On this edition of Mythbusters we ask if "there are doubles, threes and fours with a greater chance than other simple ones."
(well, maybe we ain't Mythbusters, but let's see what we can do to solve this one)
I'm going to use a 4/35 game (4 balls drawn of a possible 35). In a 4 ball game there are 6 possible positions in which a double can hit. Charted it looks like so...
N1 |
N2 |
12 |
13 |
14 |
23 |
24 |
34 |
1 |
2 |
528 |
0 |
0 |
0 |
0 |
0 |
1 |
3 |
496 |
32 |
0 |
0 |
0 |
0 |
1 |
4 |
465 |
62 |
1 |
0 |
0 |
0 |
1 |
5 |
435 |
90 |
3 |
0 |
0 |
0 |
1 |
6 |
406 |
116 |
6 |
0 |
0 |
0 |
1 |
7 |
378 |
140 |
10 |
0 |
0 |
0 |
1 |
8 |
351 |
162 |
15 |
0 |
0 |
0 |
1 |
9 |
325 |
182 |
21 |
0 |
0 |
0 |
1 |
10 |
300 |
200 |
28 |
0 |
0 |
0 |
1 |
11 |
276 |
216 |
36 |
0 |
0 |
0 |
1 |
12 |
253 |
230 |
45 |
0 |
0 |
0 |
1 |
13 |
231 |
242 |
55 |
0 |
0 |
0 |
1 |
14 |
210 |
252 |
66 |
0 |
0 |
0 |
1 |
15 |
190 |
260 |
78 |
0 |
0 |
0 |
1 |
16 |
171 |
266 |
91 |
0 |
0 |
0 |
1 |
17 |
153 |
270 |
105 |
0 |
0 |
0 |
1 |
18 |
136 |
272 |
120 |
0 |
0 |
0 |
1 |
19 |
120 |
272 |
136 |
0 |
0 |
0 |
1 |
20 |
105 |
270 |
153 |
0 |
0 |
0 |
1 |
21 |
91 |
266 |
171 |
0 |
0 |
0 |
1 |
22 |
78 |
260 |
190 |
0 |
0 |
0 |
1 |
23 |
66 |
252 |
210 |
0 |
0 |
0 |
1 |
24 |
55 |
242 |
231 |
0 |
0 |
0 |
1 |
25 |
45 |
230 |
253 |
0 |
0 |
0 |
1 |
26 |
36 |
216 |
276 |
0 |
0 |
0 |
1 |
27 |
28 |
200 |
300 |
0 |
0 |
0 |
1 |
28 |
21 |
182 |
325 |
0 |
0 |
0 |
1 |
29 |
15 |
162 |
351 |
0 |
0 |
0 |
1 |
30 |
10 |
140 |
378 |
0 |
0 |
0 |
1 |
31 |
6 |
116 |
406 |
0 |
0 |
0 |
1 |
32 |
3 |
90 |
435 |
0 |
0 |
0 |
1 |
33 |
1 |
62 |
465 |
0 |
0 |
0 |
1 |
34 |
0 |
32 |
496 |
0 |
0 |
0 |
1 |
35 |
0 |
0 |
528 |
0 |
0 |
0 |
So what we see is there are on 528 possible ways any pair can hit. If you add all the position totals from 12 to 34, each row produces 528 results from pair 1,2 to pair 34,35.
Since every pair has the same 528 possibles, none has an advantage. We could play with our brain and convince ourselves there are more ones than twos and more twos than threes, etc., but even that's a false assumption since each number in the matrix (between 1 and 35) appears 5984 times.
What is true that some pairs, like some numbers, do hit better in some positions like 14, 15....
