-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathLottery-Analysis.Rmd
251 lines (164 loc) · 12.4 KB
/
Lottery-Analysis.Rmd
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
---
title: "{height=240}"
subtitle: "秦彩庄三码福彩分析"
author: "[®γσ, Lian Hu](https://englianhu.github.io/) <img src='figure/ENG.png' width='24'> <img src='figure/RYO.png' width='24'>®"
date: "`r lubridate::today('Asia/Tokyo')`"
output:
html_document:
number_sections: yes
toc: yes
toc_depth: 4
toc_float:
collapsed: yes
smooth_scroll: yes
---
# 介绍
彩票市场在中国内地甚至全球的市场占有份额日益增加，越来越多赌徒热爱购买彩票。今天僕尝试分析随机内地彩票---**三码福彩（千字、福彩3D）**为数据，分析是否可能从中获利。
**美国马萨诸塞州`Cash Winfall`彩票有漏洞!**文献中阐述：
> `Cash Winfall`彩票有一条特殊的规则：当头奖达到两百万美元而无人领取后，较小的奖项奖金金额将会变大，比如末奖能从5美元增加到几十美元。统计学家称，任何人只要购买十万美元以上的彩票就要保证盈利。因此每隔几个月，当头奖金额累积到两百万美元后，由精明的赌徒组成的小团体就会短暂控制整个博彩，他们有的来自美国麻省理工大学，有的来自东北大学，训练有素，他们会投入数十万美元购买彩票，每次能获得几十万美元的收入，这些盈利还没有计算获得头奖的可能性。麻州的博彩官员正开始采取行动限制大量购买，比如每个彩票点每天只能出售五千美元的彩票...
## 环境设置
环境设置与读取程序包。
```{r setup, message=FALSE}
## Remove all objects (includes hidden objects).
rm(list = ls(all = TRUE))
options(warn = -1) #Do not display warning messages.
suppressPackageStartupMessages(library('BBmisc'))
pkgs <- c('devtools', 'knitr', 'kableExtra', 'rvest', 'plyr', 'dplyr', 'magrittr', 'stringr', 'lubridate', 'devtools', 'openxlsx', 'DT', 'mvtnorm', 'PoisNor', 'flexmix', 'poilog', 'kfoots', 'mvrpois', 'rstan', 'matrixStats')
##https://github.com/lamortenera/kfoots
#'@ suppressAll(library('kfoots')) ##Fit mixture model or a hidden markov model
suppressAll(lib(pkgs))
rm(pkgs)
## Modified or call hidden functions in mvrpois.
l_ply(dir(paste0(getwd(), '/函数/')), function(funs) source(paste0(getwd(), '/函数/', funs)))#, local = TRUE))
```
# 读取数据
[福彩3D: 直选走势](http://sports.sina.com.cn/l/tubiao/3d_jibenzoushitu.html)数据从*2016158期*至*2017158期*，一共有三百圆个观测数据。该福彩类型规则乃预测三个随机数字，从`000`至`999`。
```{r read-data}
##
## http://baidu.lecai.com/lottery/draw/list/52?type=latest&num=100 ##要下载txt或xlsx文件，需要登入账户
#'@ read_html('http://sports.sina.com.cn/l/tubiao/3d_jibenzoushitu.html') %>% html('table_A')
## http://zst.sina.aicai.com/gaopin_cqssc/?sDate=&eDate=&q=t100&sortTag=up ##时时彩上至五个随机变量，比福彩3D复杂
## http://sports.sina.com.cn/l/tubiao/3d_jibenzoushitu.html ## 快三
ltry_data <- read.xlsx(xlsxFile = './诸子百家学府/福彩3D/lottery_data.xlsx', detectDates = TRUE) %>% .[1:5] %>% tbl_df %>% mutate(Result = as.numeric(paste0(Result1, Result2, Result3)))
datatable(ltry_data)
```
*数据图2.1：福彩3D开彩数据*
从以上数据图2.1，首先僕绘制个频率图。
```{r plot-1}
##观测数据量
length(ltry_data$Result)
##过滤重复开彩成绩
length(unique(ltry_data$Result))
hist(ltry_data$Result, main = "3D Lottery Histogram", xlab = "Number (Digit from 0 to 999)")
```
*数据图2.2：福彩3D开彩数据频率图*
以 000 至 999 三位数随机变量，一般上会以普通频率分布分析，然而由于三位数字非出现在同一个单位（slot）里而是个别三个随机变量，因此*多变量泊松模式*将能分析。
# 数学模式
- `kfoots`：[kfoots](https://github.com/lamortenera/kfoots)程序包使用马克夫链，举例此期开彩010，该模式将分析及预测每当开彩该成绩后的下一个成绩（状态的转换率）的机率
- `PoisNor`：[PoisNor](https://cran.r-project.org/package=PoisNor)程序包提供多随机变量产生器及相关系数分析
- `poilog`：[poilog](https://cran.r-project.org/package=poilog)程序包分析双变量泊松模式
- `mvrpois`：[mvrpois](https://github.com/alekdimi/mvrpois)程序包分析多变量泊松模式
在此，僕使用`mvrpois`多变量泊松模式分析**仨变量泊松**3D彩票数据，有关详情请查阅*Dimitris Karlis and Loukia Meligkotsidou (2005)^[**7.3 参考文献**中的4th文献]*和*Dimitris Karlis (2002)^[**7.3 参考文献**中的3rd文献]*。
