What Are The Odds? Chance in Everyday Life by Mike Orkin

My friend J_ from high school recommended this book, and then gave me a copy when he was in town last. He had brought it up when we were discussing coincidence versus omens on our high school drama alumni message board a while back.

It’s a slim book with not much math to it. It covers some basic probability, some long odds stuff like lotteries, and then delves into 4 chapters on gambling (where I learned the rules of craps). The last three chapters are on game theory, such as the Prisoner’s Dilemma, and then attempts to apply game theory to the conflict between NATO and Yugoslavia.

Aside from the rules of craps, I didn’t pick up much new from this book, though I appreciate going over covered grounds in a fresh way. The language is very accessible even to the non mathematically minded.

I come away from the book wondering if the point of the book was to discuss probability theory, or to pull people in with probability theory and then explain what NATO did wrong in Yugoslavia. The last chapter of the book has language that deviates from the more specifically analytical tone of the earlier parts, and basically boils down to “NATO didn’t consider the long term consequences”, which is associated with the game theory strategies, sure, but without a more extensive overall analysis of the choices it just feels like preaching.

The book was published in January, 2000 (apparently now out of print). The NATO bombing of Yugoslavia had ended 6 months before. It seems like Mike Orkin got riled up by the NATO bombing and whipped out a quick book in his discipline so he could add his two cents to the debate.

So, there are probably better probability books out there.

But that didn’t stop me from being in a probability frame of mind when terracinque brought up relative genetic similarity in siblings and parent/children. With some refresher genetics research, I learned that siblings share anywhere between 0% and 100% of their genes. So, it is theoretically possible that you could have no chromosomes in common with your sibling, meaning for each chromosome pair in both parents, you inherited the opposite one than your theoretical sibling.

terracinque countered that “[t]he chance of two siblings with the same parents sharing zero genes must be so close to zero that I will state with confidence that it has never happened in the entire history of Mammalia.” With my mind fresh from probability reading, I did the math:

We can calculate the odds… according to this “tour of the basics” of genetics (http://learn.genetics.utah.edu/units/basics/tour/), each parent has 2 sets of 23 chromosomes, call them A and B, of which they received one from his/her dad, one from his/her mom.

But when they contribute one half their chromosomes to their child, they can take a little from column A, a little from column B to put together a 23 chromosome set.

So, for a 0% matching sibling set, each child must have gotten A where the other got B in each instance of 46 chromosomes. (As a by-product of this requirement, our theoretical siblings must not be of the same gender… both brothers means they share the father’s Y, both sisters means they share the father’s X)

So, with a 50/50 chance of getting the opposite chromosome on any given pair as a given sibling, I believe the odds are (0.5)^46, or 1.42e-14, or 1.42e-12%, or 1 in 70.4 trillion for humans¹. If I’m remembering my probability calculations correctly. So, not likely, even with all the siblings in history.

The kangaroo (and marsupials in general), however, may be a different story. Wikipedia says 12 chromosomes (6 pairs), another source I saw said 14 (7 pairs). So, the worst case odds become (0.5)^14, or 0.006% or 1 in 16,384.

Which is why you see so much squabbling in kangaroo families.

Out of curiosity, I looked up how many humans there have been, because due to the law of very large numbers, even the highly improbable becomes probable when you have a lot of chances (otherwise, no one would ever win the lottery). According to this analysis, 106,456,367,669 humans have been born between 50,000 B.C. and 2002. If we assume that all those people had a sibling, that makes roughly 53 billion sibling pairs. So, with a 1 in 70.4 trillion chance, 53 billion tries probably isn’t enough to make the improbable probable.

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¹ Also roughly the odds that Marty McFly would still be the same Marty McFly after he messed up his parent’s meeting.