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Reading the draws and working out what chance predicts.

LotteryOracle · F-43

Chance Detective

Three simulated machines. Which would you investigate?

Main drum: 6 of 60. Bonus balls are excluded.

2026-09-23 · UTC400 DrawsSimulated evidence

Every machine here is simulated. No real lottery is being accused or predicted.

Machine A

Read the data table

Number	Observed	Expected
1	31	40
2	34	40
3	44	40
4	48	40
5	40	40
6	40	40
7	43	40
8	41	40
9	55	40
10	51	40
11	42	40
12	35	40
13	35	40
14	45	40
15	42	40
16	33	40
17	38	40
18	39	40
19	41	40
20	37	40
21	34	40
22	33	40
23	43	40
24	32	40
25	31	40
26	40	40
27	41	40
28	38	40
29	41	40
30	39	40
31	45	40
32	39	40
33	46	40
34	45	40
35	38	40
36	32	40
37	31	40
38	43	40
39	42	40
40	39	40
41	44	40
42	47	40
43	37	40
44	41	40
45	48	40
46	36	40
47	48	40
48	38	40
49	33	40
50	40	40
51	50	40
52	38	40
53	36	40
54	50	40
55	40	40
56	38	40
57	40	40
58	42	40
59	28	40
60	40	40

Your judgmentInvestigateInsufficient evidence

Machine B

Read the data table

Number	Observed	Expected
1	6	40
2	8	40
3	11	40
4	152	40
5	11	40
6	136	40
7	14	40
8	9	40
9	9	40
10	8	40
11	11	40
12	8	40
13	14	40
14	156	40
15	5	40
16	168	40
17	16	40
18	14	40
19	17	40
20	11	40
21	16	40
22	11	40
23	9	40
24	159	40
25	10	40
26	158	40
27	11	40
28	12	40
29	14	40
30	14	40
31	10	40
32	9	40
33	11	40
34	151	40
35	14	40
36	159	40
37	16	40
38	9	40
39	12	40
40	11	40
41	14	40
42	9	40
43	8	40
44	159	40
45	12	40
46	141	40
47	22	40
48	14	40
49	13	40
50	14	40
51	9	40
52	15	40
53	11	40
54	161	40
55	9	40
56	150	40
57	13	40
58	11	40
59	9	40
60	6	40

Your judgmentInvestigateInsufficient evidence

Machine C

Read the data table

Number	Observed	Expected
1	29	40
2	50	40
3	30	40
4	42	40
5	40	40
6	32	40
7	41	40
8	49	40
9	46	40
10	38	40
11	43	40
12	51	40
13	23	40
14	34	40
15	39	40
16	45	40
17	50	40
18	34	40
19	40	40
20	40	40
21	43	40
22	36	40
23	49	40
24	41	40
25	36	40
26	41	40
27	41	40
28	35	40
29	31	40
30	46	40
31	48	40
32	44	40
33	39	40
34	30	40
35	45	40
36	47	40
37	46	40
38	44	40
39	33	40
40	41	40
41	42	40
42	49	40
43	42	40
44	33	40
45	27	40
46	36	40
47	46	40
48	28	40
49	32	40
50	41	40
51	39	40
52	41	40
53	35	40
54	49	40
55	34	40
56	45	40
57	54	40
58	41	40
59	41	40
60	33	40

Your judgmentInvestigateInsufficient evidence

Make a judgment for all three machines before the reveal.

199 independent fair histories; 3 comparisons. · chance-detective-v1 · seed 3328425753

The maths, in plain language

One fixed frequency statistic is tested per machine. Independent fair histories use the same sample size and draw format. Add-one Monte Carlo p-values are corrected across all three machines with Bonferroni. The sample is fixed before testing; a non-alert is not a certificate of fairness.

E = Dk/N; Q = Σ(O − E)²/E; p = (1 + #{Qnull ≥ Q})/(R + 1); padj = min(1, 3p)

NIST · Binomial · NIST · Bonferroni

The story behind it

Three simulated machines. Which would you investigate?

Knowing the generator and detecting it from a short record are different things. A quiet test cannot certify fairness.

Chance Detective

Three simulated machines. Which would you investigate?

