The chance of each number of heads in up to 20 tosses of a fair coin

Name: The chance of each number of heads in up to 20 tosses of a fair coin
Creator: Unlabeled
License: Original computation by Unlabeled; nothing copied from the source

In 20 tosses, 10 heads is the likeliest count, yet it comes up only 17.6% of the time. All 20 heads is 1 chance in 1,048,576.

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y ↑: Heads (count)
x →: Tosses (count)
Given: Chance (%)

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The data: 230 points

Tosses (count)	Heads (count)	Chance (%)
1	0	50
2	0	25
3	0	12.5
4	0	6.25
5	0	3.12
6	0	1.56
7	0	0.78
8	0	0.39
9	0	0.2
10	0	0.1
11	0	0.05
12	0	0.02
13	0	0.01
14	0	0.01
15	0	0
16	0	0
17	0	0
18	0	0
19	0	0
20	0	0
1	1	50
2	1	50
3	1	37.5
4	1	25
5	1	15.62
6	1	9.38
7	1	5.47
8	1	3.12
9	1	1.76
10	1	0.98
11	1	0.54
12	1	0.29
13	1	0.16
14	1	0.09
15	1	0.05
16	1	0.02
17	1	0.01
18	1	0.01
19	1	0
20	1	0
2	2	25
3	2	37.5
4	2	37.5
5	2	31.25
6	2	23.44
7	2	16.41
8	2	10.94
9	2	7.03
10	2	4.39
11	2	2.69
12	2	1.61
13	2	0.95
14	2	0.56
15	2	0.32
16	2	0.18
17	2	0.1
18	2	0.06
19	2	0.03
20	2	0.02
3	3	12.5
4	3	25
5	3	31.25
6	3	31.25
7	3	27.34
8	3	21.88
9	3	16.41
10	3	11.72
11	3	8.06
12	3	5.37
13	3	3.49
14	3	2.22
15	3	1.39
16	3	0.85
17	3	0.52
18	3	0.31
19	3	0.18
20	3	0.11
4	4	6.25
5	4	15.62
6	4	23.44
7	4	27.34
8	4	27.34
9	4	24.61
10	4	20.51
11	4	16.11
12	4	12.08
13	4	8.73
14	4	6.11
15	4	4.17
16	4	2.78
17	4	1.82
18	4	1.17
19	4	0.74
20	4	0.46
5	5	3.12
6	5	9.38
7	5	16.41
8	5	21.88
9	5	24.61
10	5	24.61
11	5	22.56
12	5	19.34
13	5	15.71
14	5	12.22
15	5	9.16
16	5	6.67
17	5	4.72
18	5	3.27
19	5	2.22
20	5	1.48
6	6	1.56
7	6	5.47
8	6	10.94
9	6	16.41
10	6	20.51
11	6	22.56
12	6	22.56
13	6	20.95
14	6	18.33
15	6	15.27
16	6	12.22
17	6	9.44
18	6	7.08
19	6	5.18
20	6	3.7
7	7	0.78
8	7	3.12
9	7	7.03
10	7	11.72
11	7	16.11
12	7	19.34
13	7	20.95
14	7	20.95
15	7	19.64
16	7	17.46
17	7	14.84
18	7	12.14
19	7	9.61
20	7	7.39
8	8	0.39
9	8	1.76
10	8	4.39
11	8	8.06
12	8	12.08
13	8	15.71
14	8	18.33
15	8	19.64
16	8	19.64
17	8	18.55
18	8	16.69
19	8	14.42
20	8	12.01
9	9	0.2
10	9	0.98
11	9	2.69
12	9	5.37
13	9	8.73
14	9	12.22
15	9	15.27
16	9	17.46
17	9	18.55
18	9	18.55
19	9	17.62
20	9	16.02
10	10	0.1
11	10	0.54
12	10	1.61
13	10	3.49
14	10	6.11
15	10	9.16
16	10	12.22
17	10	14.84
18	10	16.69
19	10	17.62
20	10	17.62
11	11	0.05
12	11	0.29
13	11	0.95
14	11	2.22
15	11	4.17
16	11	6.67
17	11	9.44
18	11	12.14
19	11	14.42
20	11	16.02
12	12	0.02
13	12	0.16
14	12	0.56
15	12	1.39
16	12	2.78
17	12	4.72
18	12	7.08
19	12	9.61
20	12	12.01
13	13	0.01
14	13	0.09
15	13	0.32
16	13	0.85
17	13	1.82
18	13	3.27
19	13	5.18
20	13	7.39
14	14	0.01
15	14	0.05
16	14	0.18
17	14	0.52
18	14	1.17
19	14	2.22
20	14	3.7
15	15	0
16	15	0.02
17	15	0.1
18	15	0.31
19	15	0.74
20	15	1.48
16	16	0
17	16	0.01
18	16	0.06
19	16	0.18
20	16	0.46
17	17	0
18	17	0.01
19	17	0.03
20	17	0.11
18	18	0
19	18	0
20	18	0.02
19	19	0
20	19	0
20	20	0

Source: Binomial distribution, NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.6.6.18, calculated by Unlabeled
Licence: Original computation by Unlabeled; nothing copied from the source
Read: 2026-10-16
Drawn: 230 points as the puzzle showed them · scatter

Ran in puzzle #22 on October 18, 2026. Play it

The chance of each number of heads in up to 20 tosses of a fair coin

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