This is off, by a fair way, happy to be corrected on this, the post just seemed off.
I worked it to be 1 in 65,536 which is a lot of difference. And 1 In a million not appearing till 20 flips
Flip Nr Chance 1 In ;
1 50.000000% 1 In 2
2 25.000000% 1 In 4
3 12.500000% 1 In 8
4 6.250000% 1 In 16
5 3.125000% 1 In 32
6 1.562500% 1 In 64
7 0.781250% 1 In 128
8 0.390625% 1 In 256
9 0.195313% 1 In 512
10 0.097656% 1 In 1,024
11 0.048828% 1 In 2,048
12 0.024414% 1 In 4,096
13 0.012207% 1 In 8,192
14 0.006104% 1 In 16,384
15 0.003052% 1 In 32,768
16 0.001526% 1 In 65,536
17 0.000763% 1 In 131,072
18 0.000381% 1 In 262,144
19 0.000191% 1 In 524,288
20 0.000095% 1 In 1,048,576
21 0.000048% 1 In 2,097,152