$$(X_{1},X_{2},X_{3})_{i} ~ 3 - Pois(\theta_{1i},\theta_{2i},\theta_{3i},\theta_{12i},\theta_{13i},\theta_{23i}) \dots equation\ 3.1$$
- $log(\theta_{1i}) = \alpha_{1} + \beta_{1}z_{i}$
- $log(\theta_{2i}) = \alpha_{2} + \beta_{2}z_{i}$
- $log(\theta_{3i}) = \alpha_{3} + \beta_{3}z_{i}$
- $log(\theta_{12i}) = \alpha_{4} + \beta_{4}z_{i}$
- $log(\theta_{13i}) = \alpha_{5} + \beta_{5}z_{i}$
- $log(\theta_{23i}) = \alpha_{6} + \beta_{6}z_{i}$
联合分布函数将为：
$$P(X = x) = \sum_{(y_{12},y_{13},y_{23})\in C}\frac{exp(-\sum\theta_{i})\theta_{1}^{x_{1}-y_{12}-y_{13}}\theta_{2}^{x_{2}-y_{12}-y_{23}}\theta_{3}^{x_{3}-y_{13}-y_{23}}\theta_{12}^{y_{12}}\theta_{13}^{y_{13}}\theta_{23}^{y_{23}}}{(x_{1}-y_{12}-y{13})!(x_{2}-y_{12}-y{23})!(x_{3}-y_{13}-y{23})!y_{12}!y_{13}!y_{23}!} \dots equation\ 3.2$$
而 $C \subset N^3$ 设为：
$$C = (y_{12},y_{13},y_{23}) \in N^3 : \{y_{12}+y_{13}\leq x_{1}\} \cup \{y_{12}+y_{23}\leq x_{2}\} \cup \{y_{13}+y_{23}\leq x_{3}\} \neq \theta$$
**Rerefences for multivariate Poisson models : **
- [Can a Multivariate Poisson Distribution be implemented in Stan?](https://groups.google.com/forum/#!topic/stan-users/3VHq_GxGWEw)
- [n-mixture model in Stan? marginalizing](https://groups.google.com/forum/#!newtopic/stan-users/stan-users/9mMsp1oB69g)
- [karlis-ntzoufras-reproduction/model.stan](https://github.com/Torvaney/karlis-ntzoufras-reproduction/blob/master/model.stan)
- [Reproductions of models for football (soccer) matches in Stan/PyStan](https://github.com/Torvaney/soccerstan)^[So far, the following models have been implemented:] ^[1) Maher (1982) - Modelling Association Football Scores - maher] ^[2) Dixon and Coles (1997) - Modelling Association Football Scores and Inefficiencies in the Football Betting Market - dixon-coles] ^[3)Karlis and Ntzoufras (2008) - Bayesian modelling of football outcomes (using the Skellam's distribution) - karlis-ntzoufras]
```{r trvPois, eval=FALSE}
## =========================== eval=FALSE ==============================
## get the trivariate sample data and convert to matric format.
m <- ltry_data %>% select(Result1, Result2, Result3) %>% as.matrix
#'@ m <- ltry_data %>% select(Date, Result1, Result2, Result3) %>% as.matrix
#'@ adply(m, 1, transform, mvp = mvp.fit(method = 'HMC'))
## ------------------------ PENDING --------------------------------------
## 1) missing files : 'karlis.stan' and 'karlis.covariates.stan'.
## 2) missing codes : cov() inside gibbs() inside mvp.fit.R
## ------------------------ PENDING --------------------------------------
## Hamiltonian Monte Carlo (HMC)
fit.HMC <- mvp.fit(m, method = 'HMC')
## Gibbs MCMC
fit.Gibbs <- mvp.fit(m, method = 'Gibbs')
## ==============================================================================
## 1) method = Monte Carlo samples, default iterations : n.mc = 10000.
tv.mc <- mvp.prob(m, seq(0, 9), logarithm = FALSE, method = 'MC')
adply(m, 1, transform, prob = mvp.prob(m[, c('Result1', 'Result2', 'Result3')], seq(0, 9), logarithm = FALSE, method = 'MC'))
## 2) method = 'recursive', but it is equal to 'analytical'.
tv.rc <- mvp.prob(m, seq(0, 9), logarithm = FALSE, method = 'recursive')