Main drum: 6 of 60. Bonus balls are excluded.

2026-09-23 · UTC400 DrawsSimulated evidence

Every machine here is simulated. No real lottery is being accused or predicted.

Machine A

Read the data table

Number	Observed	Expected
1	31	40
2	34	40
3	44	40
4	48	40
5	40	40
6	40	40
7	43	40
8	41	40
9	55	40
10	51	40
11	42	40
12	35	40
13	35	40
14	45	40
15	42	40
16	33	40
17	38	40
18	39	40
19	41	40
20	37	40
21	34	40
22	33	40
23	43	40
24	32	40
25	31	40
26	40	40
27	41	40
28	38	40
29	41	40
30	39	40
31	45	40
32	39	40
33	46	40
34	45	40
35	38	40
36	32	40
37	31	40
38	43	40
39	42	40
40	39	40
41	44	40
42	47	40
43	37	40
44	41	40
45	48	40
46	36	40
47	48	40
48	38	40
49	33	40
50	40	40
51	50	40
52	38	40
53	36	40
54	50	40
55	40	40
56	38	40
57	40	40
58	42	40
59	28	40
60	40	40

Your judgmentInvestigateInsufficient evidence

Machine B

Read the data table

Number	Observed	Expected
1	6	40
2	8	40
3	11	40
4	152	40
5	11	40
6	136	40
7	14	40
8	9	40
9	9	40
10	8	40
11	11	40
12	8	40
13	14	40
14	156	40
15	5	40
16	168	40
17	16	40
18	14	40
19	17	40
20	11	40
21	16	40
22	11	40
23	9	40
24	159	40
25	10	40
26	158	40
27	11	40
28	12	40
29	14	40
30	14	40
31	10	40
32	9	40
33	11	40
34	151	40
35	14	40
36	159	40
37	16	40
38	9	40
39	12	40
40	11	40
41	14	40
42	9	40
43	8	40
44	159	40
45	12	40
46	141	40
47	22	40
48	14	40
49	13	40
50	14	40
51	9	40
52	15	40
53	11	40
54	161	40
55	9	40
56	150	40
57	13	40
58	11	40
59	9	40
60	6	40

Your judgmentInvestigateInsufficient evidence

Machine C

Read the data table

Number	Observed	Expected
1	29	40
2	50	40
3	30	40
4	42	40
5	40	40
6	32	40
7	41	40
8	49	40
9	46	40
10	38	40
11	43	40
12	51	40
13	23	40
14	34	40
15	39	40
16	45	40
17	50	40
18	34	40
19	40	40
20	40	40
21	43	40
22	36	40
23	49	40
24	41	40
25	36	40
26	41	40
27	41	40
28	35	40
29	31	40
30	46	40
31	48	40
32	44	40
33	39	40
34	30	40
35	45	40
36	47	40
37	46	40
38	44	40
39	33	40
40	41	40
41	42	40
42	49	40
43	42	40
44	33	40
45	27	40
46	36	40
47	46	40
48	28	40
49	32	40
50	41	40
51	39	40
52	41	40
53	35	40
54	49	40
55	34	40
56	45	40
57	54	40
58	41	40
59	41	40
60	33	40

Your judgmentInvestigateInsufficient evidence

Make a judgment for all three machines before the reveal.

199 independent fair histories; 3 comparisons. · chance-detective-v1 · seed 3328425753

The maths, in plain language

E = Dk/N; Q = Σ(O − E)²/E; p = (1 + #{Qnull ≥ Q})/(R + 1); padj = min(1, 3p)

NIST · Binomial · NIST · Bonferroni

The story behind it

Three simulated machines. Which would you investigate?

Knowing the generator and detecting it from a short record are different things. A quiet test cannot certify fairness.

