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Reverse Martingale Roulette Strategy

Right before we get started, I’d like to point out that this the best roulette strategy there is in my opinion. It excels because of its foreseeable time of play, high return to players and a chance to win potentially massive wins. I will get to that later on.

The Reverse Martingale strategy takes its name from the infamous Martingale strategy, which consists in increasing bet sizes after each loss. The Reverse Martingale strategy is the opposite of that – instead of increasing the bet size after each loss, you increase it after each win, with a goal of turning a short streak of winning game rounds into a massive win.

Keep reading this article and learn:

  • why I think this is the best and most balanced roulette strategy there is,
  • how it works in action (supported by simulations),
  • how you can use high volatility for your advantage using this strategy,
  • what is the chance to turn $10 into more than $4,500 using this system.

Note: This article is a part of my series about best roulette strategies, with the Reverse Martingale strategy being the one with the best results and the one I find the most interesting. However, if you haven’t already, I strongly advise you to read the main article on roulette strategies before focusing on the specific strategies.

Table of contents:

  1. How the Reverse Martingale strategy works
  2. Simulations
  3. Results of simulations explained and recommendations
  4. Conclusion

How the Reverse Martingale strategy works

The Reverse Martingale strategy is relatively simple to use. I’ll try to summarize it in a few steps:

  1. You choose your starting bankroll and the amount you would like to exit the casino with – the target amount.
  2. You start by wagering a small part of your bankroll in each roulette spin. This will be your "basic bet". The choice of bet types is up to you, however, some are better than others, as I will demonstrate using my simulations later on.
  3. Every time you win, you wager the entire amount you’ve won again (including your original bet). Every time you lose, you get back to placing your basic bets.
  4. You repeat until you lose your entire bankroll or reach your target amount.
EXAMPLE

To make this strategy a bit clearer, here’s a simple example of what the Reverse Martingale roulette strategy might look in action. Let’s say a player starts with $100 and places $1 basic bets on a number straight up. He would like to walk away with at least $1,000. He loses first 27 spins and then manages to win one, resulting in a $36 win (including his original stake). He places these $36 on a number Straight up and loses. Then he gets back to placing his basic bets of $1 until he loses everything or wins two spins in a row, which would get his bankroll over his target amount ($1 * 36 * 36 = $1,296).

As you might have already noticed, this strategy has only two possible outcomes. You either lose your entire bankroll, or manage to win a satisfying amount. The Reverse Martingale strategy is very similar to the All-in roulette strategy from this point of view. The Reverse Martingale strategy can be seen as many rounds of the All-in strategy played one after another, but with much smaller budget in each instance.

Before using the Reverse Martingale roulette strategy, you’ll have to decide:

  • how much money you are willing to (and can afford to) lose in one session – your bankroll,
  • what your basic bet will be,
  • what type of bets you will place,
  • how much you would like to win – your target amount.

Your chances of succeeding (i.e. reaching the target amount) depends on these factors. In the simulations that I will get to later on in this article, I will test multiple combinations of them to figure out the probability of winning and the long-term return to the player for each of them.

Not wagering the entire win at once

The idea of wagering the entire win from the previous spin in just one game round might seem too risky to some players, even though it’s statistically the best option. There is also an option to wager just a part of the winnings after each win instead of wagering the entire win amount.

For example, instead of betting the basic bet of $1 on a number and then betting the entire $36 in case of a win, you can place a $18 bet or let’s say a $12 bet. Simply put, you choose a percentage of each win you want to wager again and stick to it. Let’s say you choose to bet 50% of each win. After winning the first spin, you would bet $18. The potential win from that spin would be $648, so your next bet size in a succession would be $324.

This version of the Reverse Martingale strategy might be more attractive to some players, because they don’t have to place all of their winnings back into the game. However, it’s inferior to the "classic" version of the Reverse Martingale strategy in terms of expected value.

Note: In my simulations and the rest of this article, I will work with the classic version of the Reverse Martingale strategy, in which you wager the entire winnings from the previous spin at once. I just wanted you to know that there are other options.

We actually turned the idea of not wagering the entire win at once into a separate strategy, which is also very interesting and might be more suitable for some players than the Reverse Martingale strategy. We called it the Progressive bet strategy. Check it out and decide for yourselves which option you find more interesting.

Advantages of the Reverse Martingale strategy

In the beginning of this article I’ve stated that I think this is the best roulette strategy there is. That is a strong claim, which is why I think it’s necessary I also present the reasons why I think that.

