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The Dice Game

Dice games are the most ancient games in the world. They have been played from the earliest stages of civilization, with the first mentions of them appearing over 5000 years ago. Civilizations perished, but the passion born by dicing has persisted.

However, in the grand scheme of things, everything depends on the result of a throw, and the outcome of the game depends not only on one’s good luck but also on the probability of certain combinations occurring.

The majority of players think that all participants always have identical chances to win. However, thinking so would be a big mistake! Often certain combinations have a higher probability of occurring than the other. It is especially important when the players are rolling in turn and you are to exceed the result of the previous player. If you know which combinations have more chances to occur, you can win big prizes, especially if you play for money. Even if you are not playing for money, you will play more successfully and derive more pleasure from playing if you grasp the underlying mathematical principles of dicing.

Just as a die is a simple game tool, so too the game theory is simple and intelligible enough and comes down to the simple calculation of the probability of certain combinations occurring, and serious players use it successfully.

The theory of rolling a die is identical to the theory of throwing a coin. The only difference lies in the fact that a bone has 6 sides numbered from 1 to 6, each of them representing one of the six probable events. The probability theory has arisen in the middle of a XVII-th century. The first works on the probability theory, which belong to French scientists B. Pascal and P. Fermat and the Dutch scientist Huygens, have appeared in connection with calculation of various probabilities in gambling. The probability theory outstanding success is connected with a name of the Swiss mathematician J. Bernoulli who has established the law of large numbers for the scheme of independent tests with two outcomes.

The following (second) period of history of probability theory (XVIII century and beginning ?I? century) is connected with names A. Moivre (England), P. Laplace (France), K. Gauss (Germany) and S. Poisson (France). It is the period when the probability theory already finds a number of rather actual applications in natural sciences and the technician (mainly in the theory of errors of the supervision, the geodesy which have developed in connection with requirements and astronomy, and in the shooting theory).

The third period of history of probability theory, (second half XIX century) is connected basically with names of Russian mathematicians of P. L. Chebychev, And. M. Lyapunov and A. A. Markov (senior). The Probability theory developed in Russia and earlier (in XVIII century a number of works under the probability theory has been written by L. Euler, N. Bernoulli and D. Bernoulli; during the second period of development of probability theory it is necessary to note M. V. Ostrogradskiy's works concerning the probability theory, connected with mathematical statistics, and V. J. Bunjakovskiy’s essays on probability theory applications to insurance business, statistics and a demography).

Probability theory is the mathematical science allowing on probabilities of one casual event to find probability of other casual events, connected with the first. The statement that any event comes with the probability equal, for example, l, yet does not represent in itself definitive value as we aspire to authentic knowledge. Those results of probability theory which allow to assert have definitive informative value that the probability of approach of any event And is rather close to unit or (that the same) probability not approaches of event And is rather small. According to a principle "neglects small enough probabilities" fairly consider such event almost authentic. Therefore it is possible to tell also that the probability theory is the mathematical science which is finding out laws which arise at interaction of a great number of random factors.

Possibility of application of methods of probability theory to studying of the statistical regularities concerning areas rather far from each other of a science is based that probabilities of events always satisfy to some simple parities about which it will be told more low. Studying of properties of probabilities of events on the basis of these simple parities also makes a probability theory subject. The basic concepts of probability theory as mathematical discipline within the limits of so-called elementary probability theory are most simply defined.

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