I'm no expert and certainly have a lot to learn, but its my understanding that its more than just one gene from each parent, but a set of genes, which when combined with the set of genes from the other parent create a mixture that results in what the chick becomes.
There's dominant and recessive genes. Its possible for a parent to pass on a recessive gene that wasn't expressed, possibly for generations. If the other parent also passes on that same recessive gene, also unexpressed, there is a possibility for it to express in the chick, depending on what other genes are in the mix. The more offspring that pair of chickens would have, the greater the chances of one of those recessive, unexpressed traits to show up.
There's dominant and recessive genes. Its possible for a parent to pass on a recessive gene that wasn't expressed, possibly for generations. If the other parent also passes on that same recessive gene, also unexpressed, there is a possibility for it to express in the chick, depending on what other genes are in the mix. The more offspring that pair of chickens would have, the greater the chances of one of those recessive, unexpressed traits to show up.