Number	Observed	Expected
1	31	40
2	34	40
3	44	40
4	48	40
5	40	40
6	40	40
7	43	40
8	41	40
9	55	40
10	51	40
11	42	40
12	35	40
13	35	40
14	45	40
15	42	40
16	33	40
17	38	40
18	39	40
19	41	40
20	37	40
21	34	40
22	33	40
23	43	40
24	32	40
25	31	40
26	40	40
27	41	40
28	38	40
29	41	40
30	39	40
31	45	40
32	39	40
33	46	40
34	45	40
35	38	40
36	32	40
37	31	40
38	43	40
39	42	40
40	39	40
41	44	40
42	47	40
43	37	40
44	41	40
45	48	40
46	36	40
47	48	40
48	38	40
49	33	40
50	40	40
51	50	40
52	38	40
53	36	40
54	50	40
55	40	40
56	38	40
57	40	40
58	42	40
59	28	40
60	40	40

Number	Observed	Expected
1	6	40
2	8	40
3	11	40
4	152	40
5	11	40
6	136	40
7	14	40
8	9	40
9	9	40
10	8	40
11	11	40
12	8	40
13	14	40
14	156	40
15	5	40
16	168	40
17	16	40
18	14	40
19	17	40
20	11	40
21	16	40
22	11	40
23	9	40
24	159	40
25	10	40
26	158	40
27	11	40
28	12	40
29	14	40
30	14	40
31	10	40
32	9	40
33	11	40
34	151	40
35	14	40
36	159	40
37	16	40
38	9	40
39	12	40
40	11	40
41	14	40
42	9	40
43	8	40
44	159	40
45	12	40
46	141	40
47	22	40
48	14	40
49	13	40
50	14	40
51	9	40
52	15	40
53	11	40
54	161	40
55	9	40
56	150	40
57	13	40
58	11	40
59	9	40
60	6	40

Number	Observed	Expected
1	29	40
2	50	40
3	30	40
4	42	40
5	40	40
6	32	40
7	41	40
8	49	40
9	46	40
10	38	40
11	43	40
12	51	40
13	23	40
14	34	40
15	39	40
16	45	40
17	50	40
18	34	40
19	40	40
20	40	40
21	43	40
22	36	40
23	49	40
24	41	40
25	36	40
26	41	40
27	41	40
28	35	40
29	31	40
30	46	40
31	48	40
32	44	40
33	39	40
34	30	40
35	45	40
36	47	40
37	46	40
38	44	40
39	33	40
40	41	40
41	42	40
42	49	40
43	42	40
44	33	40
45	27	40
46	36	40
47	46	40
48	28	40
49	32	40
50	41	40
51	39	40
52	41	40
53	35	40
54	49	40
55	34	40
56	45	40
57	54	40
58	41	40
59	41	40
60	33	40

Number	Observed	Expected
1	31	40
2	34	40
3	44	40
4	48	40
5	40	40
6	40	40
7	43	40
8	41	40
9	55	40
10	51	40
11	42	40
12	35	40
13	35	40
14	45	40
15	42	40
16	33	40
17	38	40
18	39	40
19	41	40
20	37	40
21	34	40
22	33	40
23	43	40
24	32	40
25	31	40
26	40	40
27	41	40
28	38	40
29	41	40
30	39	40
31	45	40
32	39	40
33	46	40
34	45	40
35	38	40
36	32	40
37	31	40
38	43	40
39	42	40
40	39	40
41	44	40
42	47	40
43	37	40
44	41	40
45	48	40
46	36	40
47	48	40
48	38	40
49	33	40
50	40	40
51	50	40
52	38	40
53	36	40
54	50	40
55	40	40
56	38	40
57	40	40
58	42	40
59	28	40
60	40	40

Number	Observed	Expected
1	6	40
2	8	40
3	11	40
4	152	40
5	11	40
6	136	40
7	14	40
8	9	40
9	9	40
10	8	40
11	11	40
12	8	40
13	14	40
14	156	40
15	5	40
16	168	40
17	16	40
18	14	40
19	17	40
20	11	40
21	16	40
22	11	40
23	9	40
24	159	40
25	10	40
26	158	40
27	11	40
28	12	40
29	14	40
30	14	40
31	10	40
32	9	40
33	11	40
34	151	40
35	14	40
36	159	40
37	16	40
38	9	40
39	12	40
40	11	40
41	14	40
42	9	40
43	8	40
44	159	40
45	12	40
46	141	40
47	22	40
48	14	40
49	13	40
50	14	40
51	9	40
52	15	40
53	11	40
54	161	40
55	9	40
56	150	40
57	13	40
58	11	40
59	9	40
60	6	40

