The roulette betting calculators available online also compute high-risk betting units, suitable for the type of player, who prefers to bet big and collect greater profits, respectively. The roulette betting calculator has computed a high-risk betting unit of £8 for the bankroll of £200, used in this example. The roulette betting calculators available online also compute high-risk betting units, suitable for the type of player, who prefers to bet big and collect greater profits, respectively. The roulette betting calculator has computed a high-risk betting unit of £8 for the bankroll of £200, used in this example.

Read how you can win $500 with an 80% probability, playing with a roulette strategy!

Roulette is a classic casino game, where you play against the casino. The game consists of a wheel, which, in European Roulette is divided into 37 numbered spaces from 0 to 36. 18 of the fields are black, 18 of the fields are red, and a single field (0) is green.

In American roulette, there’s an extra field (00), but since the payout of winnings is typically the same, the probability of winning in the American game is reduced compared to European roulette, which makes dealing with it any further uninteresting. In addition to the wheel, there is a game board, where bets are made using chips.

All calculations on this page are based on the European version of roulette, which has 37 fields of play.

You can set up many different game combinations on the board. You may focus, for example, on “red”, “even”, “black”, “odd”, but also on specific numbers or a variety of numeric series, such as “1-18” and “19-36”. Obviously, your payout increases with a decreased likelihood of your bet coming out a winner.

Probability in Roulette Games

As mentioned earlier, we are basing this on European Roulette, which consists of 37 fields. We can easily calculate the probability of hitting for example “black” in a game in the following manner:

Thus, the probability of hitting black is 48.65%. The number 18 in this calculation reflects the number of black boxes, and the number 37 is an expression of the total number of fields.

The relationship between the number of winning fields against the total number of fields therefore means that we can calculate the probability of the various outcomes:

If we want to predict the likelihood of hitting black five times in a row, for example, we must bring the fraction to the fifth power:

2.72%. Note that this is about predicting one game sequence of 5 games before having played the first game. It does not mean that when we get to 4 out of 5 games, the probability of hitting “black” is 2.72%. Coincidence has no memory!

When the probability is calculated over several games, the starting point is always looking at the entire game series as one probability without breaking it up during the game.

This mathematical model could be used to calculate the probability of other outcomes of the game as well. If you want to calculate the probability of hitting the number “5” in a game, it can be calculated as follows:

2.70% is the probability of hitting a randomly selected number. What, then, is the probability of hitting “8” twice in a row?

It’s 0.073% – meaning very, very low.

The probability of hitting the same color several times in a row

Below is a schedule of probabilities for hitting the same color between 1 and 10 times in a row.

Number of spins Probability

1. 48.65%
2. 23.70%
3. 11.51%
4. 5.60%
5. 2.72%
6. 1.33%
7. 0.645%
8. 0.314%
9. 0.153%
10. 0.075 10%

European Roulette Probability Calculator Worksheet

Winnings and Bets on the Roulette Wheel

So how do you win at the roulette? As mentioned previously, different “bets” have different “payouts”.

When betting on black, the payout is 100% of the bet. If, for example, you bet $50 on black and win, you will have $100. Total in-hand money. Your initial wager is $50 + 100% of $50, so $100.

Thus, you could say that in this case the wager was multiplied by 2. Knowing this, we can figure out payout percentages for the game. Starting with betting on black, we can draw the following mathematical model:

This means that in theory the players will get – on average – 97.30% back of their starting amount, if they just keep betting on black infinitely. The reason for this is that the odds of the roulette game favor the casino because of the green zero field. If we calculate this into our model, we will also see that the sum equals 100%:

This casino advantage applies generally to all bets that can be created on the board. In terms of gaming psychology, this will often play out a little differently, because the tendency is to continue the game until all is lost, or until the player has increased his starting money amount significantly.

In other words, few people play roulette with $1000 and leave the table an hour later with $800 or $1200 in their pocket. A good roulette tip is therefore, that you should always set an amount you can afford to lose, and set amount of money that you are satisfied with winning.

The Martingale roulette system

Martingale is a roulette system where, in theory, you will always win. It requires only that you have infinite resources, and that there is no betting limit where you play. The system assumes that you bet on either red or black. Every time you lose, you double your wager from the previous game. If you win, you go back to your original wager.

A game series in Martingale is defined from your starting wager until once again you go back to your starting wager. For each game series, you will be able to add your starting wager to your income. Let’s look at an example, where the starting wager is $1:

Roulette wager Account
$1 on black Lands on red – $1
$2 on black Lands on red – $3
$4 on red Lands on black – $7
$8 on red Lands on black – $15
$16 on red Lands on red $1 (- $15 + $16)

This was the first game series. Now, we’ll start over for the next game series.

Roulette wager Account
$1 on red Lands on black $0 ($1 – $1)
$2 on black Lands on red $-2
$4 on red Lands on red $2 (- $2 + $4)

As you can see, each successful game series means that you can add your starting wager to your balance. Although six out of eight games were lost, the roulette wheel still left you with a profit.

