The D’Alembert Roulette Betting System

Jean le Rond d'Alembert

What is it?

The D’Alembert system is a negative progression betting system, meaning bet amounts are increased following losses and decreased following wins. It can be applied to many different gambling games but is popularly used playing roulette.

What are its origins?

We have the system’s namesake, 18th century French mathematician Jean-Baptiste le Rond d’Alembert to thank for the D’Alembert betting system. He left an indelible footprint across a range of academic disciplines, giving the world the D’Alembert criterion; D’Alembert’s form of the principle of virtual work; D’Alembert’s formula; the D’Alembert equation for waves;  the D’Alembert operator; D’Alembert’s paradox and the D’Alembert’s principle.

He won much acclaim and received many honors along the way, including an honorary membership of the American Academy of Arts and Sciences.

It’s fair to say that his work on probability applying to the toss of a coin (the foundation of the D’Alembert system) was probably not his best effort.

It’s hard to imagine how a bloke who can come up with something like this…

“the sum of the differences between the forces acting on a system of mass particles and the time derivatives of the momenta of the system itself along any virtual displacement consistent with the constraints of the system, is zero”

Can also come to the conclusion that…

“the probability of a coin landing heads increased for every time that it came up tails”

We all have our off days.

How does it work?

Let’s not mince words here. It doesn’t.

The system has as it’s foundation the gambler’s fallacy that past outcomes do influence future outcomes for independent random events (like the toss of a coin, the spin of a roulette wheel) because in the end results must balance out. An infinite number of 50/50 coin tosses should result in just as many heads as tails. So if a run of tails occurs, it follows that more heads are on the way to restore equilibrium. And if we know this, we should increase our bets on heads.

Problem is, regardless of what’s occurred in the past, the chance of heads being tossed on the next flip is still 1 in 2.

Here’s how the D’Alembert system is applied to a game of roulette.

Choose a starting bet value and stake that amount on an even money bet (red/black, odd/even, high/low). You then increase or decrease subsequent bets by a single unit, depending on whether you win or lose according to the following rule:

  • if the previous bet won, then subsequent bet is decreased by a single unit
  • if the previous bet lost, then subsequent bet is increased by a single unit


Bet number Bet type Bet amount Win or Loss Net position
1 Red $5 Win $10
2 Red $4 Win $14
3 Red $3 Loss $11
4 Red $4 Loss $7
5 Red $5 Loss $2
6 Red $6 Win $8

Devotees of Martingale roulette will note some similarities with their system: play even money bets; raise stakes when you lose; drop stakes when you win. Of course the big difference is the aggressiveness of bet progression. For Martingale losing bets are doubled and a win returns you to your original stake amount.

D’Alembert won’t get you into trouble as quickly as Martingale. But it also won’t guarantee you a win.

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