How are the gene sequences of individual sperm and egg cells “randomized”?

Question

What I mean by "randomized" is, in the place where an egg cell or sperm cell is made, what is the mechanism by which each one is not made identically? Though I am a layman, I'm pretty sure that if the sperm cell that was right next to "me" had made it to the egg instead of the one that did, the resultant human would have a different genomic sequence and different features.

Answer 1

Meiosis is the type of cell division responsible for the diversification of genetic material among egg and sperm cells. The diversity comes primarily from crossing over (Prophase I) and the cell divisions (Telophase I & II) later on in the process.

Meiosis begins with one diploid cell containing two copies of each chromosome—one from the organism's mother and one from its father—and produces four haploid cells containing one copy of each chromosome. Each of the resulting chromosomes in the gamete cells is a unique mixture of maternal and paternal DNA, ensuring that offspring are genetically distinct from either parent. This gives rise to genetic diversity in sexually reproducing populations, which provides the variation of physical and behavioural attributes (phenotypes) upon which natural selection acts.

Further detail of the precise phases can be found in the Wikipeida article.

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Answer 2

I think we can attribute this to sheer probability. The human genome contains around 3 billion base pairs. When you consider recombination from chromosomal crossover that occurs in germ line cells, there is an astronomically huge number of possible unique combinations that can be made.

Of course, males generate many many sperm, so some of these are bound to be similar. But the number of sperm produced by any individual doesn't come anywhere close to the number of possible unique sperm that he could produce.