As I mentioned in the main article on roulette strategies, my strategies are based on finding a balance between four factors. The Reverse Martingale strategy is great because it ranks well for all of these:

  • RTP (Return to Player) – The Reverse Martingale strategy has great RTP, because you don’t keep wagering the same money over and over, which would result in a significantly lower strategy RTP.
  • Chance to win big – With the Reverse Martingale strategy, you can have a really reasonable chance to achieve a big win, which depends on the target amount you want to win. Of course, the higher the target amount, the lower are your chances of hitting it.
  • Play time – Because of the nature of this strategy, the expected play time is predictable to a great degree. I will focus on this later on.
  • Thrill – The thrill factor of the Reverse Martingale strategy is also amazing. Most of the time, you’ll be placing the small basic bets, but every once in a while (if you place Straight up bets) or even quite often (if you place bets on Color), you’ll get to place higher bets with a potential to win big.

All of my strategies rank well in at least some of the factors. The Constant bet strategy and the Constant proportion strategy do well in terms of the play time, but their chance to win big is very small and their RTP tends to get quite low with increasing bet sizes and the thrill factor is also lackluster.

The All-in strategy has great RTP, a good chance to win and a huge thrill factor (even too high for most people), but you’ll only get to play one or two spins in most cases, which means the play time is not that great if you want to enjoy the game for some time.

The balance of the aforementioned four factors is what makes the Reverse Martingale strategy the best in my opinion. I am not saying it’s the best option for everybody, but I am pretty much sure it’s the best overall option that you should definitely consider if you are looking for an efficient and enjoyable way to play roulette.

Potential issues with bet size limits

When using the Reverse Martingale strategy, you might run into issues with bet size limits in the brick-and-mortar or online casino you play at. Just as with the All-in strategy, the bet sizes keep increasing quite rapidly when you are winning, which means the bet limits might be a problem if you don’t plan for them.

Just as I mentioned in my article on the All-in roulette strategy, you should always check the table limits before you start playing, so that you pick a specific bet type and target amount you can actually go through with. If you find out that the bet size limits can prevent you from reaching your target amount, you should reconsider your strategy and change your target amount.

I am aware of the fact that most of the people reading this article play casino games online, so I thoroughly checked online roulette bet size limits and I struggled to find a version in which you can bet more than $500 Straight up or $20,000 on a Color. There are versions with higher bet size limits, but access to those might be limited by your VIP status in a casino or your current balance. That being said, I tried to limit the values in my simulations to levels reachable by any recreational player, so that they can actually be used in real life.

Note: The All-in strategy has even bigger issues with the bet size limits, but I didn’t go into such details in my article about it. It’s simply because I present Reverse Martingale as the best strategy, so I want everything to be clear, realistic and usable.

Achievable amounts

The Reverse Martingale strategy is all about trying to multiply the basic bet as many times as needed to reach the predetermined target amount. By purposefully creating a sequence of different bet types to wager the money on, you can get close to pretty much any round multiple of your desired win. I’ll demonstrate that in the table below.

Desired win with a $1 basic bet Bets in a sequence Potential win calculation
$200Straight up – Six line$1 * 36 * 6 = $216
$500Straight up – Split$1 * 36 * 18 = $648
$1,000Straight up – Straight up$1 * 36 * 36 = $1,296
$2,000Straight up – Straight up – Color$1 * 36 * 36 * 2 = $2,592
$3,000Straight up – Straight up – Dozen$1 * 36 * 36 * 3 = $3,888
$5,000Straight up – Straight up – Six line$1 * 36 * 36 * 6 = $7,776
$10,000Straight up – Straight up - Corner$1 * 36 * 36 * 9 = $11,664
$20,000Straight up – Straight up – Split$1 * 36 * 36 * 18 = $23,328
Table #1: Different multiples of the basic bet achievable by various bet sequences

Note: Although different amounts are reachable by combining different bet types in a sequence, I’ve decided only to use one bet type in each simulation. That way the results are a clear sign which bet type is statistically the best and the simulations are easier to create and understand.

Expected time of play

One of the advantages of the Reverse Martingale strategy is the expected play time, which highly predictable and doesn’t change that much. Because of the nature of this strategy, it’s even calculable with a great degree of precision.

