Tag Archives: Roulette

How does the D’Alembert strategy work?

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How does the D’Alembert strategy work?

The D’Alembert strategy is designed for betting on ‘even’ bets on games such as roulette, blackjack and baccarat.

The strategy relies on the logic that the number of wins and losses eventually even out. If you, for example, look at the game of roulette, at the end of a long session, there must be roughly the same amount of spins on Black as Red numbers.

To start using the D’Alembert strategy, the first step is to determine the size of your stake unit (for example $1), a bet size that can be any amount you prefer.

You start betting with one ‘unit’, and every time you lose a bet, you increase your next bet with one ‘unit’. If you win, you decrease your next bet with one ‘unit’.

The advantage of this approach is that it is very straightforward to implement. It works great if you aim for an equal amount of losses and wins as long as you do not have more than 5 losses in a row.

An example of a winning D’Alembert strategy

Example 1: Here you see when the D’Alembert strategy works well. In this example we have applied the D’Alembert strategy as a roulette strategy.

You always bet on Black and start with one unit (which could be $1).

winning d alembert strategy

Even when the number of wins and losses are equal, you end with a profit. The D’Alembert strategy works well if the number of wins and losses are pretty balanced.

An example where the D’Alembert strategy fails

Example 2: Here you see when the D’Alembert strategy gives negative results.

You always play black. You start with one unit (which could be $1).

failing d alembert roulette strategy

If you have a few more losses than wins, and it stays that way, your stakes end up to be relatively large at the end of the session. In particular, if you lose the last 2 or 3 spins (with the higher stakes), you end up negative.

The weakness of the D’Alembert strategy is that the stakes become substantial at some stage (after the number of losses are greater than the number of wins).

One way to mitigate the downside risk is to apply limits. For example, you determine beforehand that your stake cannot exceed 5 units.

This way, you get to control the level of the stakes.

How does the Fibonacci strategy work?

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The Fibonacci strategy has its origin from the famous Fibonacci sequence. You probably have seen it at school.

In this sequence, every next number is the sum of the two previous numbers in the series. It applies for ‘even’ bets, so betting on Red-Black, Odd-Even or 1-18/19-36 at roulette or betting Punto or Banco at baccarat.

In the Fibonacci strategy, the sequence is as follows:

1-1-2-3-5-8-13-21-34-55-89-144-233-377-610-987-….

 The numbers of the sequence represent the amount you should bet. If you lose a bet, you follow the series and increase your next stake according to the sequence, until you manage to win a bet.

Once, you have won your bet, you start at the beginning again, with 1 unit (for example $1).

The table below summarises how the Fibonacci strategy works.

FIBONACCI BETTING SEQUENCE

The strategy looks very promising, at first glance.

Unfortunately, it does not give you any guarantees. It is just a sequence of numbers telling you how much to bet. It does not change the odds of you winning a game.

If you lose 8 or more times in a row, your losses become more significant. You need to make up winning many times on your first spin, to get your profits back to the desired level.

An example of a winning Fibonacci strategy

Example 1: Here you see when the Fibonacci strategy is beneficial.

You always bet on Black. You start with one unit (which could be $1).

  • You win the 1st and the 2nd
  • The 3rd round, you lose. You follow the Fibonacci sequence. You lose again and continue with the sequence and stake 1 units in round 4.
  • You lost round 4, and in round 5, you continue the sequence and stake 2 units.
  • You also lost round 5, and in round 6, you stake 3 units.
  • You also lost round 6, and in round 7, you stake 5 units.
  • You win round 7, and in round 8 you start the sequence again with one unit.
  • You win round 8, and in round 9 you start again with 1 unit. You win round 9.
  • In round 10 you start again with 1 unit. You lose round 10.

FIBONACCI BETTING STRATEGY WORKS

Here, you end up with a profit of 1 unit (a $1 profit) after 10 spins, even though the number of your wins (5 times Black) exactly match your number of losses (also 5 times Red or Zero).

The Fibonacci strategy is less progressive and less risky than the Martingale Strategy, as the increments of the sequence are less aggressive.

In Martingale the steps are doubled each time (1->2->4->8->16->32 etc.). The sequence is steep (large increments). The steps in the Fibonacci sequence are not as steep (1->1->2->3->5->8->13 etc).

An example where the Fibonacci strategy fails

Example 2: Here you see when the Fibonacci strategy does not work.