Number	Observed	Expected
1	29	40
2	50	40
3	30	40
4	42	40
5	40	40
6	32	40
7	41	40
8	49	40
9	46	40
10	38	40
11	43	40
12	51	40
13	23	40
14	34	40
15	39	40
16	45	40
17	50	40
18	34	40
19	40	40
20	40	40
21	43	40
22	36	40
23	49	40
24	41	40
25	36	40
26	41	40
27	41	40
28	35	40
29	31	40
30	46	40
31	48	40
32	44	40
33	39	40
34	30	40
35	45	40
36	47	40
37	46	40
38	44	40
39	33	40
40	41	40
41	42	40
42	49	40
43	42	40
44	33	40
45	27	40
46	36	40
47	46	40
48	28	40
49	32	40
50	41	40
51	39	40
52	41	40
53	35	40
54	49	40
55	34	40
56	45	40
57	54	40
58	41	40
59	41	40
60	33	40

Number	Observed	Expected
1	31	40
2	34	40
3	44	40
4	48	40
5	40	40
6	40	40
7	43	40
8	41	40
9	55	40
10	51	40
11	42	40
12	35	40
13	35	40
14	45	40
15	42	40
16	33	40
17	38	40
18	39	40
19	41	40
20	37	40
21	34	40
22	33	40
23	43	40
24	32	40
25	31	40
26	40	40
27	41	40
28	38	40
29	41	40
30	39	40
31	45	40
32	39	40
33	46	40
34	45	40
35	38	40
36	32	40
37	31	40
38	43	40
39	42	40
40	39	40
41	44	40
42	47	40
43	37	40
44	41	40
45	48	40
46	36	40
47	48	40
48	38	40
49	33	40
50	40	40
51	50	40
52	38	40
53	36	40
54	50	40
55	40	40
56	38	40
57	40	40
58	42	40
59	28	40
60	40	40

Number	Observed	Expected
1	6	40
2	8	40
3	11	40
4	152	40
5	11	40
6	136	40
7	14	40
8	9	40
9	9	40
10	8	40
11	11	40
12	8	40
13	14	40
14	156	40
15	5	40
16	168	40
17	16	40
18	14	40
19	17	40
20	11	40
21	16	40
22	11	40
23	9	40
24	159	40
25	10	40
26	158	40
27	11	40
28	12	40
29	14	40
30	14	40
31	10	40
32	9	40
33	11	40
34	151	40
35	14	40
36	159	40
37	16	40
38	9	40
39	12	40
40	11	40
41	14	40
42	9	40
43	8	40
44	159	40
45	12	40
46	141	40
47	22	40
48	14	40
49	13	40
50	14	40
51	9	40
52	15	40
53	11	40
54	161	40
55	9	40
56	150	40
57	13	40
58	11	40
59	9	40
60	6	40

Number	Observed	Expected
1	29	40
2	50	40
3	30	40
4	42	40
5	40	40
6	32	40
7	41	40
8	49	40
9	46	40
10	38	40
11	43	40
12	51	40
13	23	40
14	34	40
15	39	40
16	45	40
17	50	40
18	34	40
19	40	40
20	40	40
21	43	40
22	36	40
23	49	40
24	41	40
25	36	40
26	41	40
27	41	40
28	35	40
29	31	40
30	46	40
31	48	40
32	44	40
33	39	40
34	30	40
35	45	40
36	47	40
37	46	40
38	44	40
39	33	40
40	41	40
41	42	40
42	49	40
43	42	40
44	33	40
45	27	40
46	36	40
47	46	40
48	28	40
49	32	40
50	41	40
51	39	40
52	41	40
53	35	40
54	49	40
55	34	40
56	45	40
57	54	40
58	41	40
59	41	40
60	33	40