## 3) method = 'analytical', but it is equal to 'recursive'.
tv.an <- mvp.prob(m, seq(0, 9), logarithm = FALSE, method = 'analytical')
```
# 投注模式
**understanding the kelly capital growth investment strategy**文中提及，尽管中马票的机率非常渺茫，但是运用凯利模式长期投注的话还是可以获利，不过可能得花上百万年时间，请查看下图。
由于凯利投资模式，在此使用该模式。有关凯利模式投注，请参阅：
- [Application of Kelly Criterion model in Sportsbook Investment](https://github.com/scibrokes/kelly-criterion)
- [Job Application - Quantitative Analyst (binary.com)](https://github.com/englianhu/binary.com-interview-question)
```{r}
```
# 盈利
```{r}
```
# 结论
Summary of the betting
```{r}
```
```{r close-Opt}
options(warn = 0)
```
# 附录
## 文献明细
以下乃此文献资讯：
- 文件建立日期：2017-06-15
- 文件最新更新日期：`r today('Asia/Tokyo')`
- `r R.version.string`
- R语言版本：`r getRversion()`
- [**rmarkdown** 程序包](https://github.com/rstudio/rmarkdown)版本：`r packageVersion('rmarkdown')`
- 文件版本：1.0.1
- 作者简历：[®γσ, Eng Lian Hu](https://beta.rstudioconnect.com/content/3091/ryo-eng.html)
- GitHub：[源代码](https://github.com/englianhu/binary.com-interview-question)
- 其它系统资讯：
```{r info, echo=FALSE, warning = FALSE, results = 'asis'}
suppressMessages(require('dplyr', quietly = TRUE))
suppressMessages(require('formattable', quietly = TRUE))
sys1 <- devtools::session_info()$platform %>% unlist %>% data.frame(Category = names(.), session_info = .)
rownames(sys1) <- NULL
sys1 %<>% rbind(., data.frame(Category = 'Current time', session_info = paste(as.character(now('Asia/Tokyo')), 'JST')))
sys2 <- data.frame(Sys.info()) %>% mutate(Category = rownames(.)) %>% .[2:1]
names(sys2)[2] <- c('Sys.info')
rownames(sys2) <- NULL
cbind(sys1, sys2) %>%
kable(caption = 'Additional session information:') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
rm(sys1, sys2)
```
## 版本
- 文献版本: 1.0.0 - *"2017-06-15 20:47:50 JST"*
## 参考文献
1. [**Bayesian Multivariate Poisson Regression for Models of Injury Count, by Severity** *by Jianming Ma and Kara M. Kockelman (2006)*](https://github.com/englianhu/lottery/tree/master/reference/Bayesian%20Multivariate%20Poisson%20Regression%20for%20Models%20of%20Injury%20Count%2C%20by%20Severity.pdf)
2. [**FlexMix - An R package for finite mixture modelling** *by Bettina Grun and Friedrich Leisch (2007)*](https://github.com/englianhu/lottery/tree/master/reference/FlexMix%20-%20An%20R%20package%20for%20finite%20mixture%20modelling.pdf)
3. [**Multivariate Poisson Models** *by Dimitris Karlis (2002)*](https://github.com/englianhu/lottery/tree/master/reference/Multivariate%20Poisson%20Models.pdf)
4. [**Multivariate Poisson Regression with Covariance Structure (Preview)** *by Dimitris Karlis and Loukia Meligkotsidou (2005)*](https://github.com/englianhu/lottery/tree/master/reference/Multivariate%20Poisson%20Regression%20with%20Covariance%20Structure%20(Preview).pdf)
5. [**Package 'poilog'** *by Vidar Grøtan and Steinar Engen (2015)*](https://github.com/englianhu/lottery/tree/master/reference/Package%20'poilog'.pdf)
6. [**Resampling Methods for Longitudinal Data Analysis** *by Yue Li (2005)*](https://github.com/englianhu/lottery/tree/master/reference/Resampling%20Methods%20for%20Longitudinal%20Data%20Analysis.pdf)
7. [**彩票的数学知识** *by 阮一峰 (2018)*](http://www.ruanyifeng.com/blog/2018/04/lottery-mathematics.html)
8. [**00后买彩票2个月疯狂吸金50万** *by 财经观察 (2018)*](http://www.tw294.cn/)
9. [Mass. Changes Rules To Cash WinFall Lottery After Easy Wins](https://www.huffingtonpost.com/2011/08/03/mass-changes-lottery-rules_n_916972.html)
10. [程阳：美国马萨诸塞州 Cash Winfall 彩票有漏洞! ](http://chengyangblog20.blog.163.com/blog/static/2108302022011771480468/)
11. [美国夫妇钻开奖漏洞 简单计算后的“必赢”结论](http://sports.sohu.com/20110806/n315531364.shtml)
12. [Understanding the Kelly Capital Growth Investment Strategy](https://github.com/scibrokes/kelly-criterion/blob/master/references/Understanding%20the%20Kelly%20Capital%20Growth%20Investment%20Strategy.pdf)
13. [數學家中14次樂透賺進9億元！ 美、澳因他被迫修法](https://www.ettoday.net/news/20180829/1246651.htm)
14. [樂透能偷吃步？ 經濟學家用這招中14次頭彩賺9億](https://udn.com/news/story/6810/3337660)
## 感言
---
**Powered by - Copyright® Intellectual Property Rights of <img src='figure/oda-army.jpg' width='24'> [Scibrokes®](http://www.scibrokes.com)**