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What is the D’Alembert Betting System?

Author Samuel Karugu

Approved by Rumen Morfov

Updated:

15 September 2026

The D’Alembert betting system is a negative progression gambling strategy that was created by Jean Baptiste Le Rond D’Alembert, a French philosopher, mathematician, and physicist from the 1700s. It is primarily associated with even-money bets, such as pass/don’t pass bets in craps or red/black bets on a roulette table. The D’Alembert system determines how much you should wager based on the outcome of your previous bet.

In this betting strategy article, we will explain the D’Alembert Principle in greater detail. We will also provide a real-life example and some tips on how to use the system correctly.

Dr Catalin Barboianu, Mathematician and Philosopher of Science PhD

D’Alembert is a negative progression betting system, very easy to be applied, and falls within the category of safe progressive systems; however, safety is always relative in gambling.

The math behind D’Alembert is also easy to understand: In the expression of the profit/loss accumulated in a sequence with an equal number of wins and losses, there are as many negative numbers as positive numbers, and the absolute difference between any two consecutive terms is 1; hence, the result of that expression is actually the number of those negative (or positive) numbers, which is positive.

If the number of wins equals the number of losses in a successful cycle, you will always be in profit, but this fact is not particularly surprising since the probability of winning an even-money bet is close to 1/2. However, long losing streaks are possible at any length, as in any sequence of independent outcomes; it’s just that losses accumulate at a
far lower rate than in other progressive systems.

As a low-risk system, D’Alembert is suitable for low to medium bankrolls in medium- to long-run play, as long as your base stake is small enough.

The D’Alembert Principle in Gambling Explained

The D’Alembert betting strategy is a negative progression system that can be applied to games such as roulette and craps where even-money bets are available. The basic principle is simple: you increase your wager by one unit after a loss and decrease it by one unit after a win, usually without going below your original base stake.

The theory behind the system is that wins and losses will eventually balance out. However, this assumption should be treated with caution. Each spin or roll is an independent event, so a previous loss does not make a win more likely on the next bet.

Unlike more aggressive betting strategies, the D’Alembert principle aims for smaller and more gradual changes in stake size. While this can make the strategy easier to manage, there is no guarantee of profits because the house edge remains in place.

Samuel Karugu, Betting Expert & Writer for SilentBet

This betting system is one of many approaches I have used when playing games such as roulette and craps. What I like about D’Alembert is that the stake progression is relatively simple and less aggressive than systems that increase bets exponentially. However, it is important to remember that no betting system can remove the house edge.

How the D’Alembert Betting System Works

The way the D’Alembert system works may seem complicated at first glance, but the basic principle is quite simple. You determine a base unit that represents the amount you are comfortable wagering on your first bet.

For example, let’s presume you are working with a $2,000 bankroll and decide your base unit should equal 2% of your bankroll. In this case, you would start with a one-unit bet of $40 on your game of choice.

If you lose, the D’Alembert system stipulates that you increase your next bet by one unit. If you win, you decrease your next bet by one unit, normally stopping at your original base stake rather than going below it.

For example, with a $40 base unit, a losing sequence could result in bets of $40, $80, $120, and $160. A win at $160 would then bring the next stake down to $120. To help you understand the risks and potential results in greater detail, we have included a D’Alembert example in the section below.

D’Alembert System Example

The example below shows a theoretical 16-bet session using the D’Alembert system with a base unit of $40. The player starts with a $40 wager, increases the stake by one $40 unit after each loss, and decreases it by one $40 unit after each win, without going below the $40 base stake. The table shows the bet amount, the outcome, and the cumulative profit or loss after each bet.

The player wins seven of the sixteen bets and loses nine. Despite having more losses than wins, the player finishes the session with a $40 net profit. This is possible because the size of the wagers changes throughout the sequence, with several of the winning bets being placed at higher stakes.

The progression can be seen clearly in the middle of the session. After consecutive losses, the stake increases from $40 to $80, $120 and eventually $160. When a bet wins, the next stake is reduced by one $40 unit. After the $200 win on the 14th bet, for example, the cumulative result moves from -$200 to $0. A subsequent $160 loss takes the player back to -$160, before the final $200 win brings the session to a $40 profit.

This example also highlights an important limitation of the D’Alembert system. A favourable sequence can produce a short-term profit, but the system does not change the underlying odds of the game or eliminate the house edge. A different sequence of wins and losses could produce a very different result, while a prolonged losing streak could require increasingly larger wagers.

Keep in Mind the Gambler’s Fallacy

The D’Alembert system is often associated with the gambler’s fallacy, which is the mistaken belief that previous independent outcomes influence the probability of future outcomes.

For example, if a roulette player loses five consecutive bets on red, they may believe that red is now more likely to appear. It is not. On a standard European roulette wheel, the previous spins do not change the probability of the next spin.

D’Alembert’s progression is based on adjusting the stake after wins and losses, partly on the assumption that winning and losing streaks will eventually balance out. While sequences can certainly contain periods of balance, there is no mathematical requirement for a particular number of wins to follow a series of losses.

If you want to learn more about this concept, you can review our Gambler’s Fallacy examples here.

Tips for Using This System the Right Way

Given the nature of this system, you can find out more about other betting strategies if D’Alembert isn’t for you. However, if you want to put it into practice, here are a few tips for using the D’Alembert system responsibly.

• Tip 1: Set a Realistic Bet Unit – Your base unit should be small enough to withstand a potentially long losing streak. A larger base unit can cause your required stakes to become uncomfortable very quickly.
• Tip 2: Focus on Even-Money Bets – D’Alembert is traditionally associated with even-money bets because the system is designed around relatively balanced win/loss outcomes. However, choosing an even-money bet does not eliminate the house edge.
• Tip 3: Establish a Loss and Profit Limit – Before you start playing, decide how much you are prepared to lose and when you will stop if you reach your target profit. This can help prevent you from continuing to gamble in an attempt to recover losses.

Samuel Karugu, Betting Expert & Writer for SilentBet

I learned long ago that there is a right way and a wrong way to use a betting strategy. I might not always win, but sticking to the basics and knowing when to stop is the better approach.

Pros & Cons

Reverse D’Alembert Basics

The Reverse D’Alembert is a positive progression strategy that works in the opposite direction to the standard D’Alembert system. Simply put, you increase your bet size after a win and decrease it after a loss.

Unlike the standard D’Alembert, the Reverse D’Alembert focuses on capitalizing on winning streaks rather than increasing stakes after losses. This means your exposure can grow while you are winning and fall back toward the base stake after losses.

Like the standard D’Alembert, the Reverse D’Alembert does not change the underlying odds of the casino game. A winning streak can increase your stakes and potential returns, but it can also be followed by losses that reduce or eliminate previous profits.

The Bottom Line: Is It Really Worth It?

The D’Alembert system may be worth considering if you’re the type of player who prefers a simple and relatively gradual approach to adjusting bet sizes. However, it is important to understand what the system can and cannot do.

D’Alembert does not give you an advantage over the casino, does not guarantee profits, and cannot prevent losing streaks. Its main appeal is that it increases stakes by one unit after a loss rather than using the much more aggressive progression of systems such as the Martingale.

Ultimately, the D’Alembert system is best viewed as a bet-sizing method rather than a way to beat the house. Your base stake, bankroll limits, and willingness to stop during a losing session are more important than the progression itself.

Samuel Karugu, Betting Expert & Writer for SilentBet

The D’Alembert betting system is an easy-to-use betting strategy. It may not be for everyone, but if you are new to betting systems, it can be a useful way to understand how progressive staking works. Just remember that a betting system cannot change the underlying odds of the game.

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