Number	Observed	Expected
1	31	40
2	34	40
3	44	40
4	48	40
5	40	40
6	40	40
7	43	40
8	41	40
9	55	40
10	51	40
11	42	40
12	35	40
13	35	40
14	45	40
15	42	40
16	33	40
17	38	40
18	39	40
19	41	40
20	37	40
21	34	40
22	33	40
23	43	40
24	32	40
25	31	40
26	40	40
27	41	40
28	38	40
29	41	40
30	39	40
31	45	40
32	39	40
33	46	40
34	45	40
35	38	40
36	32	40
37	31	40
38	43	40
39	42	40
40	39	40
41	44	40
42	47	40
43	37	40
44	41	40
45	48	40
46	36	40
47	48	40
48	38	40
49	33	40
50	40	40
51	50	40
52	38	40
53	36	40
54	50	40
55	40	40
56	38	40
57	40	40
58	42	40
59	28	40
60	40	40

Number	Observed	Expected
1	6	40
2	8	40
3	11	40
4	152	40
5	11	40
6	136	40
7	14	40
8	9	40
9	9	40
10	8	40
11	11	40
12	8	40
13	14	40
14	156	40
15	5	40
16	168	40
17	16	40
18	14	40
19	17	40
20	11	40
21	16	40
22	11	40
23	9	40
24	159	40
25	10	40
26	158	40
27	11	40
28	12	40
29	14	40
30	14	40
31	10	40
32	9	40
33	11	40
34	151	40
35	14	40
36	159	40
37	16	40
38	9	40
39	12	40
40	11	40
41	14	40
42	9	40
43	8	40
44	159	40
45	12	40
46	141	40
47	22	40
48	14	40
49	13	40
50	14	40
51	9	40
52	15	40
53	11	40
54	161	40
55	9	40
56	150	40
57	13	40
58	11	40
59	9	40
60	6	40

Number	Observed	Expected
1	29	40
2	50	40
3	30	40
4	42	40
5	40	40
6	32	40
7	41	40
8	49	40
9	46	40
10	38	40
11	43	40
12	51	40
13	23	40
14	34	40
15	39	40
16	45	40
17	50	40
18	34	40
19	40	40
20	40	40
21	43	40
22	36	40
23	49	40
24	41	40
25	36	40
26	41	40
27	41	40
28	35	40
29	31	40
30	46	40
31	48	40
32	44	40
33	39	40
34	30	40
35	45	40
36	47	40
37	46	40
38	44	40
39	33	40
40	41	40
41	42	40
42	49	40
43	42	40
44	33	40
45	27	40
46	36	40
47	46	40
48	28	40
49	32	40
50	41	40
51	39	40
52	41	40
53	35	40
54	49	40
55	34	40
56	45	40
57	54	40
58	41	40
59	41	40
60	33	40

Chance Detective

A Machine A

B Machine B

C Machine C

Chance Detective

A Machine A

B Machine B

C Machine C

Machine A

Machine B

Machine C

Machine A

Machine B

Machine C

Number	Observed	Expected
1	31	40
2	34	40
3	44	40
4	48	40
5	40	40
6	40	40
7	43	40
8	41	40
9	55	40
10	51	40
11	42	40
12	35	40
13	35	40
14	45	40
15	42	40
16	33	40
17	38	40
18	39	40
19	41	40
20	37	40
21	34	40
22	33	40
23	43	40
24	32	40
25	31	40
26	40	40
27	41	40
28	38	40
29	41	40
30	39	40
31	45	40
32	39	40
33	46	40
34	45	40
35	38	40
36	32	40
37	31	40
38	43	40
39	42	40
40	39	40
41	44	40
42	47	40
43	37	40
44	41	40
45	48	40
46	36	40
47	48	40
48	38	40
49	33	40
50	40	40
51	50	40
52	38	40
53	36	40
54	50	40
55	40	40
56	38	40
57	40	40
58	42	40
59	28	40
60	40	40

Number	Observed	Expected
1	6	40
2	8	40
3	11	40
4	152	40
5	11	40
6	136	40
7	14	40
8	9	40
9	9	40
10	8	40
11	11	40
12	8	40
13	14	40
14	156	40
15	5	40
16	168	40
17	16	40
18	14	40
19	17	40
20	11	40
21	16	40
22	11	40
23	9	40
24	159	40
25	10	40
26	158	40
27	11	40
28	12	40
29	14	40
30	14	40
31	10	40
32	9	40
33	11	40
34	151	40
35	14	40
36	159	40
37	16	40
38	9	40
39	12	40
40	11	40
41	14	40
42	9	40
43	8	40
44	159	40
45	12	40
46	141	40
47	22	40
48	14	40
49	13	40
50	14	40
51	9	40
52	15	40
53	11	40
54	161	40
55	9	40
56	150	40
57	13	40
58	11	40
59	9	40
60	6	40

