Advantages of Static and Progressive Betting Systems in Roulette: Part 2

Author: Dr. Catalin Barboianu

Welcome to the second part of our two-part blog series on progressive betting systems. In the first part, we explored the fundamental mechanics and appeal of static and progressive betting strategies, such as Martingale and Fibonacci. Now, we delve deeper into the financial parameters that define these systems and analyze their profit rates.

Despite the allure of recovering losses through wins, the reality reveals a low profit margin and significant risks. In this blog, we'll review key financial metrics, compare statistical parameters with static betting, and discuss why safety and bankroll management play a crucial role in choosing a betting strategy.

Risks of Low Profit Rates in Progressive Betting Systems

Another aspect that counts in the disadvantages side of progressive betting is the low profit rate. In the most popular progressive roulette systems, the net profit after the winning (or losing) spin is the stake of the first bet (like in Martingale or Fibonacci) or twice that stake (in Paroli).

In the tables bellow you may see the profit rate and possible loss for the Martingale and Fibonacci systems, for some lengths of their series.

Table 1: Martingale financial parameters:

In the second column of table 1 is noted the profit rate for a series of length as given in the first column, where the last spin is winning and the previous ones are losing. In the third column is noted the loss in units of initial stake, provided that all spins in the series are losing.

Table 2: Fibonacci financial parameters:

Table 2 shows the financial parameters of the Fibonacci system for a few particular series of bets. In the first column, L means a losing spin and W a winning spin. The third column notes the overall loss in units of initial stake, provided that the series ends with a loss and the player does not have enough bankroll to continue it.

The low profit rates raise the question of why should one choose a progressive system rather than a static bet with the same total stake and a higher profit rate. The question stands even though in progressive roulette betting with a win the previous cumulated loss is recovered. The only valid answer is safety (as basing on a higher probability of making the overall profit), however the risk of depleting the bankroll or reaching the bet size limit still weights in the balance. The uncertainty about the length of the series, which also reflects the time of playing, is also a factor to consider when conceiving a personal strategy of betting

Statistical Parameters of Progressive Betting Systems in Roulette

We already saw that in general the profit rates of the progressive systems are low compared to those of the simple static bets and consequently the expectations (as statistical averages) cannot be higher than in the latter case, despite the high probabilities of completing successfully the progressive series. For example, in the text table are the statistical parameters of the Martingale played in European roulette, for an even-money bet, for lengths of 3 up to 10 of the betting series.

Table 3: Martingale statistical parameters:

The numbers in the first column should be interpreted as the maximal number of bets you afford to lose with respect to your bankroll, which is noted in the second column (in units of the initial stake, assumed 1). The winning probability (in the third column) is the probability of winning with the given bankroll and with a number of bets lower than or equal to the given length of the series. The last column notes the average number of winning sessions for each losing session, if the player keeps playing indefinitely.

We can see very high probabilities of winning for each series, increasing with the length of the series (implicitly with the bankroll). They are much higher than most of the winning probabilities of the large-coverage static bets. But these higher probabilities do not automatically mean an advantage compared to the other form of betting. This is because the gambling math of a Martingale says that the expected value of a martingale as a stochastic process (conditional expectation) is always equal to the expected value of the initial bet.

Hence in the long run we can expect the same 2.70% to be our average loss, despite those high probabilities. The house edge stands. This constancy is reflected in the figures of the last column of the above table, where we can see high number of wins required to compensate a loss.

Hence in the long run we can expect the same 2.70% to be our average loss, despite those high probabilities. The house edge stands. This constancy is reflected in the figures of the last column of the above table, where we can see high number of wins required to compensate a loss.

These statistical features with high probabilities of winning (relative to sufficient bankroll) and constant expectation (as of the static bets) in the long run stand for all the progressive systems.

In table 4 are shown the results of a simulation (performed by games mathematician Michael Shackleford) of over 25 billion sessions for the D’Alembert system played in European roulette with an even-money bet.

Table 4: D’Alembert statistical parameters (by simulation)

On the first row are the various bankrolls in units. The stakes are assumed increased with one unit in the D’Alembert progression. The second row notes the average number of bets per session, the third the average total stake per session, the fourth the expected gain (loss) per session and the fifth the average ratio between loss and total stake.

We can see that, despite the high winning probabilities, one can expect an average loss in the long run and the average ratio loss to total stake is actually near the standard 2.70% house edge of the European roulette. The more you play this system, the more this ratio will approach this house edge.

Effectiveness of Static and Progressive Roulette Betting

Progressive betting systems are based on the principle of chasing wins against losses. In fact, we do that in static betting also. Even though this principle is backed up with mathematical truths, the real effectiveness of such systems depends decisively on the available bankroll.

This is why any comparison between static and progressive betting in terms of advantages and effectiveness cannot be absolute, but relative to several criteria, of which some are subjective, depending on everybody’s style of playing and various goals. We have identified safety as the main criterion of comparison. Safety in this case may be of two kinds: safety as high probability of winning and safety as low risk of bankroll depletion.

The profit rate is another criterion for comparison and we found that the profit rates of the progressive betting systems as in general as low as the profit rates of the large-coverage static bets. What the two also have in common are the high probabilities of winning, with a plus for the progressive systems.

The common element of any static bet and any progressive system is the constant expectation, which reflects the house edge of the game in the long run. If we were to turn this analysis into a theoretical recommendation for choosing the more advantageous strategy of betting depending on the mentioned criteria of comparison, we should tune it to the type of play (short, medium, or long run). This would generate the following results:

On the first row there are the main criteria of choosing. ‘S’ means that static betting is theoretically recommended. ‘P = S’ means that no choice is recommended. ‘P ≥ S’ means that in general progressive betting is recommended (P), but no choice is recommended (P = S) if certain bets are considered for comparison (a wide category of large-coverage bets). ‘S*’ means that exceptions are in effect: For instance, in the Labouchere system, you set your own profit target and run the system accordingly; this could turn it into one with a high profit rate, if successful.

The dash in the expected value column means that the theoretical expectation does not get materialized, so we cannot take it to be an applicable criterion of choosing. Of course, many factors that determine a certain play and style of playing are not covered in this general table. For instance, players going to high roller casinos may not prioritize any safety against depletion. Thus, they may incline toward the progressive betting in the long run.

Final Thoughts

As an overall image, someone may fairly ask why one should complicate their life with a progressive system, since both static and progressive betting exhibit about the same statistical values, have the same effect in the long run, and the latter also pushes them to run the risk of disaster. The math says that this question is legitimate and the myth of the progressive systems (induced by the overconfidence many people have in the word ‘system’) should not add to the already existing misconceptions about gambling.