For the analysis of mathematical models lottery analysis literature review

[Abstract] Based on the lottery of the mathematical model and analysis of sorting out the literature to illustrate how the probability of statistical analysis tools to play on lottery prizes and awards set analysis, and the kinds of tools for lottery sales program, lottery selection probability of winning lottery numbers and analyze all have such significance.

[Keywords] lottery, mathematical model, the probability

Hu Rong lock, money Guohua (2007) for traditional, Lotto-type lottery prize winning probability of each level of a detailed analysis of the probability formula is derived, and gives awards to the expectations of high-level calculations Jiange formula of the typical number of quantitative three lottery program data, based on extensive statistical analysis, to the Lottery to provide a scientific method of rational choice lottery numbers.

Xue Chunguang, the first rain and Zhang Guangyuan Dong (2006) analysis, with the recent "Xinjiang style" popular welfare lottery Computer Xinjiang, more and more people to join the "Lottery" in the ranks of present mainly in Xinjiang Computer Welfare Lottery "Lotto-type" that combinatorial betting method, namely a large "35 select 7," medium "25 select 7," small "18 select 7" and mini "10 select 7" play, then the probability of winning, how much? the number of occurrences are What distribution? Lottery and how scientific bets? variety of betting options in the award winning probability is much to buy lottery tickets, they generally only know of the Lottery award from low to higher awards, winning the difficulty is increasing, but The prize is not clear what is the probability that much. Based on the prize rules, the use of the knowledge of probability theory to calculate the probability of winning programs.

YANG Gui-yuan (2004) in Anhui Sports Lottery "61" numbers you play a statistical number that appears to make a line graph, and conducted chi-square test, you arrive at the figures 0,1,2,3, 4,5,6,7,8,9 probability is the same conclusion.

Caihuan Xing, high-Wei, Wang Guangqing (2006) for the lottery program how to set a reasonable question, by analyzing a variety of award winning rate, awards and prize money of settings, and the attractiveness of the Lottery and other factors, the use of analytic hierarchy process (AHP) to construct a goal hierarchy with the relationship guidelines, established on the basis of a multi-objective level planning model, weighted by a linear multi-objective problem into single objective programming problem, created a lottery program evaluation of the reasonableness of the objective function respectively set the weight of each factor, write the corresponding algorithm, and ultimately solve the practical problems.

Li Desheng, Zhang Cai Xian (2006), combinatorics and probability from the statistical perspective, Statistics and probability analysis of the relationship between lottery and lottery probability of winning each prize that the probability of winning the lottery has nothing to do with the lottery sequence, and gives how to increase the chance of winning techniques.

Wan Min Feng (2008) analysis, lottery in order to obtain huge returns, according to their own experience have found some forecasting methods, and some lottery experts also give their point of view, predict the next winning numbers. However, these lottery analysis and forecasting Technology is still in the exploration and development stage, there is no effective prediction method of the paper on the application background color ball lottery-depth study of analysis techniques and its main contents include: first proposed based on Mull Markov chain model of the color ball lottery method of analysis and forecast The forecast method does not require dynamic changes of the color ball lottery system with in-depth understanding of the mechanism, only through its transition probability matrix, the Statistics can be a color ball lottery system, the main parameters of the dynamic changes Relative to other models, this method provides the model significantly effective, and easy to use, simple calculation. Experiments show that the predictive model can effectively improve the probability of winning the lottery. Second, the paper presents a RBF neural network based color ball Lottery analysis and forecasting methods which prediction method using radial basis neural network a powerful nonlinear mapping ability, combined with the color ball distribution from the theory of algorithms and models, parameter selection to start, the data pre-processing, after training determine the hidden layer nodes, the future of the color ball lottery lottery prediction, and achieved good initial results. Third, proposed a lottery based on the integration of knowledge and reasoning color ball lottery prediction framework.

