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: 2026-09-21
Download CSV (100,000 spin rows)

Segments	Spins	χ²	df	Critical 0.05	Result	Max deviation
2	10,000	1.9044	1	3.841	pass	1.38%
3	10,000	2.5598	2	5.991	pass	2.17%
4	10,000	6.0232	3	7.815	pass	3.28%
6	10,000	2.9768	5	11.07	pass	3.68%
8	10,000	2.9072	7	14.067	pass	3.36%
10	10,000	4.494	9	16.919	pass	3.7%
12	10,000	6.3272	11	19.675	pass	4.52%
16	10,000	17.664	15	25	pass	8.8%
20	10,000	17.528	19	30.144	pass	8%
36	10,000	30.7304	35	49.998	pass	13.6%

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.

This simulation evaluates the random-selection and landing-angle model used by the wheel; it does not measure physical-wheel effects such as friction or pointer mechanics.

2 segments, 10,000 spins

χ² = 1.9044 (df = 1, critical 0.05 = 3.841), uniform (pass) · max deviation 1.38%

Slice index	Observed	Expected	Deviation %
0	5069	5000	1.38%
1	4931	5000	-1.38%

3 segments, 10,000 spins

χ² = 2.5598 (df = 2, critical 0.05 = 5.991), uniform (pass) · max deviation 2.17%

Slice index	Observed	Expected	Deviation %
0	3261	3333.33	-2.17%
1	3388	3333.33	1.64%
2	3351	3333.33	0.53%

4 segments, 10,000 spins

χ² = 6.0232 (df = 3, critical 0.05 = 7.815), uniform (pass) · max deviation 3.28%

Slice index	Observed	Expected	Deviation %
0	2534	2500	1.36%
1	2582	2500	3.28%
2	2457	2500	-1.72%
3	2427	2500	-2.92%

6 segments, 10,000 spins

χ² = 2.9768 (df = 5, critical 0.05 = 11.07), uniform (pass) · max deviation 3.68%

Slice index	Observed	Expected	Deviation %
0	1649	1666.67	-1.06%
1	1657	1666.67	-0.58%
2	1671	1666.67	0.26%
3	1728	1666.67	3.68%
4	1643	1666.67	-1.42%
5	1652	1666.67	-0.88%

8 segments, 10,000 spins

χ² = 2.9072 (df = 7, critical 0.05 = 14.067), uniform (pass) · max deviation 3.36%

Slice index	Observed	Expected	Deviation %
0	1208	1250	-3.36%
1	1246	1250	-0.32%
2	1240	1250	-0.8%
3	1253	1250	0.24%
4	1274	1250	1.92%
5	1247	1250	-0.24%
6	1284	1250	2.72%
7	1248	1250	-0.16%

10 segments, 10,000 spins

χ² = 4.494 (df = 9, critical 0.05 = 16.919), uniform (pass) · max deviation 3.7%

Slice index	Observed	Expected	Deviation %
0	963	1000	-3.7%
1	996	1000	-0.4%
2	1031	1000	3.1%
3	1025	1000	2.5%
4	1023	1000	2.3%
5	1000	1000	0%
6	983	1000	-1.7%
7	1011	1000	1.1%
8	978	1000	-2.2%
9	990	1000	-1%

12 segments, 10,000 spins

χ² = 6.3272 (df = 11, critical 0.05 = 19.675), uniform (pass) · max deviation 4.52%

Slice index	Observed	Expected	Deviation %
0	850	833.33	2%
1	799	833.33	-4.12%
2	813	833.33	-2.44%
3	829	833.33	-0.52%
4	840	833.33	0.8%
5	837	833.33	0.44%
6	856	833.33	2.72%
7	871	833.33	4.52%
8	856	833.33	2.72%
9	816	833.33	-2.08%
10	819	833.33	-1.72%
11	814	833.33	-2.32%

16 segments, 10,000 spins

χ² = 17.664 (df = 15, critical 0.05 = 25), uniform (pass) · max deviation 8.8%

Slice index	Observed	Expected	Deviation %
0	644	625	3.04%
1	659	625	5.44%
2	630	625	0.8%
3	591	625	-5.44%
4	616	625	-1.44%
5	669	625	7.04%
6	643	625	2.88%
7	606	625	-3.04%
8	628	625	0.48%
9	650	625	4%
10	611	625	-2.24%
11	609	625	-2.56%
12	570	625	-8.8%
13	593	625	-5.12%
14	637	625	1.92%
15	644	625	3.04%

20 segments, 10,000 spins

χ² = 17.528 (df = 19, critical 0.05 = 30.144), uniform (pass) · max deviation 8%

Slice index	Observed	Expected	Deviation %
0	468	500	-6.4%
1	497	500	-0.6%
2	506	500	1.2%
3	503	500	0.6%
4	529	500	5.8%
5	519	500	3.8%
6	507	500	1.4%
7	490	500	-2%
8	540	500	8%
9	489	500	-2.2%
10	517	500	3.4%
11	461	500	-7.8%
12	483	500	-3.4%
13	510	500	2%
14	486	500	-2.8%
15	463	500	-7.4%
16	495	500	-1%
17	498	500	-0.4%
18	525	500	5%
19	514	500	2.8%

36 segments, 10,000 spins

χ² = 30.7304 (df = 35, critical 0.05 = 49.998), uniform (pass) · max deviation 13.6%

Slice index	Observed	Expected	Deviation %
0	299	277.78	7.64%
1	267	277.78	-3.88%
2	272	277.78	-2.08%
3	288	277.78	3.68%
4	287	277.78	3.32%
5	276	277.78	-0.64%
6	277	277.78	-0.28%
7	262	277.78	-5.68%
8	270	277.78	-2.8%
9	254	277.78	-8.56%
10	282	277.78	1.52%
11	283	277.78	1.88%
12	297	277.78	6.92%
13	293	277.78	5.48%
14	253	277.78	-8.92%
15	281	277.78	1.16%
16	240	277.78	-13.6%
17	266	277.78	-4.24%
18	266	277.78	-4.24%
19	293	277.78	5.48%
20	274	277.78	-1.36%
21	276	277.78	-0.64%
22	291	277.78	4.76%
23	290	277.78	4.4%
24	298	277.78	7.28%
25	287	277.78	3.32%
26	297	277.78	6.92%
27	256	277.78	-7.84%
28	267	277.78	-3.88%
29	287	277.78	3.32%
30	295	277.78	6.2%
31	296	277.78	6.56%
32	266	277.78	-4.24%
33	277	277.78	-0.28%
34	289	277.78	4.04%
35	248	277.78	-10.72%