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Casino and Science: Maths and Statistics at the gaming tables

Maths and Statistics at the gaming tables

A casino is primarily a fun leisure activity, but not a source of income. Nevertheless, many players are determined to win. They are interested in what are the chances of winning a prize or activating a prize game. Beginners and experienced visitors 2 pound deposit casino and other online establishments study the algorithms of entertainment, trying to understand under what conditions the prize falls out. If the first “one-armed bandits” had a simple structure, then, with the development of special programmes to predict the result became almost impossible. Nevertheless, it is possible to estimate the frequency and probability of winning, using knowledge of the basics of probability theory, mathematical statistics.

Mathematics and casino games

Calculations and numbers allow you to determine the probability of winning. This makes the choice of casino games and bet sizes more reasonable, promotes rational use of money.

Probability is one of the basic mathematical concepts in casinos. It shows what percentage of a certain outcome of the game. Suppose there are 20 different outcomes with equal odds. A player betting on one of the events can expect to win with a chance of (1/20) x 100% = 5%. Using the knowledge of probabilities, the visitor chooses a game with a greater chance of success.

Statistics is another definition that is important for casino players. It shows the frequency of occurrence of an event. You can use statistics to determine which events are the most frequent and how this will affect the results of the game.

The pace of development of the slot industry is very dynamic. Slot machines on modern online casino sites are equipped with a random number generator. Therefore, it is impossible to predict a particular result. Nevertheless, when choosing a machine it is desirable to pay attention not only to the theme and design, but also to the mathematical characteristics, the payout table. Bright design and original “chips” should not distract from the main thing – the chances of winning the prize.

Slot machines and maths

The mathematical characteristics of an online casino machine are two:

  • payout percentage;
  • variance.

Let’s take a closer look at both parameters.

Payback of slot machines

The percentage of return (payout) is the expectation of winning, a part of the total amount of bets that the user returns to himself in the form of winnings during a long gaming session. This indicator is necessarily given in the characteristics of the video slot. The bigger it is, the obviously better it is. Most of the machines in a modern online casino has an RTP of 95-96%.

The percentage of return in some machines reaches 97-98%. Models with returns below 90% are much rarer. The remaining percentage (on average, it is 4-5%) is the casino’s profit. “One hundred per cent” machines do not exist. Otherwise, the very existence of online casinos is meaningless. The RTP indicator is laid down by the developer company at the stage of creating a video slot and remains constant. All this applies only to certified software, which are used by casinos from the review of


Sometimes this indicator is also called volatility. If the RTP parameter is nothing but the mathematical expectation, then volatility determines the “spread”, the degree of deviation from this value. Volatility determines the degree of risk when playing a certain machine. The lower the variance, the more often small wins fall out. High-volatility machines are characterised by rare, but relatively large prizes.

Video slots with different volatility may have the same payout percentage, but the nature of the game on them will be completely different. The machine with a small dispersion dispenses frequent wins in small parts, and high volatility gives a large prize after a long losing streak. Naturally, in the second case the chances of risking to lose the bankroll is higher, but there is a chance to become the owner of a large prize for one spin.

Slots with low and medium volatility suitable for beginners and players who are used to playing cautiously, with small stakes. Machines with high volatility – the choice of players with large amounts in the account. This helps to wait out a streak of bad luck, to then compensate for the costs of a large won amount. It is important to remember that all these considerations are probabilistic. Each player has a chance of both success and loss.

Estimating the variance value

Depending on the dispersion value, all slot machines offered by casinos from the Casino City rating can be categorised:

  • low-;
  • medium;
  • high volatility.

The most popular are the machines with an average dispersion index. You can estimate this parameter using such information:

  • payout tables;
  • playing in free mode;
  • the presence of an accumulative jackpot.

Studying the payout tables is a simple and effective option for assessing volatility. If the highest payout ratio does not exceed the threshold of increasing the bet by 5 thousand times – we are talking about low dispersion. If the ratio of these parameters exceeds 10 thousand – it means that the machine has high volatility; 5-10 thousand – average. A small difference between the coefficients when falling out combos of 3, 4 and 5 identical combos speaks of low dispersion, significant – about high. Wild, Scatter and other special symbols are more common in slot machines with medium and low volatility.

