Lotto Sums analysis 6/49 (long) - You _can_ win.
Mike H.
Since it is clear that Sums remain a mantra to many I have posted some
analysis results here.
The first part is a frequency analysis for all possible sums. ie for a sum
of 249 it shows how many combinations (ie tickets) will produce this sum.
It will not surprise the weenies to see that it is pretty close to a Normal
distribution (bell curve or tit to the non-weenies). You will also be amazed
to see that the total permutations for all the sums adds up to the total
number of tickets.
The second (much shorter part is a sequence analysis bit. It gives counts
for combinations of sequences - starting from sequences of 6 such as
'1,2,3,4,5,6' through to non-sequences '1,3,5,7,9,11'. You will also not be
surprised to see that non-sequences amount for about half of all possible
tickets.
Sums Analysis
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21 1
22 1
23 2
24 3
25 5
26 7
27 11
28 14
29 20
30 26
31 35
32 44
33 58
34 71
35 90
36 110
37 136
38 163
39 199
40 235
41 282
42 331
43 391
44 454
45 532
46 612
47 709
48 811
49 931
50 1,057
51 1,206
52 1,360
53 * 1,540
54 * 1,729
55 * 1,945
56 * 2,172
57 * 2,432
58 * 2,702
59 * 3,009
60 * 3,331
61 * 3,692
62 * 4,070
63 ** 4,494
64 ** 4,935
65 ** 5,426
66 ** 5,940
67 ** 6,506
68 *** 7,097
69 *** 7,748
70 *** 8,423
71 *** 9,163
72 **** 9,933
73 **** 10,769
74 **** 11,637
75 ***** 12,579
76 ***** 13,552
77 ***** 14,603
78 ****** 15,690
79 ****** 16,856
80 ******* 18,059
81 ******* 19,349
82 ******* 20,673
83 ******** 22,087
84 ********* 23,540
85 ********* 25,082
86 ********** 26,663
87 ********** 28,340
88 *********** 30,051
89 ************ 31,860
90 ************ 33,706
91 ************* 35,648
92 ************** 37,625
93 ************** 39,703
94 *************** 41,809
95 **************** 44,016
96 ***************** 46,253
97 ****************** 48,586
98 ****************** 50,944
99 ******************* 53,402
100 ******************** 55,875
101 ********************* 58,446
102 ********************** 61,031
103 *********************** 63,706
104 ************************ 66,388
105 ************************* 69,161
106 ************************** 71,928
107 *************************** 74,781
108 **************************** 77,624
109 ***************************** 80,542
110 ****************************** 83,440
111 ******************************* 86,412
112 ******************************** 89,348
113 ********************************* 92,350
114 ********************************** 95,311
115 ************************************ 98,324
116 ************************************* 101,285
117 ************************************** 104,295
118 *************************************** 107,235
119 **************************************** 110,215
120 ***************************************** 113,119
121 ****************************************** 116,048
122 ******************************************* 118,889
123 ******************************************** 121,751
124 ********************************************* 124,507
125 ********************************************** 127,274
126 *********************************************** 129,930
127 ************************************************ 132,581
128 ************************************************* 135,109
129 ************************************************** 137,629
130 *************************************************** 140,008
131 **************************************************** 142,370
132 **************************************************** 144,587
133 ***************************************************** 146,771
134 ****************************************************** 148,800
135 ******************************************************* 150,794
136 ******************************************************* 152,617
137 ******************************************************** 154,397
138 ******************************************************** 156,004
139 ********************************************************* 157,554
140 ********************************************************** 158,923
141 ********************************************************** 160,236
142 ********************************************************** 161,354
143 *********************************************************** 162,410
144 *********************************************************** 163,273
145 *********************************************************** 164,062
146 ************************************************************ 164,654
147 ************************************************************ 165,176
148 ************************************************************ 165,490
149 ************************************************************ 165,732
150 ************************************************************ 165,772
151 ************************************************************ 165,732
152 ************************************************************ 165,490
