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: 2026-07-14
Download CSV (100,000 spin rows)

Segments	Spins	χ²	df	Critical 0.05	Result	Max deviation
2	10,000	1.1664	1	3.841	pass	1.08%
3	10,000	1.6274	2	5.991	pass	1.61%
4	10,000	4.5784	3	7.815	pass	3.28%
6	10,000	3.9584	5	11.07	pass	2.74%
8	10,000	4.1376	7	14.067	pass	3.68%
10	10,000	8.004	9	16.919	pass	5.1%
12	10,000	19.3616	11	19.675	pass	9.68%
16	10,000	19.5296	15	25	pass	8.64%
20	10,000	18.5	19	30.144	pass	8%
36	10,000	34.6832	35	49.998	pass	12.52%

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 = 1.1664 (df = 1, critical 0.05 = 3.841), uniform (pass) · max deviation 1.08%

Slice index	Observed	Expected	Deviation %
0	4946	5000	-1.08%
1	5054	5000	1.08%

3 segments, 10,000 spins

χ² = 1.6274 (df = 2, critical 0.05 = 5.991), uniform (pass) · max deviation 1.61%

Slice index	Observed	Expected	Deviation %
0	3330	3333.33	-0.1%
1	3283	3333.33	-1.51%
2	3387	3333.33	1.61%

4 segments, 10,000 spins

χ² = 4.5784 (df = 3, critical 0.05 = 7.815), uniform (pass) · max deviation 3.28%

Slice index	Observed	Expected	Deviation %
0	2457	2500	-1.72%
1	2448	2500	-2.08%
2	2582	2500	3.28%
3	2513	2500	0.52%

6 segments, 10,000 spins

χ² = 3.9584 (df = 5, critical 0.05 = 11.07), uniform (pass) · max deviation 2.74%

Slice index	Observed	Expected	Deviation %
0	1697	1666.67	1.82%
1	1636	1666.67	-1.84%
2	1621	1666.67	-2.74%
3	1701	1666.67	2.06%
4	1646	1666.67	-1.24%
5	1699	1666.67	1.94%

8 segments, 10,000 spins

χ² = 4.1376 (df = 7, critical 0.05 = 14.067), uniform (pass) · max deviation 3.68%

Slice index	Observed	Expected	Deviation %
0	1251	1250	0.08%
1	1204	1250	-3.68%
2	1243	1250	-0.56%
3	1269	1250	1.52%
4	1278	1250	2.24%
5	1274	1250	1.92%
6	1217	1250	-2.64%
7	1264	1250	1.12%

10 segments, 10,000 spins

χ² = 8.004 (df = 9, critical 0.05 = 16.919), uniform (pass) · max deviation 5.1%

Slice index	Observed	Expected	Deviation %
0	966	1000	-3.4%
1	1025	1000	2.5%
2	1014	1000	1.4%
3	954	1000	-4.6%
4	995	1000	-0.5%
5	968	1000	-3.2%
6	1051	1000	5.1%
7	1012	1000	1.2%
8	1006	1000	0.6%
9	1009	1000	0.9%

12 segments, 10,000 spins

χ² = 19.3616 (df = 11, critical 0.05 = 19.675), uniform (pass) · max deviation 9.68%

Slice index	Observed	Expected	Deviation %
0	802	833.33	-3.76%
1	889	833.33	6.68%
2	786	833.33	-5.68%
3	801	833.33	-3.88%
4	800	833.33	-4%
5	822	833.33	-1.36%
6	850	833.33	2%
7	854	833.33	2.48%
8	839	833.33	0.68%
9	823	833.33	-1.24%
10	820	833.33	-1.6%
11	914	833.33	9.68%

16 segments, 10,000 spins

χ² = 19.5296 (df = 15, critical 0.05 = 25), uniform (pass) · max deviation 8.64%

Slice index	Observed	Expected	Deviation %
0	665	625	6.4%
1	612	625	-2.08%
2	640	625	2.4%
3	648	625	3.68%
4	654	625	4.64%
5	590	625	-5.6%
6	610	625	-2.4%
7	608	625	-2.72%
8	571	625	-8.64%
9	619	625	-0.96%
10	648	625	3.68%
11	626	625	0.16%
12	576	625	-7.84%
13	651	625	4.16%
14	645	625	3.2%
15	637	625	1.92%

20 segments, 10,000 spins

χ² = 18.5 (df = 19, critical 0.05 = 30.144), uniform (pass) · max deviation 8%

Slice index	Observed	Expected	Deviation %
0	494	500	-1.2%
1	494	500	-1.2%
2	468	500	-6.4%
3	481	500	-3.8%
4	509	500	1.8%
5	538	500	7.6%
6	493	500	-1.4%
7	472	500	-5.6%
8	509	500	1.8%
9	495	500	-1%
10	495	500	-1%
11	462	500	-7.6%
12	540	500	8%
13	540	500	8%
14	488	500	-2.4%
15	493	500	-1.4%
16	503	500	0.6%
17	501	500	0.2%
18	504	500	0.8%
19	521	500	4.2%

36 segments, 10,000 spins

χ² = 34.6832 (df = 35, critical 0.05 = 49.998), uniform (pass) · max deviation 12.52%

Slice index	Observed	Expected	Deviation %
0	248	277.78	-10.72%
1	295	277.78	6.2%
2	268	277.78	-3.52%
3	270	277.78	-2.8%
4	290	277.78	4.4%
5	271	277.78	-2.44%
6	280	277.78	0.8%
7	295	277.78	6.2%
8	283	277.78	1.88%
9	312	277.78	12.32%
10	275	277.78	-1%
11	270	277.78	-2.8%
12	252	277.78	-9.28%
13	298	277.78	7.28%
14	274	277.78	-1.36%
15	288	277.78	3.68%
16	310	277.78	11.6%
17	280	277.78	0.8%
18	256	277.78	-7.84%
19	269	277.78	-3.16%
20	289	277.78	4.04%
21	301	277.78	8.36%
22	280	277.78	0.8%
23	279	277.78	0.44%
24	243	277.78	-12.52%
25	288	277.78	3.68%
26	253	277.78	-8.92%
27	262	277.78	-5.68%
28	267	277.78	-3.88%
29	272	277.78	-2.08%
30	292	277.78	5.12%
31	296	277.78	6.56%
32	264	277.78	-4.96%
33	274	277.78	-1.36%
34	276	277.78	-0.64%
35	280	277.78	0.8%