The D’Alembert and Reverse D’Alembert Strategy in Betting Practice

In this article, we will look at the D’Alembert and Reverse D’Alembert strategy, its variations, advantages and disadvantages; and learn how to use the strategy on practical examples.

The Basics of the Dalembert Strategy

The D’Alembert betting strategy is similar to Martingale, except that in D’Alembert we use algebraic and not geometric sequence. The strategy is named after the 18th-century scientist Jean le Rond d’Alembert who benefited the world with his works in the areas of mathematics and physics.

You may be surprised but the D’Alembert strategy is used more often than Martingale, as it is considered less risky.

But first things first.

The Rules of Betting with the D’Alembert System

The two basic strategy rules are:

  • The odds for events must be more than 2.0.
  • The maximum amount of the first bet should not exceed 1/20 of the bankroll.

On the internet, you can come across three variations of the strategy:

How to Bet with the D’Alembert Strategy: Version 1

I don’t recommend this variant and you will see why later.

Let’s assume that your first bet amount is 10 dollars. For our purpose, we will call it one ‘unit’.

  • If the ‘unit’ wins, the cycle is over. We have earned 2 ‘units’ (20 dollars).
  • If the bet loses, the next one must be increased strictly by one ‘unit’, that is, 10 dollars. You are supposed to continue betting like this until your bet wins. After a bet has won, the cycle is over. Time to count the earnings and start a new cycle.

For better understanding, let us present the calculations in the table. Suppose, your first bet amount is 50 dollars and the odds are 3.0.

Bet #OddsBet AmountOutcomeProfit
23.050+50 =100Loss-150
33.0100+50 =150Loss-300
43.0150+50 = 200Loss-500
53.0200+50 =250Loss-750
63.0250+50 = 300Win-150

Strangely, even though we strictly follow the strategy rules, after the 6th bet, we are still in the red.

Why this result? According to this variation of the D’Alembert strategy, after every win, the bet amount is increased only by 50 dollars which means that, given the odds are 3.0, the strategy will work right until the 5th bet. The more the odds, the longer the strategy will last, but then the probability to win is lower, too.

Verdict: The strategy is nonsense.

The Rules of Version 2: An Example of Betting with D’Alembert System

Suppose, our first bet amount is 50 dollars. We take it as one ‘unit’.

  • If the bet loses, we increase the amount by one ‘unit’.
  • If the bet wins, we decrease the amount by one ‘unit’.

Let us look at a practical example:

Punters often choose to bet on draws because the odds for this kind of bets are almost always higher than 3.0.

In our example, we will use Swansea City’s games in the 2015/2016 English Premier League.

The first bet is 50 dollars. The odds are 3.48. The bankroll is 1,000 dollars.

dalembert strategy example

As you can see, Swansea is losing. 1,000-50=950 dollars.

We increase the bet amount by a ‘unit’, that is, bet 100 dollars with odds of 3.84.

dalembert system example

Again, a loss. 950-100=850 dollars.

Now we bet 150 dollars with odds of 3.64.

dalembert strategy betting

This time, Swansea is stronger than their opponents, but we bet on a draw. 850 — 150 = 700 dollars.

Bet 4 — 200 dollars with odds of 5.15.

reverse dalembert system example

A win. 700 + 830 = 1,530 dollars

Bet 5. We decrease the amount by a ‘unit’ and bet $150 with odds of 6.05.

reverse dalembert strategy

Quite suddenly, Swansea players get a big away win. But for us, it means a loss. 1,530 — 150 = 1,380 dollars

Resume: 1 bet out of 5 won. The net profit is 380 dollars.

By way of illustration, let us present all the actions in a table:

Bet #OddsBet AmountOutcomeProfit
Bet 13.48$50Loss-50
Bet 23.84$100Loss-50-100 = 150
Bet 33.64$150Loss150-150 = -300
Bet 45.15$200Win-300+830 = +530
Bet 56.05$150Loss530-150 = 380

Version 3: How to Bet with the Reverse D’Alembert

The Reverse D’Alembert strategy is based on the D’Alembert system.

The main difference from the D’Alembert strategy is that you are supposed to do everything in reverse:

  1. If the bet won, the bet amount is increased by one ‘unit’.
  2. If the bet lost, the bet amount is decreased by one ‘unit’.

Can You Win by Using the D’Alembert or the Reverse D’Alembert Systems?

I should say, the d’Alembert strategy is widely reviewed on the internet and is favored by many professional bettors. It sufficiently reduces the risk of facing bookmaker limits. But remember that you should not make the first bet right away. Instead, wait for some favorable streak (like when one team has non-draw results for five matches in a row).

Your bank is also of importance here. Don’t be greedy. The amount of your first bet should make 1/30 or even 1/50 of the bankroll.

Food for thought: If your first bet makes 1% of the bank, it will take 13 unfortunate bets to lose your bankroll.

True story: I was waiting for a ‘total over 3.5’ for Juventus. We all know that under Conte’s guidance ‘the old lady’ demonstrated rather reserved matter-of-fact football, which was why I was left with no profit for a long time. To be honest, I was pretty nervous as, for three months, the ‘zebras’ just wouldn’t play as I wanted them to. It got to the point where the bookmaker I always bet with cut my limit.

Luckily, there are other bookmakers in our city, so I quickly solved this issue. I couldn’t place my bet online, so I bet live with several bookmakers at once. Of course, the odds were not quite as I wanted them to be, but I simply had no choice. Finally, Juventus won 5-0 and I earned decent money.

I made a mistake of betting quite a big amount right from the start which nearly played a dirty trick on me. The money I had before the final winning bet would be enough for just one more bet. You can imagine how happy and relieved I was about Juventus’s big win.

In my opinion, both strategies are not very effective and, in the long run, can land you deep in the red.

According to the probability theory, you need to correctly predict a minimum 55% of bets with odds 2.0. What’s the point of the strategy then? You can just as well bet a certain amount with the same odds and wait for the winning outcome.

By the way, if you stick with the probability theory, to rightly predict 55% of bets with odds of 2.0 is impossible. Why? Read more on this in the article: The Value Betting Strategy. Why Do 98% of Players Lose Everything to Bookmakers.

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