
Originally Posted by
sevenshooter
Despite having won every live session played using this "new" system of mine, Mattman's simulations have shown it to be a long-term loser. Imagine that. I do thank the Mattman for all the hard work he put into taking a good, serious look at this.
I am posting the system below for your entertainment:
Premise: A series of three wins (WWW) statistically occurs once in eight trials.
1) WWW
2) WWL
3) WLL
4) WLW
5) LLL
6) LLW
7) LWW
8) LWL
One win: WWW WWL WLL WLW LLL LLW LWW LWL
"Premise: A series of three wins (WWW) statistically occurs once in eight trials." This is a very general statement and needs further clarification because the number of trials needs to be considered.
#1. WWW only happens 1 in 8 (fair coin) when the number of trials is EXACTLY 3 just as listed above.
Groups of 3.
That would make the number of trials to be 24.
a simulation shows this to be true.
OR
#2. WWW only happens 1 in 8 when WWW can be overlapping.
WWWWL would be counted as 2 streaks of length 3 for W.
WWLWWWLWWL... this sequence also has 8 groups of 3 trials. But they are overlapping groups. ( 1-3, 2-4, 3-5 etc) This makes for an average of 10 trials to see a run of length 3 using this counting method.
a simulation also shows this to be true.
Individual Gamblers do not bet like method #2. Team play would.
And most will not bet for exactly 3 groups at a time either as in #1.
So what IS the average for a run of length 3?
Your system bets UNTIL a WWW happens.This is how most gamblers play. We play a series of events. I think most Gamblers are more interested in the actual number of bets needed to be made in order to win 1 time.
Example:
How many failures until 3 wins in a row. (a run of 3) for a fair coin.
The math for the average, not the median, is P^-3 + P^-2 + P^-1 = 14. (P = 0.5)
NOt 8.
NOt even close to 1 in 8.
The formula 1/0.5^3 = 8 does not work for a streak or run of length 3 where N, the number of trials is larger than 3. It is only for 3 consecutive trials at a time.
One should avoid creating systems of play based on the law of averages... insist on knowing the actual distribution. The law of averages is for the long run, not for the short, run where every gambler plays.
A probability distribution shows everything you need to know to make better decisions on what to expect in the short run and long run.

Originally Posted by
sevenshooter
Yet as the order of events changes, it is possible for three wins to come around more than what is statistically expected:
Two wins: WWW LLL LWW WLL LWL WWL LLW WLW
Three wins: LWW WLL WLW WWL WWW LLW WLW LLL
Of course. Now you are talking about distributions. How events play out. How many streaks in N trials.
Good stuff.
One problem with streaks of any length is the wait time or how long a run of any length can disappear in an average distribution.
Check out this webpage for more on streaks and expected number of streaks in N trials.
http://www.pulcinientertainment.com/...tor-enter.html
This page still only talks about averages, it does not show the math, very complicated I might add, for me at least, or even simulations for an actual distribution of the number of streaks in N trials. But there are free software that will run these type of simulations available.
How about some simulation distributions for a fair coin toss, field bet at Craps and Banker Baccarat bet for a run of length 3.
1 million streaks of length 3 were tallied along with the number of trials needed for a success.
