despite being unaware whether these strategies are actually as reliable as they are made out to be. Let’s go over one such popular strategy known as the Martingale betting system and understand whether the returns promised by it are really worth taking a risk.
The Martingale betting system is actively used by a large number of betting tipsters and sports bettors at Bet365 and other portals, who are strong advocates of money management strategies, especially the ones that involve incremental increases in the stakes post the lost bets, in order to recover the lost amounts. In case you’re particularly interested in betting at Bet365, visit to stay updated about all the ongoing promotions and discounts on this portal.
These sports bettors and tipsters frequently refer to this strategy as a failsafe strategy based on the perception that it makes it inevitable for them to win in the end, and when they do, they recover all the previously lost money, along with their original target profit, from their earlier bets.
The smarter ones amongst you may have already spotted the basic flaw of this strategy – There’s nothing inevitable when it comes to gambling at any offline or online casino. If ever there was, you won’t call it gambling. One of the reasons why these tipsters and punters ignore this flaw, is because of two important heuristic biases – first is underestimation of the probability of losing streak and second is overconfidence that they’ll always win. Such type of money management in the field of gambling is conventionally referred to as the Martingale system.

About the Martingale betting strategy
The origin of the Martingale betting strategy lies in the offline and online casino gambling world, more specifically in the game of roulette. Red Black is a popular game you can play at the roulette wheel, wherein you must decide whether the tossed ball will land on a black number or a red one.


Disregarding the impact of house edge, you can expect the odds of every result to be 2.00. The primary idea at the root of Martingale betting strategy is doubling the bet size after every losing bet, and returning to the baseline or initial bet amount after each won bet. You can apply this betting strategy to any betting odds provided to you, using the expression below:
Martingale progression rate = odds / (odds – 1)
So, for instance, if the provided betting odds are 3.00, the Martingale progression rate for the increase in bet amounts would be:
Martingale progression rate = 3.00 / (3.00 – 1)
Martingale progression rate = 3.00 / 2.00
Martingale progression rate = 1.50

This way, one can expect to recover all the previous losses after every successful result, along with the originally targeted profit amount. It is also shown by the following wheel spin sequence:

Wheelspin no. Bet   /   Bet Amount   /   Outcome   /   Loss/Win   /   Profit   /   Running Total
1   /   Black 1   /   Red   /   Loss   /   -1   /   -1
2   /   Black 2   /   Red   /   Loss   /   -2   /   -3
3   /   Black 4   /   Red   /   Loss   /   -4   /   -7
4   /   Black 8   /   Black   /   Win   /   +8   /   +1
5   /   Black 1   /   Red   /   Loss   /   -1   /   0
6   /   Black 2   /   Black   /   Win   /   +2   /   +2
7   /   Black 1   /   Black   /   Win   /   +1   /   +3
8   /   Black 1   /   Red   /   Loss   /   -1   /   +2
9   /   Black 2   /   Red   /   Loss   /   -2   /   0
10   /   Black 4   /   Black   /   Win   /   +4   /   +4

Martingale alters the risks and not the mathematical expectations
In one of the books written on the subject, a simple yet excellent demonstration was provided regarding why Martingale system can’t possibly make something out of nothing.
If we refer to the starting 3 wheel spins in the sequence provided above, we’ll see that the 3 consecutive reds represent only one out of the total 8 possible outcomes, each one being as likely as the others.
We can go through the profit expectations for each one of these 8 possible permutations through an experiment. The impact of house edge can be discounted in this example. You can easily calculate the possibility of any outcome by multiplying the actual loss or profit from that outcome with the probability of its occurrence.
The overall expectation from this strategy can be arrived at by summing up the individual expectations for these 8 permutations. When you do it, you’ll arrive at the figure 0. Therefore, in case of a fair roulette wheel all that you can possibly hope for in the long run is to break even at some point of time.
Well, we all know that real roulette wheels are far from being absolutely fair! Every single game of red-black played in any off-line or online casino, has a negative expectation to it, and hence, the same is the case with the sum of plenty of games.
A same kind of analysis was done for level stakes, wherein all the bets were of the same size; it returned the exactly same result, that is an overall expectation of 0. Taking a closer look reveals that the Martingale strategy increased the number of times one can expect to register a profit, from 4 to 5, in relation to a level betting strategy on an individual play basis.
Unfortunately, this is experienced at the cost of one major loss. All that Martingale strategy has managed to do is alter the risk distribution. Achieving one extra outcome having a positive expectation is at the cost of another with a comparatively higher negative expectation, quite like the outcomes expected in level betting. This is also the source of an inherent danger in the Martingale betting strategy.

