Basic Rules of Probability – The Math Behind the Online Gambling Games

Basic Rules of Probability – The Math Behind the Online Gambling Games


Gambling has probably never been as popular and discussed as it is today. And this growth in the popularity of gambling entertainment is primarily driven by the development of the iGaming industry. Today, you don't have to look for the nearest gambling hall or betting agency to spin the reels of online slots or bet on a particular event in the world of sports or eSports. And while gambling games were designed for entertainment, it's hard to argue that many people are excited by the opportunity to win real money. And the advantage of gambling is that you don't need to have any extraordinary talents or skills to play and win, especially if you prefer online slots or live roulette. 

However, if you dig a little deeper, the world of gambling is full of various events and their probabilities of occurrence. While you can't exactly predict the outcome of any subsequent playing round, you still have the ability to assess the odds of it winning or losing. We're here to give you some useful insights into math and probability theory, so you can choose the right gambling games and spend your budget wisely. 

Calculating Probabilities of Events in Gambling Games

Any game of chance involves several different outcomes or events. For example, when you play online slots, at the end of a spin the reels may display a winning combination of several identical symbols. Alternatively, multiple Scatters may be drawn, triggering a bonus round. When playing roulette, the coveted event is when the ball hits the pocket of your choice. As far as the probability is concerned, this is something that refers to random events. It's a mathematical way of determining with what probability a particular event will (or will not) happen. Here are some important things you should know about probability:

  • Probability is expressed as a number between 0 and 1. It is also expressed as a percentage, where 100% corresponds to the probability of 1.
  • A probability of 0 means that a particular event will definitely not happen. For example, the probability that a game round in an online slot will end in a draw is zero, as there are only two possible events: winning or losing.
  • Probability of 1 means that the event will always happen. For example, the probability that there are 37 pockets on a European roulette wheel is 1, as this version of the classic casino game is played with a 37-pocket wheel.
  • The probabilities of events that could happen or have not been evaluated by numbers in the range 0 to 1 (or 0% to 100%). 

For a better understanding, let's look at a couple of examples. Toss a coin and see which side of the coin falls into your palm. The probability of heads or tails coming out is the same and is 0.5 or 50%. Now, let's look at a more complicated example. Suppose you have five pencils: white, black, red, blue and green. Put the pencils in a box and pull out just one without looking at them. There is a 0.2 or 20% chance that you will pull out a white pencil. However, how do we know it will be 0.2? Simple, you just need to know how many possible outcomes. Since you have 5 pencils, there are 5 possible events. The probability is calculated as P=1/5=0.2. In this formula, 1 corresponds to the number of equally possible events. Since you draw only one pencil, it can only be black, white, red, blue or green. 

Calculating the Probability of Multiple Equiprobable Events

So, the examples above give only a rudimentary idea of events and probabilities. They are enough to give you an understanding of how risky it is to bet on a single number at roulette. However, we are here to give you deeper knowledge that will help you gamble smarter.  

So, let's take the example of a dice game where you roll two six-sided dice. Each face of a die contains a number from 1 to 6. The total number of possible outcomes (events) is 36 because each number of one die can correspond to 6 different variations of the numbers rolled on the second die. Let's say we need to estimate the probability of hitting 7 points by rolling two dice. There are several pairs of numbers giving a total of 7 points: 1+6, 2+5, 3+4, 4+3, 5+2, and 6+1, that is 6 pairs of numbers (equal possible outcomes) in all. Knowing the number of possible outcomes (36) and the number of equiprobable events resulting in 7 points, you can easily calculate the probability: 6/36=0.166. You can similarly calculate the probability of hitting certain numbers on the roulette wheel or card combinations in poker - your calculations will be longer, but not more complicated.

Probability Addition and Multiplication Rules

When playing online roulette, you can bet on several numbers at once. For example, you can bet that the ball will hit pocket number 3 or pocket number 12. The probability of any particular number being hit is 1/37 (for European or French roulette). However, what is the probability that the number 3 or the number 12 will appear? According to the rules of probability theory, you have to add up the probabilities of events if you set the 'or' condition. So, the probability of number 2 is 1/37, and the probability of number 12 is also 1/37. To get the probability of number 2 or number 12, you add those probabilities together: 1/37 + 1/37 = 2/37. So, the more numbers involved in a bet, the more likely you are to win. 

Now, back to the dice to see how probability multiplication works. The multiplication rule is used when you put an 'and' condition. For example, you want to know the probability of both dice showing the same number of points on a roll. The probability of a particular number on each die is 1/6. To find out the probability of the same numbers, simply multiply the probabilities: 1/6 x 1/6 = 1/36. 

Understanding How the House Advantage Works

While slot manufacturers use the RTP, when playing online card and table games, you've probably come across the term 'house edge' or 'house advantage'. This is basically the percentage that the casino is guaranteed to make a profit. Let's say you are playing a game with a 3% house edge. With 100 bets of 1 coin each, you will lose an average of 3 coins (3% of 100 coins equals 3 coins). 

Keep in mind that house advantage in table games varies depending on what type of bet you are placing. For example, when playing American Roulette with a 38-pocket wheel, you are betting on a single number. Being the riskiest, this bet promises a rather large payout of 35 to 1. The probability of winning is 1/38. So, if you place 38 bets of 1 coin each on the same number, you'll lose 37 rounds and win one (assuming a mathematically perfect set of events). 

So, your play session involving 38 bets on the same event will result in you losing 37 coins and winning 35 coins (since the payout for correctly guessing a single number is 35 to 1). That is, your net loss is 2 coins. Dividing 2 by the 38 numbers on the roulette wheel, you get 0.0526 or 5.26%, which corresponds to the house advantage in American Roulette. 

Keep in mind that the house advantage is a long-term mathematical expectation. You can place 38 bets and win e.g. 3, or lose them all. However, after repeating the experience many times, you will find that on average you win only once in 38 bets placed. It follows that you need to catch short-term fortunes and walk away from the game in time, as the actual expected results will compensate for the casino's losses. 

Closing Thoughts

So, now you know what event probability is and how it works. Remarkably, in most cases, you won't have to do any complicated calculations, as they are already done for you. However, by understanding how probability works in casino games, you will make smarter bets. 

The truth is that the so-called law of large numbers works for casinos. For example, you can play 10 rounds in a particular slot and win them all. For you, the RTP will be 100% (which corresponds to 0% house advantage). However, popular iGaming platforms like VipArabClub have a large user base with hundreds and thousands of players spinning the slots reels. Dealing with thousands of spins per day, the casino sees an RTP that's close to the one the game maker sets. And even if you win a large sum, losing bets made by other players not only compensates for the casino's losses but also ensures a profit for it. And, importantly, that's why a really reliable online casino has no reason to cheat its players.

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