Fair Coin Toss: Average = 14. median 10. (50% or less)
Code:
flips freq freq/100----------------------
3 125534 12.55%
4 62335 6.23%
5 62285 6.23%
6 62220 6.22%
7 54748 5.47%
8 50992 5.10%
9 47144 4.71%
10 43265 4.33%
11 39446 3.94%
12 36302 3.63%
13 33312 3.33%
14 30773 3.08%
15 28211 2.82%
16 26001 2.60%
17 23781 2.38%
18 22005 2.20%
19 20341 2.03%
20 18672 1.87%
21 17089 1.71%
22 15717 1.57%
23 14561 1.46%
24 13397 1.34%
25 12231 1.22%
26 11096 1.11%
27 10354 1.04%
28 9495 0.95%
29 8667 0.87%
30 7866 0.79%
31 7617 0.76%
32 6867 0.69%
33 6208 0.62%
34 5725 0.57%
35 5142 0.51%
36 4917 0.49%
37 4608 0.46%
38 4105 0.41%
39 3768 0.38%
40 3493 0.35%
41 3290 0.33%
42 2940 0.29%
43 2676 0.27%
44 2541 0.25%
45 2186 0.22%
46 2131 0.21%
47 1953 0.20%
48 1771 0.18%
49 1605 0.16%
50 1395 0.14%
51 1395 0.14%
52 1313 0.13%
53 1217 0.12%
54 1043 0.10%
55 962 0.10%
56 875 0.09%
57 807 0.08%
58 772 0.08%
59 704 0.07%
60 661 0.07%
61 606 0.06%
62 543 0.05%
63 544 0.05%
64 473 0.05%
65 437 0.04%
66 410 0.04%
67 376 0.04%
68 323 0.03%
69 315 0.03%
70 267 0.03%
71 262 0.03%
72 247 0.02%
73 204 0.02%
74 188 0.02%
75 163 0.02%
76 160 0.02%
77 158 0.02%
78 149 0.01%
79 167 0.02%
80 120 0.01%
81 100 0.01%
82 118 0.01%
83 102 0.01%
84 72 0.01%
85 79 0.01%
86 66 0.01%
87 82 0.01%
88 66 0.01%
89 54 0.01%
90 39 0.00%
91 44 0.00%
92 32 0.00%
93 32 0.00%
94 46 0.00%
95 42 0.00%
96 30 0.00%
97 33 0.00%
98 33 0.00%
99 24 0.00%
100 23 0.00%
101 16 0.00%
102 14 0.00%
103 16 0.00%
104 14 0.00%
105 16 0.00%
106 13 0.00%
107 8 0.00%
108 11 0.00%
109 8 0.00%
110 10 0.00%
111 6 0.00%
112 5 0.00%
113 8 0.00%
114 6 0.00%
115 9 0.00%
116 6 0.00%
117 10 0.00%
118 5 0.00%
119 4 0.00%
120 4 0.00%
121 3 0.00%
122 5 0.00%
123 4 0.00%
124 1 0.00%
125 4 0.00%
126 2 0.00%
127 3 0.00%
128 3 0.00%
129 3 0.00%
130 0
131 1 0.00%
132 2 0.00%
133 1 0.00%
134 1 0.00%
135 1 0.00%
136 1 0.00%
137 1 0.00%
138 2 0.00%
139 1 0.00%
140 3 0.00%
141 1 0.00%
142 4 0.00%
143 0
144 1 0.00%
145 1 0.00%
146 0
147 0
148 0
149 0
150 0
151 1 0.00%
152 0
153 0
154 0
155 0
156 1 0.00%
157 0
158 0
159 0
160 0
161 0
162 0
163 0
164 0
165 0
166 0
167 1 0.00%
168 0
169 0
170 0
171 0
172 1 0.00%
173 0
174 1 0.00%
175 0
176 0
177 0
178 0
179 0
180 0
181 0
182 0
183 0
184 0
185 0
186 0
187 0
188 0
189 0
190 0
191 0
192 0
193 0
194 1 0.00%
grouped data
items: 1000000
minimum value: 3.00
first quartile: 5.00
median: 10.00
third quartile: 19.00
maximum value: 194.00
mean value: 13.99
midrange: 98.50
range: 191.00
interquartile range: 14.00
mean abs deviation: 8.75
sample variance (n): 141.66
sample variance (n-1): 141.66
sample std dev (n): 11.90
sample std dev (n-1): 11.90
Field Bet Craps: Average = 18.7. median 14. (50% or less)
Code:
rolls freq freq/100
3 87988 8.80%
4 48875 4.89%
5 48902 4.89%
6 48618 4.86%
7 44427 4.44%
8 42454 4.25%
9 40080 4.01%
10 37533 3.75%
11 34987 3.50%
12 33067 3.31%
13 31085 3.11%
14 29197 2.92%
15 27529 2.75%
16 26080 2.61%
17 24520 2.45%
18 22994 2.30%
19 21843 2.18%
20 20504 2.05%
