To start out on the technical side before answering your question about my chicken math experience
Typically you want a minimum of 4sqft per chicken in the coop and 10 sqft in the run, this means your coop can comfortably accommodate 4 hens, and your run 6 hens. Depending on the flock dynamics and what breeds you choose, you may do fine with 6 total in your flock. Whether you get 3 or 4 might depend on your future plans, if you do stick to not going over 6 chickens ever (LOL...) then you might want to get 3 this year, then 2 the following year, and if you've lost any, then get 2 again the following year.
We only wanted a few chickens, you know 6 or 8 for fresh eggs, then we were going to just get a few (ie: 2) replacement pullets every 2 or 3 years. That plan didn't last long, we ended up well over 20 chickens that first year, over 30 the second, a few years down the road and now this year we went over 150
For the why's... have you seen all the amazing breeds!?! then you find a breed you love and you discover they come in different varieties!!! Blue, laced, splash, chocolate, mottled!?! Just take my money!!! And then you find blue eggs, and green eggs and you just HAVE to have some of those, then Marans??? Definitely a NEED there too, then you discover you can get SPECKLED eggs

speckled in tan, brown, chocolate, green of all the hues, and blues too.
Then your favorite pullet you bought at
TSC ends up being a rooster and you love him and next thing you know you're buying an incubator. Then you discover silkies and you get some of those too, then they go broody and you don't have the heart to break them so you let them set on some eggs, and the chicks are so cute you just can't stop the hatching. Then another hen goes broody and you see that
TSC has pullets on sale, or they finally got in those Olive Eggers you NEED, so you pick up a few of them, hey, they're so small...
Then all of a sudden you wake up one day an realize your back yard has been taken over by coops, less to mow so it's all good anyway. This is chicken math, and the eggs taste delicious.