The Basic Rules of Probability

The Basic Rules of Probability


Here is an indisputable fact: every casino game is a game of probability. 

As a gambler, you should know that even though some of your actions as a player are under your control, the outcome is always dictated to some extent by chance. It is how the player weighs these odds, calculating odds and betting accordingly, that will determine whether he wins or loses in the long run.

Do you want to understand more about the basic rules of probability? 

If you are going to play in an online casino, then your answer should be yes. By knowing more about probability, you will better understand your chances. 

And why is that important?

Because probability is the engine that actually makes casinos work. In fact, without probability, the gaming industry would not be possible.

Calculating the odds isn't always easy, so we've done some of the hard work for you, by looking at two great casino games and some of the most common odds questions for each. Next time you sit down at a table, make sure you reflect about the probability behind the game you are playing. 

You might be surprised how quickly this will make you a stronger player.

So, what is probability?

Probability is simply the possibility that a certain event will occur. Toss a coin and the probability of getting heads is 50%. Getting the Queen of Hearts in a single deck of 52 cards has a probability of 1.9%. 

Probability is not exclusive of casino games, because probability is in fact a part of our everyday life. For example: 

Weather forecasts will often be presented in a similar way, such as “there is a 90% chance of rain tomorrow between 9AM and 11AM”. Does this mean it will rain? No, it means that there is a high likelihood of rain during those hours.

All games of chance are just a matter of probability. Even when playing skill games (see the difference between games of chance and games of skill here), the most skilled player still relies on probabilities in order to win. It is therefore essential to be familiar with these numbers and to know how to make the best out of them. 

This article is here to help you better understand how to calculate probability in two different casino games. 

Let’s start!


Blackjack – To HIT or to STAND?

Most blackjack hands involve some degree of risk. That’s part of the fun!

But the risk isn’t always the same and the true power lies behind knowing how much of a risk you are taking. An experienced blackjack player analyses what cards are already on the table, evaluates the probabilities around the next card to come, and acts accordingly.

Asking for cards on 12 has a small level of risk. Asking for cards at 16 has a much higher level of risk. So, what are the chances that the next card will be a burn card with each of the “dangerous” hands, 12 through 16?

Take a look at the numbers on the chart below, which represent on the left your current hand sum, and on the right the probability of busting, if you hit another card.












Keeping these numbers in mind should significantly help you in your decision making. But that’s not all… 

Remember that in order to have a smart Blackjack strategy, you obviously need to take into account not only your hand, but also what the dealer’s hand is showing.

For example, while the odds of getting a burn card at 12 are relatively low, if the dealer shows a 6, the odds are strongly in your favor if you stick with 12, as the dealer is more likely to get a burn card. 

If you're a new player, a standard Blackjack "cheat sheet" will help guide you on when to hit and to realize when it’s time to stop.

Is online roulette also one of your all time casino games favorites? Then make sure to keep reading and learn more about roulette probabilities.

Roulette – What is the probability of winning?

From an odds point of view, Roulette is very easy to understand, when compared to other online casino games. Because each round of the wheel is independent, your chances of winning do not change based on the results of the previous round, unlike other casino games such as Craps. 

Roulette is absolutely random and it is exactly because of this randomness that gamblers from all over the word describe this classic game as both easy to play and a lot of fun. 

Some of the most popular roulette bets are the outside bets, like: 

  • red or black
  • Even or odd
  • Low half (1 to 18)
  • High half (19 to 36)

These are simple even money bets. Bet on either side of these bets and you'll double your money if the ball lands on your selection.

The trick with Roulette is that the actual probability of winning any of these bets is slightly less than 50%. This is due to the addition of the green 0 (French and European Roulette) and sometimes a second 00 on the wheel (American Roulette). Both the 0 and 00 do not count as odd or even, red or black, high or low. That means that for all even money bets, if the ball lands on 0 or 00, the player loses – that is the house advantage!

Roulette strategies and probabilities 

As you probably know, the most famous roulette strategies are all progressive strategies, such as the Martingale, La Bouchére, D’Alembert and the Fibonacci. 

Want to know more about these four successful roulette strategies

Progressive strategies mean that, each time you lose, you increase the value of the next bet. This progressive approach is based on the premise that if something has a certain probability of happening, it will eventually happen, sooner or later, and that this value will compensate for previous losses.

In order to overcome short-term variance, it is essential to be consistent in following the same pattern, to let probabilities do their work in the long run.

This type of bet is placed on selections that have approximately a 50% chance of being a winner on each play, like the outside bets we mentioned above.

So, to better understand the probabilities associated with these progressive strategies, let’s see a mathematical comparison for the repetition of the selected phenomenon. For this case, let’s imagine a bet on red. So, what is the probability of red coming up 5 times in a row, for example? 












As it can be seen, as the number of rotations increases, the probability of red repeating itself rapidly decreases. 

However, keep in mind that these probabilities describe the phenomenon as a whole. The random number generator does not take into account previous results, so while a series of games where red hits 20 times in a row occurs once in every 1.813 million games, a round of 21 games will have the same advantage and probability. (i.e. 48.6%) than all other game rounds.

A very common Gambler’s Fallacy, is the belief that if one color is hit several times in a row there is a greater probability that the other color will be hit in the next round. In reality, this is not the case. 

The most famous case of this fallacy was observed in 1913 at Casino Monte Carlo, when black fell 26 times in a row at the roulette, and during almost this entire incredible stage, and even after it was over, people frantically bet on red.

Fun fact: the probability of a color being hit 26 times in a row is 0.000000730870% and occurs once in 67 million games. 

IN CONCLUSION, probabilities can be both fun and complicated, but rest assured that you do not need to be a mathematician genius in order to better understand odds. After this article, you should be well acquainted with the basic rules of probability and ready to apply them to your favorite online casino game.


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