21 19208 1.92%
22 18075 1.81%
23 16869 1.69%
24 16011 1.60%
25 15287 1.53%
26 14231 1.42%
27 13443 1.34%
28 12686 1.27%
29 11828 1.18%
30 11385 1.14%
31 10611 1.06%
32 9979 1.00%
33 9435 0.94%
34 8749 0.87%
35 8172 0.82%
36 7843 0.78%
37 7376 0.74%
38 6834 0.68%
39 6552 0.66%
40 6139 0.61%
41 5689 0.57%
42 5447 0.54%
43 5138 0.51%
44 4798 0.48%
45 4590 0.46%
46 4284 0.43%
47 3957 0.40%
48 3768 0.38%
49 3550 0.36%
50 3446 0.34%
51 3167 0.32%
52 2993 0.30%
53 2817 0.28%
54 2725 0.27%
55 2514 0.25%
56 2354 0.24%
57 2114 0.21%
58 2126 0.21%
59 2011 0.20%
60 1822 0.18%
61 1691 0.17%
62 1616 0.16%
63 1596 0.16%
64 1417 0.14%
65 1268 0.13%
66 1308 0.13%
67 1191 0.12%
68 1166 0.12%
69 1048 0.10%
70 985 0.10%
71 968 0.10%
72 888 0.09%
73 837 0.08%
74 771 0.08%
75 757 0.08%
76 660 0.07%
77 670 0.07%
78 582 0.06%
79 619 0.06%
80 521 0.05%
81 518 0.05%
82 467 0.05%
83 439 0.04%
84 421 0.04%
85 421 0.04%
86 401 0.04%
87 352 0.04%
88 345 0.03%
89 287 0.03%
90 278 0.03%
91 304 0.03%
92 290 0.03%
93 256 0.03%
94 243 0.02%
95 210 0.02%
96 221 0.02%
97 163 0.02%
98 204 0.02%
99 147 0.01%
100 150 0.02%
101 139 0.01%
102 153 0.02%
103 135 0.01%
104 122 0.01%
105 129 0.01%
106 119 0.01%
107 120 0.01%
108 76 0.01%
109 106 0.01%
110 86 0.01%
111 83 0.01%
112 93 0.01%
113 76 0.01%
114 64 0.01%
115 58 0.01%
116 65 0.01%
117 51 0.01%
118 72 0.01%
119 51 0.01%
120 45 0.00%
121 47 0.00%
122 45 0.00%
123 32 0.00%
124 31 0.00%
125 35 0.00%
126 26 0.00%
127 31 0.00%
128 22 0.00%
129 32 0.00%
130 32 0.00%
131 25 0.00%
132 23 0.00%
133 28 0.00%
134 18 0.00%
135 22 0.00%
136 23 0.00%
137 15 0.00%
138 14 0.00%
139 17 0.00%
140 12 0.00%
141 20 0.00%
142 12 0.00%
143 10 0.00%
144 9 0.00%
145 12 0.00%
146 15 0.00%
147 10 0.00%
148 12 0.00%
149 9 0.00%
150 10 0.00%
151 8 0.00%
152 7 0.00%
153 9 0.00%
154 7 0.00%
155 6 0.00%
156 9 0.00%
157 5 0.00%
158 4 0.00%
159 2 0.00%
160 4 0.00%
161 2 0.00%
162 4 0.00%
163 5 0.00%
164 2 0.00%
165 3 0.00%
166 3 0.00%
167 4 0.00%
168 5 0.00%
169 2 0.00%
170 1 0.00%
171 0
172 3 0.00%
173 2 0.00%
174 2 0.00%
175 2 0.00%
176 1 0.00%
177 1 0.00%
178 2 0.00%
179 3 0.00%
180 0
181 0
182 2 0.00%
183 1 0.00%
184 0
185 1 0.00%
186 2 0.00%
187 1 0.00%
188 1 0.00%
189 1 0.00%
190 0
191 1 0.00%
192 0
193 0
194 0
195 0
196 0
197 1 0.00%
198 2 0.00%
199 0
200 0
201 0
202 0
203 0
204 0
205 0
206 1 0.00%
207 1 0.00%
208 0
209 0
210 0
211 0
212 0
213 1 0.00%
214 0
215 0
216 0
217 0
218 0
219 0
220 0
221 0
222 0
223 0
224 0
225 0
226 0
227 0
228 0
229 0
230 0
231 0
232 0
233 0
234 0
235 1 0.00%
236 0
237 0
238 0
239 0
240 0
241 0
242 0
243 0
244 0
245 0
246 0
247 0
248 0
249 0
250 0
251 0
252 0
253 0
254 0
255 0
256 0
257 0
258 0
259 0
260 0
261 0
262 0
263 0
264 0
265 0
266 0
267 0
268 0
269 0
270 1 0.00%
grouped data
items: 1000000
minimum value: 3.00
first quartile: 7.00
median: 14.00
third quartile: 25.00
maximum value: 270.00
mean value: 18.67
midrange: 136.50
range: 267.00
interquartile range: 18.00
mean abs deviation: 12.19
sample variance (n): 273.97