When calculating the expected time of play, you have to consider two kinds of spins you’ll get to play:

  • The number of spins in which you place your basic bets in fixed and depends only on the ratio of your basic bet and your bankroll. If you go into the gameplay with $100 and place basic bets of $1, you’ll play 100 of these game rounds.
  • The number of spins in which you place higher bets depends on the type of bets you place. If you bet your bets on a number Straight up, you’ll only play a game round with a higher bet after one out of 37 one-dollar-spins (statistically). If your goal is to win more than two bets in a row, you’ll also have to consider the chances of getting to the higher bets, which are getting much smaller, but still need to be included in the calculations.

Let’s take a closer look at the specific time of play for the players using the Reverse Martingale strategy and placing their bets on Color:

  • The probability of placing the first spin with a bet size of $1 is 100%. That’s easy.
  • Whether the player places the second bet ($2) in a succession depends on the outcome of the first spin. He only gets to place it if he won the first spin, which happens with a probability of 18/37 (roughly 48.65%).
  • To play the third spin with a bet size of $4, the player needs to win the first two spins. That only happens with a probability of (18/37)^2 (roughly 23.67%).
  • The probability of the player getting to the fourth spin is (18/37)^3 (roughly 11.5%).
  • And so on and so on.

This progression is called a geometric sequence and its sum can be precisely calculated, depending on type of bets the player places. The table below displays the expected total number of spins for different bet types.

Bet type Chance to win in each spin Total expected number of spins for 100 basic bet spins
Color18/37194.74
Corner4/37112.12
Straight up1/37102.78
Table #2: Total expected number of spins depending on the bet type

The expected number of spins in the table above is calculated using an infinite series, which means the results you get might (and most likely will) be at least slightly different. The number of spins you get to play might differ, but the differences should be quite small, especially after playing a large number of game rounds.

The numbers from the simulations should correspond with the numbers from the calculations. Let’s get to the simulations to see if they really do.

Simulations of the Reverse Martingale strategy

Simulations are the best way to test strategy’s effectiveness and efficiency in action. Any real-life tests are an issue, because it’s virtually impossible to reach a sample size with a reasonable level of statistical significance. Let’s take a look at the simulations to see what kind of results the Reverse Martingale strategy brings.

Methodology and used variables

Before we get to the results themselves, it’s important to note how the simulations were carried out, so that everything is completely clear to you.

First of all, the simulations were created using my own simulation software with rules and odds of single zero roulette without any special rules like En Prison or La Partage in use. Single zero roulette should always be used, because it has much better odds for the player, which results in higher strategy RTP.

Here are the specifics of my simulations:

  • The basic bet is always $0.1 and the players start with a bankroll of $10 (100 spins with a basic bet) or $100 (1,000 spins with a basic bet).
  • The players will always go through the entire number of spins with a basic bet (100 or 1,000, depending on the bankroll), regardless of their results. If they reach their target value, they’ll simply set it aside and continue by going back to the basic bet and trying their luck one more time. That means the players can reach their target value multiple times.
  • The target values are different for each bet type, which has a very good reason. Had I chosen the same target values for all simulations (like $100, $1000 etc.), the results will be biased because of the specific win amounts of the individual bet types.

Just as for all other simulations regarding my roulette strategies, I included these three bet types:

  • Color – Red or Black (chance to win: 18/37, payout: 2x)
  • Corner – Four numbers that share one corner (chance to win: 4/37, payout: 9x)
  • Straight up – One specific number (chance to win: 1/37, payout: 36x)

Note: Because I present this strategy as the best one to use, I want to make sure there is nothing holding it back and that the specific sequences I use in my simulations are actually feasible. That’s why I decided to lower the basic bet from the originally intended value of $1 to just $0.1 in my simulations, so that the target amounts are actually reachable with bet size limits widely used in online casinos.


That being said, you can always increase the numbers, as long as the ratio of basic bet size and bankroll remains the same. For example, a simulation with a $0.1 basic bet, $10 bankroll and a target amount of $102.4 has the same results as a simulation with a $1 basic bet, $100 bankroll and a target amount of $1,024, as long as the bet type also remains the same.

For each bet type, initial bankroll and target amount, I’ve simulated 1,000,000 runs. This sample size should be big enough to make the results statistically reliable, although it’s possible that there will be some deviations in the runs with higher volatility. However, the results should be reliable to enough to draw solid conclusions.

Color bet simulations

Let’s start with the Color bet type and a $10 bankroll, which is enough for 100 spins with the basic bet. Because bets on Color have a very low volatility, the players will have to win a higher number of spins in a row to achieve a nice win. Let’s see how many of them managed to do it.

