The following is a research article that won the second prize of national mathematical modeling in 2002, about the relationship between mathematics and lottery.
Mathematical model of lottery scheme
The mathematical model of lottery schemes is established, the rationality of 29 lottery distribution schemes is analyzed, and a better scheme is designed based on set evaluation function.
In this paper, a general formula for calculating the winning probability of each prize in "traditional" and "lottery" lottery tickets is given, and the expected value of each prize amount in each scheme is calculated. Considering the amount of the first, second and third prizes, the winning probability of the first prize, the total winning probability of the second and third prizes and the total winning probability of the fourth and seventh prizes, the evaluation function is constructed according to the linear weighted sum method, and the attractiveness of each scheme to the lottery players is analyzed. It is concluded that the schemes No.23, No.5 and No.6 are more attractive to the lottery players. Comprehensive analysis of the rationality of each scheme leads to the conclusion that "lottery" lottery is better than "traditional" lottery; On the basis of Scheme 5, the optimal value is searched by limiting the value range, and the prize amount of each award is increased, and a better scheme is given.
Finally, suggestions are made to lottery management department and lottery players respectively.
Lottery attachment
In recent years, various lottery tickets have been sold all over the country. The lure of high bonuses has made more and more people buy lottery tickets and join the lottery team. The whole lottery market is extremely hot. As a rational lottery player, we should have a correct understanding of lottery.
There are many kinds of lottery tickets, and now the common ones are traditional digital and lottery tickets. The winning numbers of these two lottery tickets are completely random, and the probability of winning by buying any number is equal, which is the most basic principle that must be followed in designing the lottery issuance plan. If the winning number is really predictable as some so-called "experts" or software say, then they don't need to make a few small money by publishing books and selling software, just buy lottery tickets. Of course, there will be a certain gap between theory and reality, but through various normative measures, realistic lottery players can be as equal as possible in the face of opportunities.
Although the probability of winning the lottery is small, it does exist, which brings infinite longing to the lottery. The uncertainty of the future is an expectation and a stimulus for lottery players. If you become the lucky one, you will naturally be surprised; I missed the grand prize and had a little regret, so I will make up for it later. The joys and sorrows brought by buying lottery tickets enrich people's spare time to some extent, which is consistent with the nature of their games.
At present, the lottery issuing department has launched a variety of lottery schemes. The traditional digital type has simple rules and rich lottery types. Lottery players can't choose whether to win or not, but they can choose different lottery games. Some people have a special liking for games with high prizes, and traditional numbers and large lottery tickets (such as 7 out of 35) suit their tastes. Some people like to play games with many rewards and great chances of winning. These lottery players can invest in small-cap lottery tickets (such as 5 out of 23). This fully shows that buying lottery tickets is a voluntary activity and a personal preference of lottery players.
Rational lottery players should not gamble, should not put huge sums of money in one basket, but should buy lottery tickets as much as they can with a normal, healthy and participatory attitude.