The Probability Of Upgrading Online Game

For designing online games, setting and regulating the probability of passing game are the key problems. If the probability of passing game is too high, then it is very easy to pass the game, and hence it would make game players to lose interest. However, if the probability is too low, it would make the game player to lose confidence. Meanwhile, the duration of passing game is also related to the economic benefits, so to research the passing game probability is an important mathematical problem.The main content of this paper is to extend the theory of solving the problem of three levels proposed by Liu Chengshi to any level, and then obtain the corresponding exact formulas. Moreover, creatively this theory is applied to solve other probability problems and provide new method to these topics. To analyze the game mode, we take the probability and the attempts of passing the game as a probability space{Ω,F,p}, which can be considered as the algebraic foundation to apply probability theory, stochastic process theory and evaluation methods to solve the problem of online game upgrading. By the detailed analysis for online upgrading game, some universal hypothesis to solve the problem are given abstractly as follows: when the game has m levels, the probability of passing online game can be described by a sequence of real numbers (?) , and now the probability of passing the game by n playing is(?)In the paper difference equation is used to validate the normalization of the probability of passing a level, and the expectation of passing all levels(?) is obtained,where 10a(28). By aiming at probability of passing level and expectation of times, the generation function method and Markov chain method have been established. These results include the generation function(?) the generation function(?) of the n-step transition probability matrix of Markoff process and so on. In addition, the corresponding MATLAB programs have been given according to above algorithms.In final, the above methods are applied to solve the problems of specific game and other related fields and get meaningful results.