The OP asked if it’s about genetic relatedness.
The answer is no, that’s not what it means.
Yes, the simplest concept - no genetic crossover - means you have 23 pairs of chromosomes; and you either got the same one as your sibling, or a different one. (most obvious - boys get dad’s Y, girls get dad’s X). The odds here are a simple coin toss, 50-50.
Let’s say you get mom’s X1, sibling also gets mom’s X1. However, in duplication during your egg’s creation, some of mom’s X2 switched to X1 (and vice versa); but didn’t for sis) or vice versa. However, you are right. these switcheroo segments could be 1 or some of genetic code, of the thousands of individual genes in the segment. So you’re right, the top-level back of the envelope calculation probably seriously underestimates the odds of convergence.
From a very simple, no-crossover, 23 chromosomes - 50-50 event, 23 tries, probablility that say match <= 6 (i.e. less than 1/4 match) is 0.0173 or about 1 in 57. The odds of no match in 23 coin tosses (or all match) is 1.19209289550781E-07 or 1 in 10 million. Of course with 23 chromosomes, assuming no crossover, you are likely either 11/23 or 12/23 match but there’s no 50-50. (as others point out, an X has more data than a Y and typically do not exchange IIRC, so again, this complicates any discussion or calculation) Add in random switches of random lengths of content in each of 46 chromosomes and the odds are even wilder of a the match is extremely low or extremely high.
Yeah, I expect that answer was the one protoboard was looking for when he posted the OP.
I am a geneticist* and would add several minor clarifications to what has been stated.
On average, a person shares the same proportion of nuclear, somatic DNA with his/her *full *siblings as with a parent, 50%.
We inherit a small amount of DNA that is not in the nucleus of the cell. This mitochondrial DNA is overwhelmingly inherited from the mother. So overall we get a tiny bit more DNA from our mothers than our fathers on this count.
The sex chromosomes are substantially different in size. So a male, with one of the smaller Y chromosomes, gets even less overall DNA from the father. Same number of chromosomes but fewer base pairs.
On average you share 50% of your DNA with your full siblings, and obviously less with half siblings. But indeed you could, by random chance, share less or more than 50% with those full siblings. The laws of probability indicate that anything very far away from 50% would be a low probability.
Then there are the truly unusual circumstances in which there are more or fewer of a particular chromosome or portion thereof) than is normal. Down Syndrome, Turner Syndrome, Kleinfelter’s, et al all have one parent donating more DNA than the other to the offspring.
Beyond truly unusual, roaming into the realm of downright weird, is Uniparental Disomy, where you inherit two somatic chromosomes from one parent and none from the other.
Finally, there are a few areas in which under normal circumstances gene expression is different depending upon which parent donated the DNA. While each parent gave a chromosome with the same gene, only the allele from one parent is used.
- well, hold a BS in genetics anyway
I have another anecdote: my grandmother has an identical cousin, as in “Met Cathy who’s lived most everywhere,” identical. It’s uncanny. They are something like 17 years apart, so it’s simple to tell them apart, but they look just amazingly alike. They are built alike, their hands are alike, their faces are identical, their hair grows identically, so much, that they even wore their hair similarly, in spite of being different ages, and get this-- different nationalities. My grandmother in a naturalized American who was born in Slovakia in 1917, and came to the US as a toddler. Her cousin was born in Czechoslovakia, and now lives in the Republic of Slovakia. Her cousin has never been to the US and doesn’t speak English.
I’m sure they share about the same amount of their DNA as ordinary cousins-- maybe a little more (they don’t even have parents who are identical twins like Patty and Cathy). It’s just a coincidence that the DNA they share codes for outward appearance.
There’s a photographer named Francois Brunelle who did a series of photos of unrelated people (mainly strangers) who happened to look like siblings, in some cases almost like twins.
Sounds interesting. How does that work?
The DNA molecule is a often described as a ladder, with base pairs forming the rungs of the ladder in an organized manner. Adenine bonded to one rail of the ladder pairs with Thymine bonded to the other rail (A + T). Similarly Guanine pairs with Cytosine (G +C).
But sometimes the bases are chemically altered. The addition of a methyl group to Adenine and/or Cytosine is read as a signal not to use that particular DNA. It is silenced. This methylation can be a normal part of cellular development. It may be a key component of how a stem cell becomes a specialized cell, by turning off those genes that will not be needed in its specialized role.
And in some specific regions of the genome that methylation takes place very early in development and in an unusual way, by methylating DNA based upon which parent it was inherited from. This broad usage of methylation in this parent specific way is known as genomic imprinting. One such area it is used is on chromosome 15.
On a specific section of chromosome 15 the paternal DNA is normally methylated, and thus silenced. So long as the matching maternal section is ok, everything is fine. But if that maternal DNA is a defective allele (or deleted*) a serious neurological condition occurs, Angelman Syndrome**. The gene in question is known as UBE3A.
A nearby section of the same chromosome 15 has the maternal DNA being methylated and thus turned off. Again, if the paternal DNA is ok, everything is fine. But if the paternal DNA is a defective allele (or deleted***) a different condition occurs, Prader-Willi Syndrome****. Several genes, including *SNRPN *and *necdin *are involved.
*deletion on the maternal chromosome is the most common reason for Angelman Syndrome.
** The genetic test for Angelman Syndrome actually tests for methylation of the neighboring *SNRPN *gene responsible for Prader-Willi Syndrome.
*** deletion on the paternal chromosome is a common reason for Prader-Willi Syndrome.
**** Actress Mayim Bialik, who plays Amy on The Big Bang Theory, completed her PhD with a dissertation on Prader–Willi syndrome, titled,“Hypothalamic regulation in relation to maladaptive, obsessive-compulsive, affiliative, and satiety behaviors in Prader-Willi syndrome.”
Just as a point of order, you do get exactly 50% from each parent, totaling 100%. But the overlap with your siblings don’t necessarily have to add up to 100% as in your example.
You and your brother each have 50% of your mother’s genetic material, but it could conceivably (no pun intended) be an exclusive 50%; the same goes for your father, meaning you and your brother could have no genes in common.
If they had no genes in common they’d be completely different species! 
That explains my family.
Let’s not forget that every human has about 99.9% of his genes in common with every other human.
More likely, you’d be from another planet! All life on earth has some genes in common.