How to Calculate Probabilities and Expected Values in Online Roulette


How to Win at Online Roulette: Intro to Probabilities and Expected Values

In Kenya roulette casinos are very popular. This is because, without any doubt, online roulette is one of the most popular casino games amongst gamblers. Although this classic game may seem quite simple to play, guessing in which pocket the ball will land is far from being easy.

If you would like to get to know more about how to win at the best roulette casino sites Kenya, keep reading. Today, we will talk about the basics of probabilities and expected values that can help you become better at playing online roulette games.

How Roulette Works in General

Before we jump right into the probabilities and expected values, let’s see first how roulette works. Although most online casinos offer a wide range of online roulette games, in Kenya roulette sites offer mostly the most popular roulette versions which are the European, American, and French roulette. The main difference between these three versions is the number of pockets you can find on the wheel. The wheel has 37 pockets in the European
and French versions, and 38 in the American version. These pockets contain all the
numbers from 0 to 36. However, the zero appears twice in the American version (there are 0 and 00). 18 of the fields are black and 18 are red. Usually the zero – or the zeros in the American version – is green.

To play the game, the players first have to make bets. They can bet on red or black numbers, even or odd numbers, high (19-36) or low (1-18) numbers, or any combination of the numbers. Then a tiny ball is spun on the wheel until it falls into one of the colored and numbered pockets. The winnings are paid to that player who has placed a successful bet.

The chance of the ball landing in a pocket is the same at each pocket.

If you would like to try yourself out in online roulette, all you have to do is to find a roulette site that is available from Kenya. Visit to find out more info on the best roulette sites in Kenya and how to choose the right one to play at.

What Does Probability Mean?

Now that you understand the basics of roulette, we can start to talk about probabilities. But what does probability mean? In general, probability is the likelihood that a certain outcome will occur. In online roulette games, it refers to the likelihood that the ball will land in a given number.

Usually, the probability is expressed in the form of a fraction, for example, “1/37” or “1 out of 37” which means the exact same thing. While the first number is the expected frequency of an outcome to occur, the second number stands for the total number of possible outcomes.

Maybe it sounds unbelievable at this point, but probabilities can help you a lot when placing a bet at the best roulette sites Kenya. Don’t worry, soon you will understand why I’m telling you this.

How to Calculate Probability in Online Roulette?

Once you understand how to calculate probability, it can help you in many online casino games, not only in online roulette. To keep things as simple as possible, in the following we will talk about only the European version of online roulette. However, you can apply this principle in all the variants of roulette games at the best online roulette casinos Kenya.

As mentioned above, a European roulette wheel has 36 numbered pockets and a single-zero pocket. This means that when the wheel is spun, there are altogether 37 possible outcomes. Let’s say that you would like to place a straight up bet on a number. For example, you choose the number 12. If you would like to know the probability of the ball landing in number 12, you can very simply calculate it. Since you bet on only one number (12), the expected frequency of winning is 1. Thus, the probability of the ball landing in number 12 is 1 to 37.

You can easily convert this to a percentage by dividing the two numbers. Just divide the total number of ways you may win by the number of the possible outcomes, then multiply the number you got as a result by 100. This is how you get the probability in percentage.

Following our example of betting on number 12 in a straight up bet:

1 / 37 = 0.0270
0.0270 x 100 = 2.7

This means that the probability of you winning at an online roulette game with a straight up bet on the number 12 is 2.7%.

It is not so complicated, isn’t it?

You can use the same method to make calculations about the probability of you winning at every online roulette bet.

But let’s see another example.

This time instead of a straight up bet we will assume that you would like to place an even money bet and you choose black. Since there are 37 pockets on the wheel of which 18 are black, 18 are red, and there is 1 single-zero pocket, the number of ways to win is 18 and there are a total of 37 possible outcomes. The probability of winning with an even-money bet on black is 18/37.

Or in percentage:
18 / 37 = 0.4865
0.4865 x 100 = 48.65%

When it comes to even-money bets, very often new gamblers think that they have a 50% chance to win or lose the game. However, due to the single-zero pocket, they have less of a chance. This gives some advantage to the house, the so-called house edge. The house edge is 2.7% in European roulette.

What Does Expected Value Mean?

Besides probability, there is another expression you should get familiar with if you would like to learn more about winning at online roulette: expected value.

Expected value can be defined as the weighted average of the possible outcomes in a game. In roulette, the probabilities will represent the weights.

How to Calculate Expected Value in Online Roulette

The calculation for expected value is quite simple in online roulette games. You will need only 4 numbers to make the calculation:

  1. the probability of winning the given bet,
  2. the amount you can win in the case your bet will win,
  3. the probability of losing the given bet, and
  4. the amount you can lose in the case your bet will lose.

Once again, to keep things simple we will make the calculation for European roulette but of course, the method can be applied for the American version as well.

Let’s say that you would like to place 1 dollar on a single number bet. In this case, the above-mentioned numbers would look like this:

  1. the probability of winning the given bet: 1/37
  2. the amount you can win in the case your bet will win: 35 (the payout is 35:1)
  3. the probability of losing the given bet: 36/37
  4. the amount you can lose in the case your bet will lose: 1 (you would lose the one dollar you placed on the bet)

Then, you have everything to solve the following equation:

Expected value = the probability of winning x the amount you can win – the probability of losing x the amount you can lose

Expected value = (1/37) x 35 – (36/37) x 1

Expected value = −0.0270

If we convert this number to a percentage, it will be -2.7%.

Is this number a coincidence? No. Remember that the casino’s advantage (house edge) is 2.7% in European roulette, and a negative expected value is actually the player’s disadvantage against the house.

Interestingly, the expected value is the same in all bets.

To demonstrate it, here is another example:

This time let’s place 1 dollar on a corner bet or so-called four-number bet. A corner bet has a payout of 8-1, so the calculation looks like this:

Expected value = (4/37) x 8 – (33/37) x 1

Expected value = -0.0270

As you can see, the result is again -0.0270 which is -2.7%.

The Bottom Line

There you have it. These were the basics of probabilities and expected values in online roulette. The next time you play a roulette game at one of the best online roulette sites Kenya, don’t hesitate to make a quick calculation before placing your bet. Chances are that it can help you win.


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