Number	Observed	Expected
1	29	40
2	50	40
3	30	40
4	42	40
5	40	40
6	32	40
7	41	40
8	49	40
9	46	40
10	38	40
11	43	40
12	51	40
13	23	40
14	34	40
15	39	40
16	45	40
17	50	40
18	34	40
19	40	40
20	40	40
21	43	40
22	36	40
23	49	40
24	41	40
25	36	40
26	41	40
27	41	40
28	35	40
29	31	40
30	46	40
31	48	40
32	44	40
33	39	40
34	30	40
35	45	40
36	47	40
37	46	40
38	44	40
39	33	40
40	41	40
41	42	40
42	49	40
43	42	40
44	33	40
45	27	40
46	36	40
47	46	40
48	28	40
49	32	40
50	41	40
51	39	40
52	41	40
53	35	40
54	49	40
55	34	40
56	45	40
57	54	40
58	41	40
59	41	40
60	33	40

Number	Observed	Expected
1	31	40
2	34	40
3	44	40
4	48	40
5	40	40
6	40	40
7	43	40
8	41	40
9	55	40
10	51	40
11	42	40
12	35	40
13	35	40
14	45	40
15	42	40
16	33	40
17	38	40
18	39	40
19	41	40
20	37	40
21	34	40
22	33	40
23	43	40
24	32	40
25	31	40
26	40	40
27	41	40
28	38	40
29	41	40
30	39	40
31	45	40
32	39	40
33	46	40
34	45	40
35	38	40
36	32	40
37	31	40
38	43	40
39	42	40
40	39	40
41	44	40
42	47	40
43	37	40
44	41	40
45	48	40
46	36	40
47	48	40
48	38	40
49	33	40
50	40	40
51	50	40
52	38	40
53	36	40
54	50	40
55	40	40
56	38	40
57	40	40
58	42	40
59	28	40
60	40	40

Number	Observed	Expected
1	6	40
2	8	40
3	11	40
4	152	40
5	11	40
6	136	40
7	14	40
8	9	40
9	9	40
10	8	40
11	11	40
12	8	40
13	14	40
14	156	40
15	5	40
16	168	40
17	16	40
18	14	40
19	17	40
20	11	40
21	16	40
22	11	40
23	9	40
24	159	40
25	10	40
26	158	40
27	11	40
28	12	40
29	14	40
30	14	40
31	10	40
32	9	40
33	11	40
34	151	40
35	14	40
36	159	40
37	16	40
38	9	40
39	12	40
40	11	40
41	14	40
42	9	40
43	8	40
44	159	40
45	12	40
46	141	40
47	22	40
48	14	40
49	13	40
50	14	40
51	9	40
52	15	40
53	11	40
54	161	40
55	9	40
56	150	40
57	13	40
58	11	40
59	9	40
60	6	40

Number	Observed	Expected
1	29	40
2	50	40
3	30	40
4	42	40
5	40	40
6	32	40
7	41	40
8	49	40
9	46	40
10	38	40
11	43	40
12	51	40
13	23	40
14	34	40
15	39	40
16	45	40
17	50	40
18	34	40
19	40	40
20	40	40
21	43	40
22	36	40
23	49	40
24	41	40
25	36	40
26	41	40
27	41	40
28	35	40
29	31	40
30	46	40
31	48	40
32	44	40
33	39	40
34	30	40
35	45	40
36	47	40
37	46	40
38	44	40
39	33	40
40	41	40
41	42	40
42	49	40
43	42	40
44	33	40
45	27	40
46	36	40
47	46	40
48	28	40
49	32	40
50	41	40
51	39	40
52	41	40
53	35	40
54	49	40
55	34	40
56	45	40
57	54	40
58	41	40
59	41	40
60	33	40