目 錄
摘要 1
1 彩票發行問題的背景 3
2 彩票的分類及設獎規則 4
2.1 “傳統型”彩票 4
2.2 “樂透型”彩票 4
2.3 發行彩票的設獎規則 5
3 提出模型要解決的問題 7
3.1 提出彩票方案需解決的問題 7
3.2 模型參數的基本假設 7
3.3 彩票各種獎項出現的可能性分析 7
4 建立彩票模型 11
4.1 1等獎期望模型 11
4.2 彩票模型的最終建立 12
4.2.1 建立彩票模型的.準備 12
4.2.2 確定吸引力函數 14
4.2.3 彩票模型的建立 15
4.2.4 對各方案合理性的分析 15
4.2.5 彩票模型的求解 16
5 模型評價及改進意見 19
5.1 模型評價 19
5.2 模型改進意見 19
參考文獻 20
致謝詞 21
附錄 22
摘 要
本設計旨在建立關於彩票發行方案的數學模型，分析現有的29種彩票發行方案的合理性，並以設定的函數爲標準，設計1種更好的方案。
針對 “傳統型”和“樂透型”兩種彩票各獎項中獎概率，計算各方案每種獎項獎額的期望。先考慮各獎項的1等獎的期望,建立1個比較簡單的1等獎期望模型。然後再綜合考慮1、2、3等獎的金額，中1等獎的概率、中2、3等獎的總概率、中4至7等獎的總概率6個方面，構造吸引力函數，分析各方案對彩民的吸引力，求出對彩民吸引力較大的方案。綜合分析“樂透型”彩票和“傳統型”彩票中各方案的合理性；結合“樂透型”彩票中的最優方案的優點並以此爲基礎，限定取值範圍搜尋最優值，改進其各獎項獎額，在此的基礎上給出1種更好的方案。
關鍵詞：彩票方案；中獎概率；頭獎期望；吸引力。
Abstract
In this design we will seek for the mathematic model of an attractive lottery ticket scheme. We analyze the rationality of 29 kinds of lottery ticket schemes and then establish a better scheme based on the objective function.
This design studies the ratio of getting the winning number in lottery in “Traditional type” and “Too happy type” lottery tickets respectively. Firstly, it calculates the expectation value of various of the first-class prize amount and we study the sum of winning the first-class, the second –class and third-class prizes, winning the first-class’s probability, the total probability of the second –class and third-class prizes, the total probability of the fifth-class, sixth-class and seventh-class, we adopt a quantitative description-“attraction” of lottery schemes and reach a conclusion which model is more appealing to buyers. Integrate analyze rationality of the “Traditional type ” and “Too happy type” lottery tickets ;According to the excellence of “Too happy type” lottery model , and at the base of this model, Limit the worth of scope and search for the superior value, Improve its each prize sum, at base of this model to give a kind of better project.
Keywords: Lottery ticket project; Win a prize all rate; First prize expectation; Attraction