Target amount (# of wins needed) Average number of rounds played Average cost Players winning 1 time Players winning 2 times Players winning 3 times Players winning 4 times Players winning 5 times
$25.6 (8)1941.97$22989535765368929515
$51.2 (9)1942.15$1318159991456301
$102.4 (10)1942.38$6902825387311
$204.8 (11)1942.6$34830627200
$409.6 (12)1952.85$17186133000
$819.2 (13)195$3.12831838000
$1638.4 (14)195$3.2541057000
$3276.8 (15)195$3.3520223000
$6553.6 (16)195$3.579840000
$13107.2 (17)195$3.864690000
Table #3: A simulation of million players using the Reverse Martingale strategy on a Color bet, with a $0.1 basic bet and a $10 bankroll

The following table displays the results of another run of simulations, but this time with a bankroll of $100, which is enough for 1,000 basic bet spins. This time I set the minimum target amount to $102.4, because that’s the first value that’s actually higher than the starting bankroll.

Target amount (# of wins needed) Average number of rounds played Average cost Players winning 1 time Players winning 2 times Players winning 3 times Players winning 4 times Players winning 5, 6, 7 and 8 times
$102.4 (10)194523.9$353522131043325776136907, 111, 12, 5
$204.8 (11)194726.1$25121845371556849129, 1, 0, 0
$409.6 (12)194727.8$14777213068751282, 0, 0, 0
$819.2 (13)1947$30.17828233729830, 0, 0, 0
$1638.4 (14)1947$31.4401378451610, 0, 0, 0
$3276.8 (15)1947$34.019709199000, 0, 0, 0
$6553.6 (16)1947$35.5972554000, 0, 0, 0
$13107.2 (17)1947$36.448425000, 0, 0, 0
Table #4: A simulation of million players using the Reverse Martingale strategy on a Color bet, with a $0.1 basic bet and a $100 bankroll

As you can clearly see, the number of winners and the average cost keep getting higher with increasing target amounts. That’s, of course, pretty self-explanatory, as the higher wins are simply less likely (therefore the lower number of winners) and players have to place higher bets to get to them, which results in bigger average cost. This will be similar for all bet types.

Corner bet simulations

The second group of simulations follows players that place their bet on a Corner bet type. Just as in the previous simulations, the first table contains results of simulations with a $0.1 basic bet and a $10 bankroll, which is enough for 100 basic spins.

Target amount (# of wins needed) Average number of rounds played Average cost Players winning 1 time Players winning 2 times Players winning 3 times Players winning 4 times
$72.9 (3)112$0.8111100870512975
$656.1 (4)112$0.88137059700
$5904.9 (5)112$1.241481100
$53144.1 (6)112$1.39162000
Table #5: A simulation of million players using the Reverse Martingale strategy on a Corner bet, with a $0.1 basic bet and a $10 bankroll

The following table contains the results of simulations with a $0.1 basic bet and a $100 bankroll, which is enough for 1,000 basic spins. The target values start at $656.1, as it’s the first possible target value higher than the starting bankroll.

Target amount (# of wins needed) Average number of rounds played Average cost Players winning 1 time Players winning 2 times Players winning 3 times Players winning 4 times
$656.1 (4)1121$10.4119102820934512
$5904.9 (5)1121$13.71439410700
$53144.1 (6)1121$14.11616000
Table #6: A simulation of million players using the Reverse Martingale strategy on a Corner bet, with a $0.1 basic bet and a $100 bankroll

Straight up bet simulations

The last two runs of simulations focus on the use of the most volatile roulette bet – the Straight up bet on a single number. The basic bet is $0.1 in both tables below and the budget is $10 (100 basic spins) in the first one and $100 (1,000 basic spins) in the second one.

Target amount (# of wins needed) Average number of rounds played Average cost Players winning 1 time Players winning 2 times Players winning 3 times Players winning 4 times
$129.6 (2)103$0.54679322461571
$4665.6 (3)103$0.871952200
$167961.6 (4)103$1.2752000
Table #7: A simulation of million players using the Reverse Martingale strategy on a Straight up bet, with a $0.1 basic bet and a $10 bankroll

Target amount (# of wins needed) Average number of rounds played Average cost Players winning 1 time Players winning 2 times Players winning 3 times Players winning 4 times
$4665.6 (3)1027$7.41951117010
$167961.6 (4)1027$9.3540000
Table #8: A simulation of million players using the Reverse Martingale strategy on a Straight up bet, with a $0.1 basic bet and a $100 bankroll

Results of simulations explained & recommendations

When you look at the simulations of each bet type individually, it’s pretty obvious that the average cost keeps growing with a higher desired win. That’s because in order to achieve greater wins, you have to also place bigger bets, which increases the costs.