As they relate to the Martingale roulette system, it is interesting to look at some practical limitations. First, we will look at the necessary amount of money you should have available in order to “endure” a given series of lost games:

1 x loss 2 x loss 3 x loss 4 x loss 5 x loss 6 x loss 7 x loss 8 x loss 9 x loss 10 x loss
$1 $2 $4 $8 $16 $32 $64 $128 $256 $512

With an initial wager of $1, for 10 lost games in a row, it takes a wager of $512 to win the game series. This means that you must have a total amount of $1023 available. The calculation looks like this:

When you are facing the first game in a game series, you can calculate the probability of the next 10 outcomes being red as follows:

This means that the probability of getting 10 reds in a row is only 0.075%. This calculation can also be reversed, so that we can calculate the probability of hitting black at least once in 10 games to be:

With $512 at your disposal and an initial wager of $1, we will therefore be able to win $1 in 99.9257% of game series. The disadvantage is that the probability of losing $1023 is 0.0175% for each game series.

Let us assume that we would like to earn $250. This will require 250 successful game series with an initial wager of $1. We can count on the probability that this will happen:

There is a 81.44% probability that you will earn $250 by playing the martingale roulette system. In other words, 4 out of 5 will make $250, but at the expense of the last person, who will lose $1023. There is no “hocus pocus” involved with the martingale roulette system – it is pure mathematics!

Depending on your risk tolerance, you can change the start deposits to $10 – where you can multiply the amounts by 10 – meaning you can earn $2500 with an 81.44% probability.

If you would like to try martingale in real life, you can do so on a smaller scale. You don’t have deposit $1023 into your gaming account first off. Let’s see how the math looks, if you don’t want to gamble with more than $255.

1 x loss 2 x loss 3 x loss 4 x loss 5 x loss 6 x loss 7 x loss 8 x loss
$1 $2 $4 $8 $16 $32 $64 $128

The total amount you need to deposit into your gaming account should be $255:

It will allow you to lose eight games in a row. Thus, the probability of winning a game series is:

Let’s assume that your aim is to earn $100. Once again, the likelihood of earning $100 can be calculated:

The probability of earning $100 playing roulette is 68.65%.

Try Martingale in real life and earn money now

If you have the courage to try out the system in real life, you can create a profile with 888casino. We recommend that you deposit at least $250 to your account. You can see how the Martingale System is used in action here.

Deposit bonus – good or bad?

Most casinos offer a first time deposit bonus. Typically, this means that they double your first deposit. If you deposit $500 to your gaming account, the casino will add another $500 for you to play with. Effectively, this means that you increase your chances and minimize your risk.

The disadvantage of these bonuses is that you have to “play them through” a certain number of times before they are payable. Normally, the games you play on the roulette are not included in this.

However, you can easily spend your money – your winnings, your initial deposit, and your welcome or deposit bonus – elsewhere in the casino, if you plan on playing anything besides roulette.

Never play for more than you can afford to lose.

This applies to all games. Never play for more than you can afford to lose. If you are addicted to gambling, you can get help here.

I love to play any kind of games on online casinos and I have tested the different strategies shown on the website.

Sign up with your email address to receive hot updates straight in your inbox.

Calculation of Casino House Edge

Roulette Probability

The house edge (HE) is defined as the casino profit expressed as a percentage of the player's original bet.

The player's disadvantage is a result of the casino not paying winning wagers according to the game's 'true odds,' which are the payouts expected considering the odds of a wager either winning or losing.

The house edge of casino games vary greatly with the game. House edges for slot machines and Keno may be up to 15% and 25% respectively.

In games which have a skill element, such as Blackjack or Spanish 21, the house edge is defined as the house advantage from optimal play (without the use of advanced techniques such as card counting), on the first hand of the shoe (container holding the cards).

The set of the optimal plays for all possible hands is known as 'basic strategy' and is highly dependent on the specific rules, and even the number of decks used. Good Blackjack and Spanish 21 games have house edges below 0.5%.

Example #1:

Calculate the house edge for American Roulette, which contains two zeros and 36 non-zero numbers (18 red and 18 black).

Solution #1:
If a player bets $1 on red, his/her chances of winning $1 is 18/38 since 18 red numbers exist out of 38. However, his/her chance of losing $1 (i.e., winning −$1) is 20/38. Therefore, the expected value may be calculted as follows:
Expected Value = (1)(18/38) + (−1)(20/38)
Expected Value = 18/38 − 20/38
Expected Value = − 2/38 = − 1/19

Expected Value = −5.26%
Therefore, the house edge is 5.26%.

Example #2:

Calculate the house edge for European Roulette, which contain a single zero and 36 non-zero numbers (18 red and 18 black).

If a player bets $1 on red, his/her chances of winning $1 is 18/37 since 18 red numbers exist out of 37. However, his/her chance of losing $1 (i.e., winning −$1) is 19/37. Therefore, the expected value may be calculted as follows:
Expected Value = (1)(18/37) + (−1)(19/37)
Expected Value = 18/37 − 19/37
Expected Value = −1/37

Expected Value = −2.7%
Therefore, the house edge is 2.7%.

Example #3:

Calculate the house edge for a game played by wagering on a number from the roll of a single die with a payout of four times the amount wagered for a winning number.

Since the probability of a winning number for a single roll of a die is 1/6, it follows the game has 5 to 1 odds. However, with a payout of only four times the amount wagered (i.e., 4 to 1) for a winning number, the house edge may be calculated as follows:
House Edge = (true odds − payout odds) / (true odds + 1)
House Edge = (5 − 4)/(5 + 1)

House Edge = 1/6
House Edge ≈ 16.67%