Spin Wheel Fairness Study, 100,000 Spins

We ran 100,000 automated spins on equal-size wheel slices using the same landing-angle geometry as our live spin wheel. Each configuration was tested for uniform distribution with Pearson's chi-square at α = 0.05. Download the CSV to cite or reproduce the results.

Summary

Total spins: 100,000
Spins per segment count: 10,000
Segment counts tested: 2, 3, 4, 6, 8, 10, 12, 16, 20, 36
Method: crypto.getRandomValues (Node crypto.randomInt) landing angle → getCurrentSegment geometry
Uniformity result: All configurations passed χ² at α = 0.05
Data as of: 2026-08-31
Download CSV (100,000 spin rows)

Segments	Spins	χ²	df	Critical 0.05	Result	Max deviation
2	10,000	0.7056	1	3.841	pass	0.84%
3	10,000	3.4586	2	5.991	pass	2.63%
4	10,000	2.5152	3	7.815	pass	2.32%
6	10,000	10.8068	5	11.07	pass	6.7%
8	10,000	10.3584	7	14.067	pass	6.08%
10	10,000	14.476	9	16.919	pass	7.5%
12	10,000	11.1872	11	19.675	pass	6.08%
16	10,000	19.1584	15	25	pass	11.2%
20	10,000	9.656	19	30.144	pass	7.2%
36	10,000	41.5232	35	49.998	pass	11.8%

Methodology

For each segment count k, we simulated 10,000 independent spins. Each spin drew a landing angle with the same secure browser randomness used in production, then mapped the angle to a slice index using the same equal-arc formula as the live wheel (pointer on the right).

Expected count per slice is n/k. We computed Pearson's chi-square statistic χ² = Σ(O−E)²/E with k−1 degrees of freedom and compared to the α = 0.05 critical value. Configurations with χ² ≤ critical value are consistent with a uniform distribution.

This study does not cover weighted slices, removed entries mid-session, or human timing, only equal segments and cryptographic landing angles.

2 segments, 10,000 spins

χ² = 0.7056 (df = 1, critical 0.05 = 3.841), uniform (pass) · max deviation 0.84%

Slice index	Observed	Expected	Deviation %
0	4958	5000	-0.84%
1	5042	5000	0.84%

3 segments, 10,000 spins

χ² = 3.4586 (df = 2, critical 0.05 = 5.991), uniform (pass) · max deviation 2.63%

Slice index	Observed	Expected	Deviation %
0	3289	3333.33	-1.33%
1	3421	3333.33	2.63%
2	3290	3333.33	-1.3%

4 segments, 10,000 spins

χ² = 2.5152 (df = 3, critical 0.05 = 7.815), uniform (pass) · max deviation 2.32%

Slice index	Observed	Expected	Deviation %
0	2554	2500	2.16%
1	2442	2500	-2.32%
2	2502	2500	0.08%
3	2502	2500	0.08%

6 segments, 10,000 spins

χ² = 10.8068 (df = 5, critical 0.05 = 11.07), uniform (pass) · max deviation 6.7%

Slice index	Observed	Expected	Deviation %
0	1699	1666.67	1.94%
1	1671	1666.67	0.26%
2	1657	1666.67	-0.58%
3	1689	1666.67	1.34%
4	1729	1666.67	3.74%
5	1555	1666.67	-6.7%

8 segments, 10,000 spins

χ² = 10.3584 (df = 7, critical 0.05 = 14.067), uniform (pass) · max deviation 6.08%

Slice index	Observed	Expected	Deviation %
0	1326	1250	6.08%
1	1286	1250	2.88%
2	1252	1250	0.16%
3	1185	1250	-5.2%
4	1252	1250	0.16%
5	1255	1250	0.4%
6	1217	1250	-2.64%
7	1227	1250	-1.84%

10 segments, 10,000 spins

χ² = 14.476 (df = 9, critical 0.05 = 16.919), uniform (pass) · max deviation 7.5%

Slice index	Observed	Expected	Deviation %
0	997	1000	-0.3%
1	964	1000	-3.6%
2	925	1000	-7.5%
3	1002	1000	0.2%
4	1054	1000	5.4%
5	1044	1000	4.4%
6	980	1000	-2%
7	976	1000	-2.4%
8	1033	1000	3.3%
9	1025	1000	2.5%

12 segments, 10,000 spins

χ² = 11.1872 (df = 11, critical 0.05 = 19.675), uniform (pass) · max deviation 6.08%

Slice index	Observed	Expected	Deviation %
0	872	833.33	4.64%
1	806	833.33	-3.28%
2	805	833.33	-3.4%
3	850	833.33	2%
4	826	833.33	-0.88%
5	804	833.33	-3.52%
6	884	833.33	6.08%
7	845	833.33	1.4%
8	791	833.33	-5.08%
9	850	833.33	2%
10	821	833.33	-1.48%
11	846	833.33	1.52%

16 segments, 10,000 spins

χ² = 19.1584 (df = 15, critical 0.05 = 25), uniform (pass) · max deviation 11.2%

Slice index	Observed	Expected	Deviation %
0	602	625	-3.68%
1	624	625	-0.16%
2	636	625	1.76%
3	627	625	0.32%
4	633	625	1.28%
5	626	625	0.16%
6	630	625	0.8%
7	668	625	6.88%
8	623	625	-0.32%
9	666	625	6.56%
10	629	625	0.64%
11	592	625	-5.28%
12	555	625	-11.2%
13	658	625	5.28%
14	630	625	0.8%
15	601	625	-3.84%

20 segments, 10,000 spins

χ² = 9.656 (df = 19, critical 0.05 = 30.144), uniform (pass) · max deviation 7.2%

Slice index	Observed	Expected	Deviation %
0	494	500	-1.2%
1	507	500	1.4%
2	476	500	-4.8%
3	517	500	3.4%
4	479	500	-4.2%
5	495	500	-1%
6	512	500	2.4%
7	536	500	7.2%
8	511	500	2.2%
9	498	500	-0.4%
10	502	500	0.4%
11	491	500	-1.8%
12	519	500	3.8%
13	503	500	0.6%
14	501	500	0.2%
15	469	500	-6.2%
16	506	500	1.2%
17	487	500	-2.6%
18	488	500	-2.4%
19	509	500	1.8%

36 segments, 10,000 spins

χ² = 41.5232 (df = 35, critical 0.05 = 49.998), uniform (pass) · max deviation 11.8%

Slice index	Observed	Expected	Deviation %
0	252	277.78	-9.28%
1	282	277.78	1.52%
2	284	277.78	2.24%
3	290	277.78	4.4%
4	267	277.78	-3.88%
5	280	277.78	0.8%
6	252	277.78	-9.28%
7	298	277.78	7.28%
8	260	277.78	-6.4%
9	245	277.78	-11.8%
10	245	277.78	-11.8%
11	278	277.78	0.08%
12	300	277.78	8%
13	289	277.78	4.04%
14	293	277.78	5.48%
15	286	277.78	2.96%
16	281	277.78	1.16%
17	293	277.78	5.48%
18	275	277.78	-1%
19	258	277.78	-7.12%
20	295	277.78	6.2%
21	261	277.78	-6.04%
22	286	277.78	2.96%
23	299	277.78	7.64%
24	274	277.78	-1.36%
25	298	277.78	7.28%
26	305	277.78	9.8%
27	300	277.78	8%
28	264	277.78	-4.96%
29	282	277.78	1.52%
30	306	277.78	10.16%
31	249	277.78	-10.36%
32	267	277.78	-3.88%
33	251	277.78	-9.64%
34	274	277.78	-1.36%
35	281	277.78	1.16%