On average how many genes / alleles do people share?
I will attempt to answer the question. Allele is defined, in simple terms, variation of a given gene, e.g. through deletions, SNPs etc. Humans are diploid organisms, meaning we have two sets of chromosomes, one from mother and one from father. Now since we have two sister chromosome, we can only have (share) two alleles of a given gene (one from mother and one from father) unless there are multiple copies of a gene or chromosome, which is mostly observed in disease conditions but that's not what we are talking about. Now since every humans have SNPs at roughly 1 every 1000 base pair, there are genetic variations between sequences of genes between humans, although there are some hot spots, which are more varied and some genes are very highly conserved due to their critical function such as cytochrome C. This just means that parents of the child you are describing (if not related to each other) are not likely to share the exact same, sequence wise, genetic code for a given gene selected at random.

The inheritance of a given allele of a gene on a chromosome happens through independent assortment (a process which happens maternally and paternally), meaning a child (offspring/zygote) would get one copy of a gene/allele (from the possible two that each parent themselves have) from maternal and one copy from paternal side at random. This is one source of genetic variation in a zygote. The other source of genetic variation is gene cross-over (through homologous recombination) meaning bits of the maternal or paternal chromosomes swap at gamete stage before the gametes are fused together to form a zygote, which makes the offspring unique and no offspring alike (except MZ twins but thats another discussion). This overall means that you can inherit a maximum of two alleles of a given gene (assuming again the parents of the child are not closely related) and even then the sequence of the offspring genes are not likely to be exactly the same as their parents, which makes every human unique. But saying that, you have a much higher gene sequence match to your parents than any other non-related human selected at random.

One thing worth noting here is that mitochondrial genes, are inherited exclusively from you mother (through the egg) and males inherit the Y chromosomes paternally so there are circumstances I guess you could say you inherit certain gene/alleles paternally or maternally.

What I speculate you might be thinking about is how many homologues (similar versions) of a given genes humans have and I think the average in the human genome is 3 but do check this! Flies (Drosophila) tends to have one, which is why its such a great model organism to study genetics and genetic interactions with as you do not tend to get redundancies.

I hope this answers your question