You always bet on Black and start with one unit (which could be $1).

  • You win the 1st and the 2nd
  • The 3rd round, you lose. You follow the Fibonacci sequence. You lose again and continue with the sequence and stake 1 units in round 4.
  • You lost round 4, and in round 5, you continue the sequence and stake 2 units.
  • You also lost round 5, and in round 6, you stake 3 units.
  • You also lost round 6, and in round 7, you stake 5 units.
  • You also lost round 7, and in round 8, you stake 8 units.
  • You also lost round 8, and in round 9, you stake 13 units.
  • You also lost round 9, and in round 10, you stake 21 units.
  • You lose round 10.

WHERE FIBONACCI BETTING STRATEGY FAILS

The bad news: With the Fibonacci strategy, you end up with significant losses if you have a long losing streak.

In this example, the losses amount to 52 units ($52) after 8 consecutive losses.

The Fibonacci Roulette strategy is less aggressive than the Martingale strategy.

The good news is that the Fibonacci strategy is less risky roulette strategy than the Martingale strategy. With the Martingale strategy, you would have ended up with a loss of 253 units (compared to the 52 units with the Fibonacci Strategy).

How does the Reverse Martingale (Paroli) strategy work?

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reverse martingale paroli strategy

The Reverse Martingale strategy is a variation of the famous Martingale strategy. It can be applied to all even bet casino games.

This betting strategy is often used as a roulette strategy, but can also be used on baccarat, blackjack and other table games.

The big advantage of this strategy is that you only decide to take more risk if you are in a winning streak. The danger is that you do not get a long winning streak (say win 4 or 5 or 6 times in a row).

The consequence is that you end up negative.

How does the Reverse Martingale (Paroli) beting strategy work?

With the Reverse Martingale strategy (also called the anti Martingale strategy or the Paroli strategy), you start with a stake of one unit (say $1). If you lose, you play again with a stake of $1.

If you win, you can “afford” more, take more risk and double your next stake. If you win again, you double the next stake again.

Set yourself a limit, where you decide to stop doubling. You “bank” your winnings and start the sequence again. You choose for example to stop doubling after you have won 4 times in a row.

Compare the Reverse Martingale Strategy with the popular TV quiz, the Weakest Link. There, winnings are doubled. When the next answer is wrong, everything is lost. The sequence starts again.

A participant can also “bank” the amount/profits built up. After the winnings are banked, the sequence starts again from the beginning.

CasinoHipster.com tip: When using the Reverse Martingale Strategy, you only take extra risks when you are winning

We have made calculations of 4 variants of the Reverse Martingale strategy:

  • The 3-step Reverse Martingale strategy (where winnings are banked after 3 consecutive wins)
  • The 4-step Reverse Martingale strategy (where winnings are banked after 4 consecutive wins)
  • The 5-step Reverse Martingale strategy (where winnings are banked after 5 consecutive wins)
  • The 6-step Reverse Martingale strategy (where winnings are banked after 6 consecutive wins)

An example of a winning Reverse Martingale Strategy

Example 1: Here you see when the Reverse Martingale strategy works in your advantage.

You always play Black. You start with one unit (could be $1)

  • You lose the 1st and the 2nd
  • You have a winning streak: you win rounds 3 to 6. As you have doubled your stake, you get cumulative profits of 13 after round 6.
  • You bank after 4 wins in a row (after round 6).
  • You lose rounds 7 to 10.

reverse martingale strategy

Here, you have won $9. Even, though you only got 4 Blacks and 6 times Red/Zero. The luck was that you won 4 times in a row, which uplifts your profits.

Bear in mind that a winning streak of 4 times, does not happen too often. The chance of winning 4 times in a row (in this example 4 Blacks in a row) is: (18/37)^4= 18/37*18/37*18/37*18/37= 5,6%.

Below, a table with the probability of consecutive wins:

reverse martingale strategy wins

An example where the Reverse Martingale Strategy fails

Example 2: Here you see a case where the Reverse Martingale strategy does not yield profits.

You always bet on Black. You start with one unit (could be $1)

  • You lose the 1st and the 2nd
  • You have a winning streak: you win rounds 3 to 5.
  • You double your stake for round 6, which you lose.
  • You lose round 7. You win round 8.
  • You double your stake for round 9, which you lose.
  • You win round 10.

reverse martingale strategy fails

Here you end up with a negative balance of 3 units (-$3), even though you have won 5 times and lost 5 times. As the winning streak was not long enough, you end up losing.

