A random walk experiment

I have been trying to understand electron diffusion equations in conductors. One is based on a random walk model and gives the probability of finding an electron at a given place at a particular time. It contains a term for the dimension of the space. I was wondering what would happen if I simplified it to one dimension. So I got a coin and tossed it 100 times. I said I was starting from position 0 and moved one to the right for HEADS and one to the left for TAILS. I tossed the coin 100 times. I haven't done that since my introductory maths class on probability in 1978!

I got 52 heads and 48 tails. The position ranged from -2 to 10. Here is a bar graph showing frequency.

It might be heading towards a bell shape. Maybe I would be able to get a Gaussian distribution eventually. I thought I'd been quite smart coming up with this idea but now I've got wifi again I can see that this is a common strategy. This link even computes the probabilities https://en.wikipedia.org/wiki/Random_walk