14 |
15 |
190 |
0 |
0 |
260 |
0 |
78 |
14 |
16 |
171 |
19 |
0 |
247 |
13 |
78 |
14 |
17 |
153 |
36 |
1 |
234 |
26 |
78 |
14 |
18 |
136 |
51 |
3 |
221 |
39 |
78 |
14 |
19 |
120 |
64 |
6 |
208 |
52 |
78 |
14 |
20 |
105 |
75 |
10 |
195 |
65 |
78 |
14 |
21 |
91 |
84 |
15 |
182 |
78 |
78 |
14 |
22 |
78 |
91 |
21 |
169 |
91 |
78 |
14 |
23 |
66 |
96 |
28 |
156 |
104 |
78 |
14 |
24 |
55 |
99 |
36 |
143 |
117 |
78 |
14 |
25 |
45 |
100 |
45 |
130 |
130 |
78 |
14 |
26 |
36 |
99 |
55 |
117 |
143 |
78 |
14 |
27 |
28 |
96 |
66 |
104 |
156 |
78 |
14 |
28 |
21 |
91 |
78 |
91 |
169 |
78 |
14 |
29 |
15 |
84 |
91 |
78 |
182 |
78 |
14 |
30 |
10 |
75 |
105 |
65 |
195 |
78 |
14 |
31 |
6 |
64 |
120 |
52 |
208 |
78 |
14 |
32 |
3 |
51 |
136 |
39 |
221 |
78 |
14 |
33 |
1 |
36 |
153 |
26 |
234 |
78 |
14 |
34 |
0 |
19 |
171 |
13 |
247 |
78 |
14 |
35 |
0 |
0 |
190 |
0 |
260 |
78 |
Here pair 14, 15 hit best in positions 2 and 3 until about 14,26/27 when it moves to the second and fourth positions.
dr sans point seems to be (I think) is to play pairs that hit as equally as possible across as many positions as possible. No pair hits equally across all positions, but some like 14, 25 play well in all positions.
And there are 6544 sets of triple, with 32 hits per set. Triple you only have four positions 123, 124, 134, 234, and they tend to bunch up in some positions and disperse fairly even in others like these....
9 |
17 |
18 |
17 |
0 |
7 |
8 |
9 |
17 |
19 |
16 |
1 |
7 |
8 |
9 |
17 |
20 |
15 |
2 |
7 |
8 |
9 |
17 |
21 |
14 |
3 |
7 |
8 |
9 |
17 |
22 |
13 |
4 |
7 |
8 |
9 |
17 |
23 |
12 |
5 |
7 |
8 |
9 |
17 |
24 |
11 |
6 |
7 |
8 |
9 |
17 |
25 |
10 |
7 |
7 |
8 |
9 |
17 |
26 |
9 |
8 |
7 |
8 |
9 |
17 |
27 |
8 |
9 |
7 |
8 |
9 |
17 |
28 |
7 |
10 |
7 |
8 |
9 |
17 |
29 |
6 |
11 |
7 |
8 |
9 |
17 |
30 |
5 |
12 |
7 |
8 |
9 |
17 |
31 |
4 |
13 |
7 |
8 |
9 |
17 |
32 |
3 |
14 |
7 |
8 |
9 |
17 |
33 |
2 |
15 |
7 |
8 |
9 |
17 |
34 |
1 |
16 |
7 |
8 |
9 |
17 |
35 |
0 |
17 |
7 |
8 |
9 |
18 |
19 |
16 |
0 |
8 |
8 |
9 |
18 |
20 |
15 |
1 |
8 |
8 |
9 |
18 |
21 |
14 |
2 |
8 |
8 |
9 |
18 |
22 |
13 |
3 |
8 |
8 |
9 |
18 |
23 |
12 |
4 |
8 |
8 |
9 |
18 |
24 |
11 |
5 |
8 |
8 |
9 |
18 |
25 |
10 |
6 |
8 |
8 |
9 |
18 |
26 |
9 |
7 |
8 |
8 |
9 |
18 |
27 |
8 |
8 |
8 |
8 |
9 |
18 |
28 |
7 |
9 |
8 |
8 |
9 |
18 |
29 |
6 |
10 |
8 |
8 |
9 |
18 |
30 |
5 |
11 |
8 |
8 |
9 |
18 |
31 |
4 |
12 |
8 |
8 |
9 |
18 |
32 |
3 |
13 |
8 |
8 |
9 |
18 |
33 |
2 |
14 |
8 |
8 |
9 |
18 |
34 |
1 |
15 |
8 |
8 |
9 |
18 |
35 |
0 |
16 |
8 |
8 |
The cool thing about triples, unlike pairs, is 9, 18, 27 has an equal chance of hitting in any position.
I'd think it's safe to say if we play pairs or triples which hit in the most possible positions we have a better chance of winning something than if we stick to playing pairs or triples that only hit in one/two positions.
G