Roulette and probability theory have many things in common. First of all, they have the same father – the famous mathematician, physicist and philosopher Blaise Pascal. The one and only described probability theory and invent roulette in the 17th century.
Although the theory of probability as such is extremely interesting, today we will focus on its real use. We will show what all gamblers are interested in above all. Chances of winning.
In the beginning, we would like to state, that all probability calculations are derived from a European roulette which has 18 black fields, 18 reds, and 1 green field with zero. We chose this roulette because of lowered house edge and it is so much better to play on it. Though not often found in land-based casinos, every online casino that offers table and card games has a European roulette in the portfolio of games.
The probability of individual bets
Every basic roulette bet covers a certain number of playing fields. Logically, then, the more fields the single bet covers, the higher are the chances of winning. The probability is simply calculated by the formula:
Number of covered fields / 37 * 100
Statistically, the most certain bets are even bets (colour, even x, odd, high x low) which cover less than half of the roulette. Chances of winning with them are 48.65% (18/37 * 100). The least sure is betting on individual numbers. These bets have only 2.7% (1/37 * 100) chance to win.
Calculating the probability of winning for consecutive bets
Now when we already have calculated the odds for individual bets, we can further calculate the chances of winning in the series of games. For this case, the original formula has to be modified:
Q – Number of covered fields
N – Number of played rounds
For our simulation of all individual bets, we have chosen a limit of 50 game rounds, which corresponds, on average, to one hour of roulette playing at a table of 4 or 5 players.
The probability of at least one win in 50 consecutive games
In the chart above you can see how the probability of winning for individual bets increases. At this point, it is very important to say that the chances never reach 100% probability.
In addition, if you are actually sitting at a roulette table, the chances of winning a single bet always depend on the probability calculation of individual bets. This means that the chance of winning a red bet will always be 48.65%, regardless of the previous one. Do not forget that this calculation tracks the game series as a whole.
You can see it clearly on the famous Monte Carlo example in 19137 when black hit 26 times in a row. The probability of this phenomenon is 0.000000007%. If we convert this number into a meaningful figure, it turns out that you would have to experience about 143 million series of 26 games to see it again.