The use of statistics in lottery Introduction       It has been 100 years since the first lottery was born at a racetrack in Australia, 1881. During this long period, the lottery industry and the legislation have developed much, and people invented more and more ways to play it. But it is still a controversial issue that whether there is a regular pattern or not in the lottery. This essay will firstly discuss whether the people can improve the probability of winning by analyzing huge number of instances with statistical tools. Following this article will do a statistical analysis on the results of the cash 3 game. Finally, it will find out its regular pattern, and improve the winning rates.             The way to increase the winning probability   1. Odd/even ratio analysis   Among the 10 numbers of 0-9, 1, 3, 5, 7, 9 are odd, and 2, 4, 6, 8, 0 are even in cash 3. So there are 4 kinds of three-digit combination: 3 odd, 3 even, 2 odd 1 even, 2 even 1 odd. In 1000 beds, there will be 125 for 3 odd or 3 even, and 375 for 2 odd 1 even or 2 even 1 odd. Thus, people are more likely to win when they collocate even with the odds in this game, theoretically.   2. Span analysis   Span can be further divided into three different types:firstly,according to the numbers, can be divided into single span 13579 and double span 02468;secondly,according to the divided by three remainder, can be classified into 0 road span 0369, 1 road span 147 and 2 road span 258;lastly,according to the mass sum numbers, can be divided into prime span 12357 and sum numbers span 04689.To span segmentation, can effectively screen number combination.   When take span for the single number structure necessity is 2 single 1 double or 2 double 1 single, which can eliminate the form of all odd and even.Span analysis method can serve as a kind of auxiliary method used in polls betting.That is to choose the number of bets, then use span analysis to corresponding to its election numbers.       A winning result statistical analysis   We select a set of winning numbers

Data	Result	Data	Result	Data	Result
12250	0  2  3	12260	4  4  2	12270	9  9  2
12251	1  9  5	12261	4  0  1	12271	1  4  0
12252	6  7  0	12262	8  6  9	12272	9  8  9
12253	4  6  6	12263	7  9  9	12273	6  6  7
12254	2  0  3	12264	7  9  7	12274	2  6  7
12255	1  3  2	12265	4  1  9	12275	4  4  7
12256	6  9  4	12266	1  8  1	12276	4  6  8
12257	7  7  3	12267	3  4  3	12277	9  9  4
12258	9  1  3	12268	3  3  9	12278	0  2  1
12259	3  4  0	12269	6  2  5	12279	5  3  8

Then statistics for the sum of three numbers, span, odd/even ratio, larger and smaller numbers of the three numbers.       Graph 1: The pie chart about span           Graph 2: histogram mapping on a total of three numbers       The definition is as follows.   We assume that the three numbers are , , .   The sum of value:It means the sum of selected numbers.       The span: It is the minimum and maximum of digital difference in the ranked number               3 of the number of bets.       The high number:It is the number that is larger than or equal 5 between the 0 to 9                   numbers. That is number 5, 6, 7, 8,9.   The low number: It is the number that is smaller than 5 in the 0 to 9 numbers of                  bets. That is number 0,1,2,3,4.           Conclusion   In conclusion, through the observation of the chart of odd and even numbers, we have a result of either the full form of an odd. So we can invest 50 bets to include all sorts of formats if it is determined to be a 1 odd and 2 even. Because there exist 2 evens, it is necessary to pick up from 2, 4, 6, 8, 0 these numbers, namely we get 50 bets by five multiply ten.       ODD-EVEN LOTTO NUMBER TIPS   When you select your Cash 3 numbers, try to have a relatively even mix of odd and even numbers. All odd numbers or all even numbers are rarely drawn, occurring less than 10 percent of the time. The best mix is to have 1/2 or 2/1 which means one odd and two even, or two odd and one even. One of these two patterns will occur in 70 percent of the drawings.       All Even numbers - 3 of the time (10.00%)   1 Odd/2 Even numbers - 13 of the time (43.33%)   2 Odd/1 Even numbers - 8 of the time (26.67%)   All Oddnumbers - 6 of the time (20.00%)           Graph 3: The pie chart about odd/even ratio       HIGH-LOW LOTTO NUMBER TIPS   Winning numbers are usually to spread of across the number field. If we take a number field and cut it in half, we will have the low half and the high half. In a 10-number game like Cash 3, numbers 0 to 4 would be in the low half, and numbers 5 to 9 would be in the high half. All high numbers or all low numbers are rarely drawn, occurring only 3 percent of the time. The best mix is to have 3/2 or 2/3 which means three high and two low, or two high and three low. One of these two patterns will occur in 65 percent of the drawings.       All High numbers - 5 of the time (16.67%)   1 Low/2 High numbers - 11 of the time (36.67%)   2 Low/1 High numbers - 5 of the time (16.67%)   All Low numbers - 9 of the time (30.00%)           Graph 4: The pie chart about high/low ratio       We can perceive a feature which the span of double and single numbers. So it can be judge span of the term 08221 as an odd number, and form which we can judge the form of the 2 odd and 1 even present number. Since this single double number only appears at the hundreds or units, while the 2odd numbers are next to other two and the won number that right is 5 2 9, so the 2 even number must appear at the hundred place.                           References:       David Freedman / Robert Pisani / Roger Purves / Ani Adhikari(1978). Statistics. W. W. Norton & Company       Frederick Mosteller , Robert F. Boruch (2002). Evidence Matters: Randomized Trials in Education Research. Brookings Inst Pr       Stephen M. Stigler(1990). The History of Statistics. Belknap Press.       Stephen M. Stigler(2002). Statistics on the Table. Harvard University Press.           Appendices

Data	Result	Large/small ratio	Odd/even ratio	Span	Sum
12250	0  2  3	0:3	1:2	3	5
12251	1  9  5	2:1	3:0	8	15
12252	6  7  0	2:1	1:2	7	13
12253	4  6  6	2:1	0:3	2	16
12254	2  0  3	0:3	1:2	3	5
12255	1  3  2	0:3	2:1	2	6
12256	6  9  4	2:1	1:2	5	19
12257	7  7  3	2:1	3:0	4	17
12258	9  1  3	1:2	3:0	8	13
12259	3  4  0	0:3	1:2	4	7
12260	4  4  2	0:3	0:3	2	10
12261	4  0  1	0:3	1:2	4	5
12262	8  6  9	3:0	1:2	3	23
12263	7  9  9	3:0	3:0	2	25
12264	7  9  7	3:0	3:0	2	23
12265	4  1  9	1:2	2:1	8	14
12266	1  8  1	1:2	2:1	7	10
12267	3  4  3	0:3	2:1	1	10
12268	3  3  9	1:2	3:0	6	15
12269	6  2  5	2:1	1:2	4	13
12270	9  9  2	2:1	2:1	7	20
12271	1  4  0	0:3	1:2	4	5
12272	9  8  9	3:0	2:1	1	26
12273	6  6  7	3:0	1:2	1	19
12274	2  6  7	2:1	1:2	5	15
12275	4  4  7	1:2	1:2	3	15
12276	4  6  8	2:1	0:3	4	18
12277	9  9  4	2:1	2:1	5	22
12278	0  2  1	0:3	1:2	2	3
12279	5  3  8	2:1	2:1	5	16