Jinhua (2007) pointed out that the 2006 single-game football quiz abnormal hot, while the national network has been dismally basket color, Guess Guangdong basketball tickets only four months on the aborted trial, the main problem is the basket color play and bonus set is not reasonable How to save the downturn in the basket color, is a worthy subject of study. For the future, Guangdong basket basket color color the mainstream market, the paper proposed to increase the prize of the Guangdong basket color award rate of return, and give guaranteed benefits, a further second prize, in this based on the use of the United States and the National Basketball League season data from 2004 to 2005 to establish the probability model to estimate the probability of winning, the bonus reasonable set provide a useful reference.

Ji Lei, Guai Song, Cai Fan (2003) through the analysis for 29 lottery draw lottery effects of three factors: high and low winning rate, degree of difficulty in winning, the expected return in the award size as the first three factors variable is a linear evaluation function, weighted by the preference factor to be reasonable under the weight of the different indices, developed on better rules of the game. Links to free download http://www.hi138.com
And then establish non-linear model gives a more general method to judge, for the reference lottery administration and finally to expand the parameters of the model, increasing the number of the actual situation is closer to the same conditions, seeking to strengthen the model's versatility.

Huo Lina (2007) analysis, lottery's ultimate goal is to achieve the maximization of lottery sales revenue, and to increase sales revenue, we must consider what kind of program in order to attract the majority of actively buying lottery tickets, Moreover, China's lottery industry development is still in its infancy, more single ticket lottery market types and constraints of the lottery games are played the expansion, and to the Lottery's survival and invasion of foreign lottery left a gap of these problems have attracted many scholars and relevant government departments attention. The text is in the common lottery program for the study, from a mathematical point of view, the use of economics, operations Research, probability theory and other relevant knowledge, to evaluate the reasonableness of the program to existing programs to determine whether this region the actual situation, and discussed whether the rule-making through the lottery to increase the attractiveness of the lottery issue, making the state and the interests of lottery win-win situation, to further promote the healthy development of China's lottery industry. Specifically, considering the total probability of winning high probability of winning prizes and the winning lottery attractive expected return and other factors that affect the use of classification methods constructed weighted function to evaluate the attractiveness of the program is reasonable, the introduction of Lottery mental curve to describe the program model the attractiveness of the Lottery, On this basis, considering the various constraints, seek to establish better lottery program model, and searches through the use of sub-constraints of a given method to calculate the optimal solution and so on.

Wang Hongjian, Fang Guoxing (2004) on China's lottery market conditions present an analysis that due to different regional economic conditions, spending levels and the Lottery psychological, there are a different "best" marketing programs. Studies suggest that, while both surface and high prizes winning prize money expected to fully mobilize the enthusiasm of Lottery, the Lottery's total sales increased, so that both profit lottery company and the Lottery this end, through the introduction of two non-negative weighting factor λ1 and λ2, reflect different surface area of ​​the Lottery for winning high prizes and prize money of preference, the problem of rationality into the meet a certain constraint conditions  3 the objective function f = λ1p + λ2xjpj optimal value, in order to find the "optimal" marketing programs. model used MATLAB to solve, j = 1 through the calculation of various types of data that it stability, the result is reasonable, easy to use.

References:
[1] Hu Rong lock, money Guohua. Mathematical analysis and lottery betting strategy [J]. Changshu Institute of Technology, 2007 (10).

[2] Xue Chunguang, Mr. Dong Yu, Zhang Guangyuan. Lottery mathematical analysis and its application [J]. Statistics and Decision, 2006 (1).

[3] YANG Gui-yuan, Anhui Sports Lottery numbers of mathematical statistical analysis [J]. Finance and Trade Research, 2004 (1).

[4] Ji Lei, Guai Song, Cai Fan. Lottery evaluation model [J]. Yangzhou University (Natural Science), 2003 (2).

[5] Wang Hongjian, Fang Guoxing. Lottery best selling program for nonlinear programming model [J]. Journal of Fuzhou University (Natural Science), 2004 (3).

[6] Cai Huanxing, high-Wei, Wang Guangqing. Lottery in mathematics [J]. Sichuan University (Natural Science), 2006 (6).

[7] Li Desheng, Zhang was sen. On the statistical probability of winning the lottery skills in the application of [J]. Science and Technology Information, 2006 (32).

Links to free download http://www.hi138.com