Would you have banked after 3 wins (instead of 4 wins), then you would have had a cumulative profit of 4. Banking after 3, 4, 5, 6 (or even more) consecutive wins matters.

If you are more of a risk taker, you could decide to bank after 4, 5 or even 6 consecutive wins.

Otherwise, you may choose to bank after 2 or 3 straight wins.

How does the Martingale strategy work?

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martingale roulette strategy

The Martingale strategy is the most famous betting strategy, by far.

It is a betting strategy that is applied to games that offer even money bets, such as roulette, blackjack and baccarat.

Several players regard the Martingale betting strategy as a strategy where you always win. Unfortunately, it is not that simple.

With the Martingale strategy, you start with a stake of one unit (for example $1) on, for example, Black.

  • If you win, that is great. You have earned $1.
  • If you lose, you double your stake to 2 units (say $2). If you win, you have staked in total $3 and have earned $4. Your result is a $1 profit.
  • If you lose again, you double your stake again to 4 units. You stake $4 at once. If you win, you have staked in total $7 and have earned $8. Your result is a $1 profit.
  •  If you lose again, you double your stake again to 8 units. You stake $ 8 at once. If you win, you have staked in total $15 and have earned $16. Your result is a $1 profit.
  • If you lose again, you double your stake once again to 32 units. You stake $16 at once. If you win, you have staked in total $31 and have earned $32. Your result is a $1 profit.
  • You continue doubling your stake after each loss, till you have won.

After you have won the $1, you start the sequence again.

The table below summarises how the Martingale strategy works.

martingale roulette strategy

The advantage to the Martingale is that you always make a $1 profit after a win. Always!

The strategy falters when you lose 7 or 8 or even more times in a row. The amount you stake could be as high as $64, $128, $256 or even more.

Doubling your stake again, might not be possible. Either you do not have that a large amount of money available, or you are facing the maximum limits that casinos and online casinos may impose.

Moreover, there is a very reasonable chance that it happens.

If you choose to win more than $1, you need to play the Martingale sequence many times. The possibility of having a losing streak of 7, 8 or more times in a row, automatically increases.

An example of a winning Martingale strategy

Example 1: Here you see when the Martingale strategy works in your advantage.

You always bet on Black. You start with one unit (could be $1)

  • You win the 1st and the 2nd
  • The 3rd round, you lose. You double your stake on the 4th You lose again, and you double again in round 5. You win round 5.
  • You start the sequence again with one unit. You win round 6.
  • You start the sequence again with one unit. You lose round 7 and double your stake in round 8, which you win.
  • You lose round 9. You double your stake in round 10 which you lose.

winning martingale strategy roulette

In this example of using the Martingale betting strategy, you end up with a profit of 2 units (a $2 profit) after 10 spins, even though the number of your wins (5 times) exactly match your number of losses (also 5 times).

An example where the Martingale strategy fails

Example 2: Here you see a scenario where the Martingale strategy fails.

You always bet on Black, and you start with one unit (could be $1),

  • You win the 1st and the 2nd
  • The 3rd round, you lose. You double your stake on the 4th You lose again, and you double again in round 5. Each time you double, and at the 10th round, you have lost 8 times in a row (the ball has landed in a Red pocket 8 consecutive times).

failed martingale strategy

This example shows the downside risk of the Martingale strategy. You end up with a hefty loss of 253 units ($253).

The probability that the ball lands 8 consecutive times in the “wrong” colour (or in the zero) is 0,48%.

On average, it happens every 207 times, when you apply the Martingale strategy.

What is the probability of consecutive losses?

Even though you might think otherwise, those “impossible” series of outcomes are not all that rare.

 You might dodge a bullet for a long time with the Martingale system, but it is a given statistical fact you will run into a rare series of losing outcomes.

Here is a table with the probability of consecutive losses, based on a roulette game with a single zero:

Probability of rare roulette outcomes

As you can see, it is not uncommon to lose 7 times in a row. In fact, in nearly 1% (0.94%, to be exact) of all sequences, you may lose 7 times in a row. Even 8 or 9 losses in a row are not uncommon.

The chance of hitting red after black has hit 8 times in a row does not increase, it is still 19/37.

Should these events occur, the Martingale system forces you to stake huge amounts of money to get a $1 dollar profit.