隨著經濟水平的提昇，時序進入廿一世紀的後工業時代，人類理財日益多樣化，由保守的傳統型轉趨積極的冒險型理財，單純的定存或債券市場股票市場，已無法滿足現代人的需求，因此金融商品日新月異，各式各樣的衍生性金融商品，諸如選擇權、期貨、認股權證等，令人目不暇給，甚至賽馬、賭狗及彩券等金錢遊戲也已不再是禁忌，尤其是彩券，在大多數國家皆由政府主辦，視之為無痛的稅收。
台灣早期僅有政府發行的愛國獎券，八O年代由於「大家樂」依附盛行，形成社會風氣敗壞，影響正常經濟體系運作，政府於焉毅然終止。但炙盛賭氣未見收斂，轉入地下化依附香港「六合彩」繼續運作，幾成全民運動。因此，社會問題層出不窮如火燎原，政府堵絕不成之餘，乃思師法國外先例順勢開辦台灣樂透彩，一方面化暗為明俾利管理，斷絕此一地下經濟衍生的社會問題根源，另則增加國庫收入，並提供殘障人士就業機會，於是台灣樂透彩於2002年初正式開辦。開辦迄今每期頭彩鉅額獎金確實讓人心動；對此種隨機性投資標的日益普及充斥且合法的環境，乃興起一探此類投資是否可行的研究動機。
本研究主要是以台灣樂透彩為投資個案，首先透過統計方法檢定台灣樂透彩中獎號碼的隨機性；進而運用統計推導不同向度的母體可能分佈，並以歷期開獎資料透過集群分析歸納待選號碼次群集，再應用馬可夫鏈為選群方法，將選定次群集在個別投資者所能承受的風險範圍，冀期提昇投注號碼開出機率；最後驗證評估坊間各種精簡投注模型工具的效益性，尋求最具效益的投入模式，以做個別投資者風險管理參考。
本研究發現，在樣本期間內台灣樂透彩中獎號碼是隨機性產生的，而中獎號碼的順序統計量為β分配，以集群分析將待選號碼分成次群集，各次群組較隨機分群皆普遍性的小幅度提昇群聚效果，而馬可夫鏈的應用對選群力則有顯著提昇效果；坊間「聰明包牌法」經評估並不能提升中獎機率，但可依個別投資者需求選用不同模型，作為風險管理工具。
做此研究是透過一看似漫無頭緒的隨機事件，探討其可能存在的模組過程，體驗遽變混沌的管理環境，管理者管理決策的心境。

Abstract
With the economic growth as well as the advent of the post-industry age in the 21st century, a variety of investment patterns for people to employ progressively appear. Moreover, there is a tendency in which people’s traditional and conservative manners for investments gradually transform into aggressive ones with a preference of risks. For instance, it has been impossible nowadays for certain simple finance-managing mechanisms, such as the Certificate of Deposit, the Bond or even Stock Markets, to satisfy general investors’ needs. Therefore, more and more financial products have become available, especially a lot of derivative securities like options, futures, or stock options. Furthermore, the activities of horseracing, dog racing or even lottery are no longer taboos in Taiwan. As far as the lotteries in most of the counties are concerned, the government is usually the main host, regarding them as additional effortless sources of tax revenue.
During the earlier periods in Taiwan, the only lottery available was the national “Ai-Guo” lottery issued by the government. Unfortunately, a lot of unlawful gambling gangs took advantage of the popularity of “Ai-Guo” lottery by utilizing it as the sources of the so-called “Da-Jia-Le” lottery, which was an illegal, yet popular underground gambling activity. The “Da-Jia-Le” lottery not only corrupted the social values and caused a lot of criminal actions, but also made an acute and serious impact on regular economic operations. Consequently, the government resolutely called a halt on the “Ai-Guo” lottery. Nevertheless, the prevailing gambling mania did decline; on the contrary, it further transformed into a covert and under-the-counter gambling operation attached to the Hong Kong lottery. The craze almost swept the entire country, resulting in more and more social problems and having troubled the authorities for a long period of time. To settle such a predicament, government decided to refer to the experiences of other countries, beginning to launch local lotteries in Taiwan, instead of prohibiting people from attending illicit gambling activities. On the one hand, the government would be able to set the lottery business back on right track and eliminate the root of the underground economic operations, which brought about many social problems. On the other hand, the local lottery would provide extra tax revenue for the administrations as well as more employment opportunities for handicapped people. Accordingly, Taiwanese Lottery was launched in the beginning of the year 2002. Until now, mainly due to the attraction of the surprisingly huge bonus shares offered by the lottery’s highest prize, the public response is overwhelming. The social environment in which the stochastic investment actions become authorized and gradually prevail directly triggers the motivation of this research in further investigating the feasibility of the investment.
The research takes Taiwan Public Welfare Lottery as an investment research case, exploring the game rules of lottery in an attempt to enhance the probability of winning prizes and further testing and evaluating the effectiveness of various simple biting tools adopted by the general public in order to obtain the most effective biting ways for individual investor’s reference. The process of this study is as follows:
1. Testing the randomness of the winning prize numbers in Taiwan Public Welfare Lottery.
2. Estimating the possible distribution of the population via the statistical application.
3. Using the cluster analysis to induce the sub-cluster of the selected numbers according to the patterns of the historical prize numbers.
4. Making use of Markov Chain to select the sub-cluster, which is within an investor’s upper limit of risks.
And consequently, this study reveals the followings:
1. The winning prize numbers are random within study samples.
2. The statistic order of the winning prize numbers is β distribution.
3. The cluster effect is slightly enhanced when the sub-cluster is chosen through the cluster analysis rather than random ways.
4. The application of Markov Chain has an obvious reinforcement on the selection of sub-cluster.
5. The so-called “Smart Package Biting”, which is adopted by the general public, cannot improve the winning possibility; however, depending on individual investor’s needs, it could be a useful tool for risk management.
Through a seemingly aimless random event, the research explores the possible development of the modeling process, so as to comprehend and experience a manager’s mental course on decision making in a dynamic, capricious or even chaotic managerial environment.

中文摘要 IV
Abstract V
誌謝詞 VII
第一章 緒論 01
第一節 研究背景與動機 01
第二節 研究目的 04
第三節 研究步驟與流程 05
第四節 研究範圍與限制 07
第二章 文獻探討 09
第一節 彩券簡史 09
第二節 彩券與機率 12
第三節 彩券的決策類型 15
第四節 彩券的隨機過程 17
第五節 彩券的集群分析 20
第六節 彩券的評估模型 23
第三章 台灣公益樂透彩概況 25
第一節 樂透彩的型態 25
第二節 樂透彩獎金分配 31
第三節 樂透彩開獎流程 35
第四節 樂透彩歷期開獎統計與各項機率 37
第四章 台灣公益樂透彩提昇中獎機率模式推估 43
第一節 中獎號碼隨機性適合度檢定 43
第二節 中獎號碼順序統計量機率分配 47
第三節 中獎號碼集群分析與驗證 52
第四節 馬可夫鏈理論於樂透彩的應用 58
第五章 台灣公益樂透彩的風險管理 63
第一節 個人風險管理 63
第二節 各種投注模式工具概觀與驗證 67
第三節 精簡投注模式工具效益性評估 70
第四節 台灣公益樂透彩綜合評估 76
第六章 結論 77
第一節 隨機性投資標的評估關鍵因素 77
第二節 後續研究之建議 80
中文參考文獻 81
英文參考文獻 83
附錄一精簡投注法有效性驗證表 84
附錄二 K-S適合度檢定表 88

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