What are the chances of winning at roulette?
The topic of the probability of Roulette winning (and online roulette) is undoubtedly one of the most discussed by players around the world. Let's see how to calculate the probability in this game and how things change when playing online.
Before going to deepen this topic we want to propose two "laws" which are always valid for the roulette: the law of large numbers and the law of the independence of the blows.
The first implies that with the increase in the number of games the combinations tend to approach their theoretical probability: when the number of shots becomes very high, if the bench has a theoretically favorable margin the player will be loss.
The second, on the other hand, implies that in the roulette with each play there are the same chances of exiting the combinations: it does not matter on which number or color the ball stopped in the previous shots.
It must be remembered that the law of independence is always valid, while that of large numbers begins to "be felt", as the name says, when the number of games becomes very large. In other words it is not meaning for a player who makes a reduced number of shots.
Simple probability to roulette
The simple probability to the roulette allow you to evaluate what are the chances of victory for each individual episode.
In general, the probability that an event will occur is given by the relationship between favorable cases and possible cases. The simplest example we can do with regard to roulette (French) is: what is the probability of a full number to come out?
The calculation is very simple: we have only one case in favor, while 37 possible cases are. The ratio is therefore 1/37, which corresponds to a percentage of approximately 2.7% (to find the percentage just multiply the result of the division by 100).
In the case of American roulette, which has 38 numbers, this value drops to 1/38, i.e. to about 2.63%.
Now that we have a clearer idea of how the calculations are made, let's see what are all the simple probability for possible bets, remembering that the possible cases in the French roulette are always 37 and in the American one always 38:
| Episode | Cases in favor | % French | % Americana |
|---|---|---|---|
| Full | 1 | 2,7% | 2,6% |
| Cavallo | 2 | 5,4% | 5,2% |
| Triplet | 3 | 8,1% | 7,9% |
| Carrè | 4 | 10,8% | 10,5% |
| Sestine | 6 | 16,2% | 15,8% |
| Colonna | 12 | 32,4% | 31,6% |
| Dozen | 12 | 32,4% | 31,6% |
| Even odd | 18 | 48,6% | 47,4% |
| Red-black | 18 | 48,6% | 47,4% |
From this table it is easy to understand how the presence of zero guarantee a margin in a theoretical margin of 2.6% - 2.7%. If in fact the zero was not present in the French variant, the numbers would be 36 in total and for example focusing on simple chances such as red or black the probability of winning would be 18/36, therefore 1/2, that is exactly 50%.
The complex chances of the roulette
When it comes to complex probability things are made, in fact, complicated! This type of probability comes into play when you want focus on multiple combinations for each play, perhaps even by choosing a number of pieces (i.e. of chips) different for each combinationnull In fact, the Roulette allows players to point an arbitrary number of combinations simultaneously, with the only constraint to respect the maximum betting limits imposed by the counter.
In these cases the calculations are not simple and the variables that come into play are many more than previously seen. Are the chosen combinations overlapping or complementary? Have different combinations have been chosen? Or with equal probability but different number of pieces?
To understand how vast this topic it is enough to think that in the decades hundreds of resources have been published in this regard, some of which are real pearls of mathematical literature. There are no shortcuts: those who want to play "seriously" at the roulette must first study. Much.
In any case, we want to propose a very simple example that shows up how to calculate the complex probability of one of the most classic game strategies: suppose to play 1 piece on the black (18 numbers) and 1 piece on the second column (12 numbers) which is rich in red numbers. In this way we try to have the greatest coverage of the possible table: with the 18 blacks and the 8 reds of the second column we cover 26 numbers, that is 70% of the possible cases.
We make an evaluation of all possible situations that can occur with a choice of this type: 4 numbers win 3 pieces, 8 numbers win 1 piece, 14 numbers that draw, 11 numbers that lose 2 pieces. We come to have a probability in favor of 20 pieces and one against 22 pieces.
The expected value (mathematical hope) and betting systems
The expected value, also called mathematical hope, is a rather complex concept but in the case of roulette we can say that it represents the weighted average of the possible results, that is, the average of "how much it is possible to win or lose".
When it aims at roulette, each bet has the same expected value. In the case of the French variant, it corresponds to -0.04. What does it mean? That theoretically on average for each euro bet you are lost 4 cents!
We do not enter the details of this reasoning, but we want to highlight a very important aspect: There are no roulette betting systems that can give the player an advantage on the counter! Those who say they have discovered one, he is lying.
The most complex and mathematically correct gaming systems rather allow to minimize errors and therefore make sure that the theoretical margin of the counter is as low as possible, nothing more. By aiming at roulette it is therefore possible to win fortunately, but it is not possible to do it with mathematical certainty in a repeated and prolonged way over time.
Probability for online roulette: what changes
If we talk about Roulette online, you need to keep in mind some online casinos that are different from a "real" tablenull The following has value only for virtual games and not for live tables, which are comparable to real tables.
The first consideration to do concerns the fact that in virtual games the possible results of the games are drawn by a random algorithm that takes the name of RNG (Random Number Generator). The average percentage of the winning results in these cases is expressed by means of the payout, i.e. the probability of winning the game. Since online casinos can apply different payout values for each virtual roulette table, it is good to keep in mind that the chances of theoretical victory in the long run can change.
Another very important aspect, mainly linked to the topic of bonuses, concerns high -coverage episodes. In fact, often the episodes that cover more than 67% of the table are not considered for the purpose of unlocking the bonuses offered. This rule varies for each mess, which is why it is in the player's interest inquire about these limitations before starting to bet.