sample variance (n-1): 273.97
sample std dev (n): 16.55
sample std dev (n-1): 16.55 Banker: Average = 13.55. median 10. (50% or less)
Code:
games freq freq/100
3 130393 13.04%
4 64378 6.44%
5 64550 6.46%
6 64176 6.42%
7 55725 5.57%
8 52206 5.22%
9 47426 4.74%
10 43473 4.35%
11 40011 4.00%
12 36154 3.62%
13 33641 3.36%
14 30458 3.05%
15 28152 2.82%
16 26001 2.60%
17 23788 2.38%
18 21657 2.17%
19 19835 1.98%
20 18222 1.82%
21 16855 1.69%
22 15340 1.53%
23 13861 1.39%
24 12846 1.28%
25 11885 1.19%
26 10737 1.07%
27 9800 0.98%
28 8985 0.90%
29 8303 0.83%
30 7568 0.76%
31 6989 0.70%
32 6484 0.65%
33 5831 0.58%
34 5372 0.54%
35 4913 0.49%
36 4507 0.45%
37 4137 0.41%
38 3954 0.40%
39 3578 0.36%
40 3135 0.31%
41 2800 0.28%
42 2696 0.27%
43 2366 0.24%
44 2255 0.23%
45 1981 0.20%
46 1872 0.19%
47 1670 0.17%
48 1603 0.16%
49 1485 0.15%
50 1300 0.13%
51 1237 0.12%
52 1123 0.11%
53 1046 0.10%
54 910 0.09%
55 912 0.09%
56 786 0.08%
57 701 0.07%
58 697 0.07%
59 602 0.06%
60 559 0.06%
61 532 0.05%
62 482 0.05%
63 423 0.04%
64 380 0.04%
65 359 0.04%
66 320 0.03%
67 309 0.03%
68 269 0.03%
69 244 0.02%
70 212 0.02%
71 202 0.02%
72 215 0.02%
73 166 0.02%
74 161 0.02%
75 141 0.01%
76 144 0.01%
77 127 0.01%
78 112 0.01%
79 103 0.01%
80 99 0.01%
81 75 0.01%
82 79 0.01%
83 59 0.01%
84 80 0.01%
85 82 0.01%
86 69 0.01%
87 47 0.00%
88 51 0.01%
89 46 0.00%
90 51 0.01%
91 34 0.00%
92 43 0.00%
93 26 0.00%
94 30 0.00%
95 23 0.00%
96 17 0.00%
97 22 0.00%
98 23 0.00%
99 22 0.00%
100 11 0.00%
101 12 0.00%
102 16 0.00%
103 16 0.00%
104 20 0.00%
105 8 0.00%
106 9 0.00%
107 8 0.00%
108 10 0.00%
109 5 0.00%
110 6 0.00%
111 7 0.00%
112 6 0.00%
113 2 0.00%
114 5 0.00%
115 3 0.00%
116 2 0.00%
117 4 0.00%
118 1 0.00%
119 6 0.00%
120 5 0.00%
121 7 0.00%
122 0
123 2 0.00%
124 1 0.00%
125 1 0.00%
126 2 0.00%
127 0
128 2 0.00%
129 2 0.00%
130 2 0.00%
131 0
132 0
133 3 0.00%
134 2 0.00%
135 2 0.00%
136 1 0.00%
137 1 0.00%
138 1 0.00%
139 0
140 0
141 0
142 0
143 0
144 0
145 0
146 0
147 0
148 0
149 0
150 0
151 0
152 1 0.00%
153 0
154 0
155 0
156 1 0.00%
157 0
158 0
159 0
160 0
161 0
162 0
163 0
164 0
165 0
166 0
167 0
168 0
169 0
170 0
171 0
172 0
173 0
174 0
175 0
176 0
177 0
178 1 0.00%
cumulative
------------------------------------------------
3 130393 13.04%
4 194771 19.48%
5 259321 25.93%
6 323497 32.35%
7 379222 37.92%
8 431428 43.14%
9 478854 47.89%
10 522327 52.23%
11 562338 56.23%
12 598492 59.85%
13 632133 63.21%
14 662591 66.26%
15 690743 69.07%
16 716744 71.67%
17 740532 74.05%
18 762189 76.22%
19 782024 78.20%
20 800246 80.02%
21 817101 81.71%
22 832441 83.24%
23 846302 84.63%
24 859148 85.91%
25 871033 87.10%
26 881770 88.18%
27 891570 89.16%
28 900555 90.06%
29 908858 90.89%
30 916426 91.64%
31 923415 92.34%
32 929899 92.99%
33 935730 93.57%
34 941102 94.11%
35 946015 94.60%
36 950522 95.05%
37 954659 95.47%
38 958613 95.86%
39 962191 96.22%
40 965326 96.53%
41 968126 96.81%
42 970822 97.08%
43 973188 97.32%
44 975443 97.54%
45 977424 97.74%
46 979296 97.93%
