# Understanding the D’Alembert system and its use in roulette

## For a bet considered to have a 50/50 chance of winning, it must have only two outcomes which are equally likely of occurring. Calling heads or tails on a fair coin would fit this criteria.

Head over to the roulette wheels within a casino and three bets are typically plugged as being 50/50 outcomes – red or black, odd or even and the two betting sections incorporating the numbers 1-18 and 19-36.

However, all of these bets would be losers should the spinning roulette ball come to rest in any green section of the wheel. Play European roulette and there is a single green 0, while American roulette also has a green 00.

These ensure that the so-called 50/50 bets do not have a 50% likelihood of occurring. Bet red on a European wheel and the probability of a win is 48.6%, while this drops to 47.4% on an American wheel.

## Martingale system

Within the gambling landscape, there are a considerable number of betting systems that brandish the promise of a guaranteed profit if followed.

One of the more recognised is the Martingale strategy, which at its core is incredibly simple to follow and focuses on these alleged 50/50 bets. A player must decide on their bet of choice and their initial stake, such as opting for black and £10.

If the bet wins, they place it identically again. If it loses, they double their stake. The stake continues to double after every loss, until eventually a win occurs. At this point, the stake returns to its initial level.

The feeling is that should a player lose £10, then £20, then £40 and £80, one winning £160 bet would not only cancel out the previous run of losses, but also provide a small profit on top.

The main drawbacks of this system are that a lengthy losing sequence could very quickly wipe a person’s bankroll and that it wouldn’t take long for the size of the stake to surpass any roulette table maximums.

## D’Alembert system

There are some clear similarities between the D’Alembert and Martingale systems. Top of these characteristics is that a player scales their bet based on the performance of the previous one.

Where the two systems differ is in the betting progression. A player is not expected to double their stake after a losing bet, just up it by a single unit. So, a losing £10 bet, becomes £20 and then £30, rather than £10 becoming £20 and then £40.

This scaling also takes place once a winning bet has been registered. Rather than immediately returning to the initial stake, a player reduces their bet size in the same way it was increased after a loss.

Using the example above, the next bet after a win at £30 using the Martingale strategy would be £10. Adopting the D’Alembert strategy would mean staking £20 for the next spin.

## Positives

The D’Alembert system is one of the more straightforward to implement, following simple calculations to either increase or decrease bet size.

Particularly compared to the Martingale, it also allows a player to stay in better control of their bankroll.

If playing on a European wheel with just the single zero, the probability of five reds, blacks, odds or evens being spun in succession is 2.72%. It is not unreasonable for a player to have to negotiate such a losing streak in every roulette session.

Using Martingale and starting by betting £10, they would be down £310 at this stage and faced with staking a further £320 on the next spin. With D’Alembert, their losses would be £150 and their next bet would be £60.

It does a far better job at keeping losses to a minimum and making a bankroll survive for longer, especially in those more troublesome moments when losses can start to mount up.

## Negatives

On the flip side of this, one single win using D’Alembert fails to wipe away a run of losses like it does in Martingale.

Using the same losing streak as above, a winning £320 Martingale bet, would not only repay the £310 previously lost, but also provide £10 profit for the session.

A win on the £60 D’Alembert bet would only return a profit of the same amount, even though £150 had been lost in the previous spins. This means the player is still down £90.

Therefore, although a player should have the balance to withstand a run of losses, they are likely to struggle to recoup it all.

## Reverse Reverse

Players also have the option of adopting a reverse D’Alembert strategy, where they increase their wager after winning a hand and decrease it after a loss.

This could prove highly favourable during a winning sequence, but leave players at a loss during an even betting sequence.

Imagine a sequence of win, loss, win, loss, win and loss. With the standard D’Alembert strategy starting at £10, a player would win £10, lose £10, win £20, lose £10, win £20 and lose £10. Thus, making a profit of £20.

With the reverse they would win £10, lose £20, win £10, lose £20, win £10 and lose £20. So, despite three winning spins and three losing ones, a player would be down £30.