In roulette, you statistically lose a portion (2.7% in European roulette) of every bet you place, which is why bigger bets equal to higher long-term cost for the players. In fact, the average cost for each bet type and desired win can be precisely calculated using this formula:

Average cost (%) = 1 – (36/37) ^ (number of wins in a row needed to reach the goal)

Note: The average cost formula above really works in the long term, but my results from the simulations are a bit different for some values, especially for those with a high volatility. For example, the average cost of getting to $167961.6 from $10 is $1.27 and from $100 is $9.3 in my simulations, but statistically it should be $1.038 and $10.38 respectively. I would have to simulate a huge number of players to get more accurate results, but it’s honestly not that important. The simulations paint a pretty accurate picture of the strategy as they are.

The probability of achieving the target amount is fair. The higher goal you set, the less likely you are to achieve it. That’s simply how statistics work in this case. If you want to win really big, you have to accept the fact that you won’t win very often.

Comparison of bet types and their costs

The size of the target amount is entirely up to you, because it can’t be objectively said which of them is the best. You are just trading a possibility of a higher win for an increased average cost.

However, what can be objectively judged is the bet type. When you take a look at the tables with the results of my simulations, you can clearly see that the average costs are much higher when placing bets on Color. That’s because a big number of wins in a row is needed, a bigger number of bets is placed and the bets tend to have a higher bet sizing.

Note: The average cost formula also makes this really clear, as it directly contains the number of win in a row needed to reach the target amount. As this number gets bigger, the average cost also increases.

The table below displays simulation results of different bet types with similar target amounts. Let’s take a look at them to draw a clear comparison between the bet types and their average costs.

Color Corner Straight up
Desired win$102.4$72.9$129.6
Number of wins in a row needed1032
Average cost$2.38$0.81$0.54
Number of winners (1x, 2x, 3x, 4x, 5x)69028, 2538, 73, 1, 1111008, 7051, 297, 5, 067932,2461, 57, 1, 0
Table #9: Comparison of simulation results with different bet types and similar desired wins

As you can clearly see, the "Straight up" column has the highest desired win of the three cases, as well as the lowest average cost. That’s a clear sign that higher volatility yields better results, just as I’ve stated in my main article on roulette strategies.

I’ve previously mentioned that higher desired wins are connected with higher average costs, but that’s true only when the bet type remains the same. By moving to higher volatility bets, you can increase the desired win and decrease the average cost at the same time. If you are looking for maximum efficiency, you should definitely stick to the Straight up bets.

The only reason to stick to the bets with lower variance is if you want to play a higher number of spins and have a bit more fun. The downside of the use of the most volatile Straight up bet is the lowest number of spins and the fact that you only get to place higher bets very rarely, which might decrease the thrill factor to some degree.

If you want to play a bit more spins, you can try placing Corner bets, but I’d definitely stay away from the Color bet, as its average cost is just so much higher.

Number of game rounds played

Earlier in this article, I’ve used a formula to calculate the total number of spins the players should play for each bet type. The simulations delivered expected results, as the table below clearly shows.

Bet type Calculated average # of spins Recorded average # of spins (rounded)
Color194.74195
Corner112.12112
Straight up102.78103
Table #10: Calculated and expected number of spins for each bet type

Conclusion

The Reverse Martingale strategy really is the best strategy I could think of. For example, it can give you a realistic chance to win $4665.6 with a bankroll of just $10. Although the chance to achieve that is lower than 0.2%, the entire gameplay will cost you only $0.87 on average. To my knowledge, there is no other roulette strategy with such a great ratio of the potential win and the average cost.

Please keep in mind that this strategy is just one of the those I included in my roulette strategies article. Although I think this one is the best, I also think you have complete information before choosing the best way to play roulette for you. Please give the main article a read and check out other strategies as well to see whether you find them better or not.

If you decided to try the Reverse Martingale strategy in action, I strongly advise you to stay away from the Color bet type and choose either Corner or Straight up bets, with the last one being statistically the best option by far.

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