You should not consider playing in the demo only as entertainment for beginner visitors to online casinos. Most of the gaming platforms give players the opportunity to test the machines for free. For example, if during the hour slot regularly gives out wins with small or medium coefficients, – we have a low- or medium-volatility machine, depending on the coefficient. If during the entire period of testing video slot gave one or two high-paying combos, correctly “eating” the bankroll – it means that the dispersion is high.

If the machine is equipped with a cumulative jackpot, then the dispersion rate is sure to be high. Such slots – the choice of those who are accustomed to risk, while having large sums on a personal account.

Choosing slot machines, you need to understand the ultimate goal, objectively consider the financial capabilities and time that can be spent on the game.

Risk game

Risk round is available in the vast majority of video slots. The principle is very simple. After each successful spin, the machine offers the user to take the winnings or try to increase it by 2 or 4 times. In the first case you need to guess the colour, in the second – the suit of the card offered by the dealer. The probability of success in the first case is 50, in the second – 25%. Risk tournament can be repeated a certain number of times, provided by gameplay, or until you lose. In this case, the participant is left with nothing: the winnings for the current spin goes in favour of the casino. Advantage casino in the risk game is absent.

 According to experienced players, the activation of the game for a double or quadruple increase makes sense in such cases:

  • If the last money left in the game, and the amount won is not able to rectify the situation. You can try to increase the prize or lose;
  • the prize amount for the current spin is small. Lose a small amount of money is not so pathetic. In addition, there is a chance to double them;
  • the possibility of a significant increase in the amount won. In some slot machines risk round involves an increase in the prize of 10 or more times.

Sometimes the risk game involves finding a card older than the dealer. The probability of success varies, as the GSC chooses 4 hidden cards randomly.

Roulette statistics

Roulette is traditionally considered a game of luck. Interesting information about this entertainment can be found on the World Casino Directory website. It is impossible to predict where exactly the ball will stop, real or virtual. However, this game is subject to the laws of mathematics. Knowing the basic specifics of the game, you can calculate the probability of different combinations. The table of probabilities for the European version of online roulette looks like this.

BetProbability, per cent.Winning
6 figures16,25:1
4 digits10,88:1
3 digits8,111:1
2 digits5,417:1
1 digit2,735:1
1-18, 18-3648,61:1

Roulette is divided into 36 sectors, and the payout value for a guessed number is 1/35. This means that the online casino advantage is built into the game in advance. For example, if a player bets on red and black, odd and even at the same time, he still runs the risk of losing if the zero falls out. In American roulette with two zeros, the casino’s advantage is even greater. But the prizes for players who bet on a certain number will also be higher.

Is it necessary to keep roulette statistics?

Experienced players believe that to keep statistics of the game in a certain type of roulette one developer should be during not only one game, but constantly. The longer the statistics are kept, the more information for analysis will be obtained. Record in the table such data:

  • dropped numbers;
  • duration of non-disappearance of numbers;
  • the order of falling out even/odd numbers, red/black;
  • the order of falling out of columns, dozens, rows.

When using any strategy should record the failure or success of each of the events.To save time and do not make mistakes, it is recommended to use special software or browser extension.

According to the reviews of roulette lovers, the best assistants are:

  • RouletteDominator – a new software that analyses the numbers that fell out last. Based on the analysis, the software makes a prediction for further play. At first, three times enter data on two spins. The software determines the approximate pattern of falling numbers “more / less” and suggests where you can bet. After each win, it is recommended to reset the programme and then enter the last 6 numbers;
  • Axa 5.0 Winner is an analyser for online roulettes of all varieties from PlayTech, NetEnt, RTG, etc. The algorithm picks the numbers that should play over the course of 3 spins;
  • Caccia Al Pieno is an analyser from Italian developers. Using information on the last numbers that fell out in the game, the programme determines which sectors can be bet on with a high probability of success. In the left part displays the history of numbers that fell out for the last spins, to the right – fields for entering the history. After the first 5-8 numbers, the user receives a hint from the advisor on which of the sectors to bet on.

However, it should be remembered that the task of such applications is only to fix statistical data and perform probabilistic forecasts, but not a “guarantee of winning” and not a “means of increasing the bankroll”. There is no programme that allows you to beat roulette with a hundred percent guarantee.

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