153 ************************************************************ 165,176
154 ************************************************************ 164,654
155 *********************************************************** 164,062
156 *********************************************************** 163,273
157 *********************************************************** 162,410
158 ********************************************************** 161,354
159 ********************************************************** 160,236
160 ********************************************************** 158,923
161 ********************************************************* 157,554
162 ******************************************************** 156,004
163 ******************************************************** 154,397
164 ******************************************************* 152,617
165 ******************************************************* 150,794
166 ****************************************************** 148,800
167 ***************************************************** 146,771
168 **************************************************** 144,587
169 **************************************************** 142,370
170 *************************************************** 140,008
171 ************************************************** 137,629
172 ************************************************* 135,109
173 ************************************************ 132,581
174 *********************************************** 129,930
175 ********************************************** 127,274
176 ********************************************* 124,507
177 ******************************************** 121,751
178 ******************************************* 118,889
179 ****************************************** 116,048
180 ***************************************** 113,119
181 **************************************** 110,215
182 *************************************** 107,235
183 ************************************** 104,295
184 ************************************* 101,285
185 ************************************ 98,324
186 ********************************** 95,311
187 ********************************* 92,350
188 ******************************** 89,348
189 ******************************* 86,412
190 ****************************** 83,440
191 ***************************** 80,542
192 **************************** 77,624
193 *************************** 74,781
194 ************************** 71,928
195 ************************* 69,161
196 ************************ 66,388
197 *********************** 63,706
198 ********************** 61,031
199 ********************* 58,446
200 ******************** 55,875
201 ******************* 53,402
202 ****************** 50,944
203 ****************** 48,586
204 ***************** 46,253
205 **************** 44,016
206 *************** 41,809
207 ************** 39,703
208 ************** 37,625
209 ************* 35,648
210 ************ 33,706
211 ************ 31,860
212 *********** 30,051
213 ********** 28,340
214 ********** 26,663
215 ********* 25,082
216 ********* 23,540
217 ******** 22,087
218 ******* 20,673
219 ******* 19,349
220 ******* 18,059
221 ****** 16,856
222 ****** 15,690
223 ***** 14,603
224 ***** 13,552
225 ***** 12,579
226 **** 11,637
227 **** 10,769
228 **** 9,933
229 *** 9,163
230 *** 8,423
231 *** 7,748
232 *** 7,097
233 ** 6,506
234 ** 5,940
235 ** 5,426
236 ** 4,935
237 ** 4,494
238 * 4,070
239 * 3,692
240 * 3,331
241 * 3,009
242 * 2,702
243 * 2,432
244 * 2,172
245 * 1,945
246 * 1,729
247 * 1,540
248 1,360
249 1,206
250 1,057
251 931
252 811
253 709
254 612
255 532
256 454
257 391
258 331
259 282
260 235
261 199
262 163
263 136
264 110
265 90
266 71
267 58
268 44
269 35
270 26
271 20
272 14
273 11
274 7
275 5
276 3
277 2
278 1
279 1
Pairs Analysis
--------------
1 Sequence of 6 44 Eg 1 2 3 4 5 6
2 Sequences of 3 946 Eg 1 2 3 8 9 10
1 Sequence of 5 1,892 Eg 1 3 4 5 6 7
1 Sequence of 4, 1 Sequence of 2 1,892 Eg 1 2 3 4 8 9
3 Sequences of 2 13,244 Eg 1 2 5 6 7 8
1 Sequence of 4 with two singles 39,732 Eg 1 3 4 5 6 8
1 sequence of 2, 1 of 3 and one single 79,464 Eg 1 2 4 6 7 8
2 sequences of 2 and 2 singles 814,506 Eg 1 2 5 6 9 10
3 singles, one sequence of 3 543,004 Eg 1 3 5 7 8 9
4 singles, one sequence of 2 5,430,040 Eg 1 2 4 6 8 10
6 singles 7,059,052 Eg 1 3 5 7 9 11
The point of this is that lots of intuitively unlikely events are actually
quite likely. The other point is that all of this information is not
helpful.
Picking 165,772 tickets with a sum of 150 is no better than picking an
equivalent number of tickets out ouf a hat. 150 as a sum is more likely than
any other sum simply because there are more ways of generating it, but all
tickets are equally likely.
OBTW This information is brought to you free of charge. :-)
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Mike H. (Software Sans Frontieres) PGP:818C97EB75366540 8A27D2AB8E7482CB
Umail 1.50 from ftp.demon.co.uk:/pub/ibmpc/umail,/pub/ibmpc/windows/umail
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