No, the newly mined bitcoins get assigned based on your hashpower. If you have more hashpower, then you get more bitcoins, if you have less hashpower you get less bitcoins. But even a small player can still get some bitcoins. As I mentioned you also need to pay for more electricity if you have more miners.

Now, when you are only an individual person that has one or two mining boxes, the way that Bitcoin works you would actually get some Bitcoin only really rarely (e.g. once in 2 years if you are lucky) and so that's why people join "mining pools" where you have somewhat guaranteed steady payouts of the bitcoin based on the hashpower you contribute to the pool.

It's quite interesting how this is actually done technically, I'm happy to explain that, but it's a bit more complicated.