Employing Martingale strategy
When it comes to the field of sports betting, Martingale betting strategy may seem like providing a sports bettor a fair chance of registering profits even in cases when he can’t possibly achieve positive expected value, as every win recovers the preceding losses and slightly extra.
However, the analysis carried out earlier may have hopefully convinced you that Martingale progression is not only inherently risky, but is also mathematically flawed, as any extended and continuous run of losses is likely to increase the bet sizes to extremely high levels. For instance, suffering 10 consecutive even money losses would increase the size of the 11th bet to 1024 units, just to win 1.
Based on the bet size you started with, this may be beyond the acceptable limits of the bookmaker or online casino you’re betting with. What more, it may be far higher compared to the size of your leftover bankroll.
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Underestimating the probability of losing streaks
How likely do you think it is to suffer a 10 consecutive losses run at even money odds? If you look at it in isolation, the mathematics behind this calculation is pretty easy. If every independent bet placed at an offline / online casino, for instance, Bet365, William Hill etc. has a losing chance or probability of 0.5 or 50%, the probability of suffering 10 consecutive losses will be 0.510 or 0.0977%.
This low probability leads to many sports bettors getting fooled into believing that the Martingale betting strategy is actually a relatively safer one to implement. However, what do you think are the chances of suffering such a run of losses, if you look at a series comprising of a significantly larger number of bets?
This calculation can be a little trickier, but it’s apparent and easily recognisable that the probability of this will be comparatively higher than the percentage quoted for an individual losing streak, as there are relatively more opportunities for it to occur. There is a pretty useful method to work out the longest losing streak you may witness during such a long series of bets. It is:
S_L = (Ln (N)) / (Ln (O_L))
S_L = length of the maximum losing streak you can expect
N = total number of wagers
Ln = natural logarithm
O_L = odds of losing any individual wager
O_L, or odds of losing any individual wager can be easily calculated using the odds of winning (O_W) or the betting odds, through the following formula:
O_L = O_W / (O_W – 1)

And therefore, for instance, if you were to consider a series of 1000 wagers, with odds of 2.00, you can expect to witness at least one run of 10 successive losses. As also explained earlier, witnessing such a losing streak would mean that your next bet would need to be 1024 times larger than the very first one.
In order to be able to handle such expectation of a losing run, you’ll need to appropriately calculate the proportional sizes of your baseline stakes as well as your bankroll. The longer will be your betting series, the smaller will be the baseline stakes in proportion to your bankroll, so that you can easily handle and overcome the worst case scenarios.
Hence, in case of 1000 even money bets, you would need your bankroll to be minimum 1000 times larger than the baseline stake size. This will mean that you’ll either need to keep baseline stakes (and resultantly the profits after wins) so low that it’d hardly make the strategy worthwhile, or you’ll run the risk of losing large amounts of money.

The risk of going bankrupt
The Martingale betting strategy has been tried over and over again, using real-world betting series, normally in the range of 150 bets, wherein the average individual win chances were 0.5 (odds of 2.00). If we consider the baseline stakes amounting to 1% of the starting bankroll, the chances of one ending up bankrupt, presuming that the person was provided fair odds, stands at 53%. This percentage goes down pretty low, to the extent of 0%, if we talk about the level staking strategy. In scenarios wherein the bookmaker such as Bet365 etc., holds a respective 5% or 10% advantage over the sports bettor, the risk of going bankrupt using the Martingale betting strategy increases to 65% or 78% respectively.
The risk would still be considerable even if we were to consider scenarios wherein the sports bettor held an advantage. The risk level was in the vicinity of 38% in case of a 5% advantage. Obviously, you may wonder why would sports bettors chase their losses at all in situations wherein they successfully secure a certain positive expected value using their forecasting skills?!

It’s an illusion
You may argue that Martingale strategy actually proves to be a winning one if we were to talk theoretically, in a scenario of infinite bets, infinite wealth, an infinitely generous bookmaker like Bet365 and infinite time.
The only exception of course is that you cannot increase the wealth infinitely, and we may question an individual’s motivation of actually trying if he already possessed a good amount of it. If we were to talk about the actual world of betting and gambling, the bottom line in regard to the Martingale betting strategy would be that the system offers the quickest possible method of incurring huge losses if you cannot consistently beat the betting odds. So why would you actually use it at all?! Putting it in an honest manner, the supposed ability of the Martingale betting strategy to convert losses into profits at core, is actually an illusion, a very risky one to be precise!
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