47 980966 98.10%
48 982569 98.26%
49 984054 98.41%
50 985354 98.54%
51 986591 98.66%
52 987714 98.77%
53 988760 98.88%
54 989670 98.97%
55 990582 99.06%
56 991368 99.14%
57 992069 99.21%
58 992766 99.28%
59 993368 99.34%
60 993927 99.39%
61 994459 99.45%
62 994941 99.49%
63 995364 99.54%
64 995744 99.57%
65 996103 99.61%
66 996423 99.64%
67 996732 99.67%
68 997001 99.70%
69 997245 99.72%
70 997457 99.75%
71 997659 99.77%
72 997874 99.79%
73 998040 99.80%
74 998201 99.82%
75 998342 99.83%
76 998486 99.85%
77 998613 99.86%
78 998725 99.87%
79 998828 99.88%
80 998927 99.89%
81 999002 99.90%
82 999081 99.91%
83 999140 99.91%
84 999220 99.92%
85 999302 99.93%
86 999371 99.94%
87 999418 99.94%
88 999469 99.95%
89 999515 99.95%
90 999566 99.96%
91 999600 99.96%
92 999643 99.96%
93 999669 99.97%
94 999699 99.97%
95 999722 99.97%
96 999739 99.97%
97 999761 99.98%
98 999784 99.98%
99 999806 99.98%
100 999817 99.98%
101 999829 99.98%
102 999845 99.98%
103 999861 99.99%
104 999881 99.99%
105 999889 99.99%
106 999898 99.99%
107 999906 99.99%
108 999916 99.99%
109 999921 99.99%
110 999927 99.99%
111 999934 99.99%
112 999940 99.99%
113 999942 99.99%
114 999947 99.99%
115 999950 100.00%
116 999952 100.00%
117 999956 100.00%
118 999957 100.00%
119 999963 100.00%
120 999968 100.00%
121 999975 100.00%
122 999975 100.00%
123 999977 100.00%
124 999978 100.00%
125 999979 100.00%
126 999981 100.00%
127 999981 100.00%
128 999983 100.00%
129 999985 100.00%
130 999987 100.00%
131 999987 100.00%
132 999987 100.00%
133 999990 100.00%
134 999992 100.00%
135 999994 100.00%
136 999995 100.00%
137 999996 100.00%
138 999997 100.00%
139 999997 100.00%
140 999997 100.00%
141 999997 100.00%
142 999997 100.00%
143 999997 100.00%
144 999997 100.00%
145 999997 100.00%
146 999997 100.00%
147 999997 100.00%
148 999997 100.00%
149 999997 100.00%
150 999997 100.00%
151 999997 100.00%
152 999998 100.00%
153 999998 100.00%
154 999998 100.00%
155 999998 100.00%
156 999999 100.00%
157 999999 100.00%
158 999999 100.00%
159 999999 100.00%
160 999999 100.00%
161 999999 100.00%
162 999999 100.00%
163 999999 100.00%
164 999999 100.00%
165 999999 100.00%
166 999999 100.00%
167 999999 100.00%
168 999999 100.00%
169 999999 100.00%
170 999999 100.00%
171 999999 100.00%
172 999999 100.00%
173 999999 100.00%
174 999999 100.00%
175 999999 100.00%
176 999999 100.00%
177 999999 100.00%
178 1000000 100.00%
grouped data
items: 1000000
minimum value: 3.00
first quartile: 5.00
median: 10.00
third quartile: 18.00
maximum value: 178.00
mean value: 13.52
midrange: 90.50
range: 175.00
interquartile range: 13.00
mean abs deviation: 8.42
sample variance (n): 130.85
sample variance (n-1): 130.85
sample std dev (n): 11.44
sample std dev (n-1): 11.44 Interested in running your own simulation for streaks?
Google: Peanut software and the Winstats package.
It is free to own and use, no malware and I use it a lot to check stuff done in Excel and visa versa.
Enjoy!
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