There’s a classic illustration of exponential growth, that goes something like this: a king agrees to play a chess match for a prize: a single grain of rice on the first square of the chessboard, two grains on the second square, and so on, doubling the number for each of the 64 squares. The king loses the match, and soon realizes that the amount of rice he would have to pay is far higher than he imagined: 18,446,744,073,709,551,615, or more than eighteen quintillion grains of rice in total. That’s a lot of rice.

Every genealogist who has gotten very far in charting all of their own ancestors has discovered that doubled numbers get large, very quickly. We all have two parents, four grandparents, and so on: the number of ancestors grows exponentially with each generation.

My closest common ancestor with Salvatore “Toto” Riina is through his mother, Maria Concetta Rizzo. We’re both descended from Giovanni Todaro and Antonina Russo, who married in 1750. Maria Concetta is the fourth great granddaughter of their son, Filippo. Filippo’s sister, Emmanuela, married Leoluca Cascio in 1770, and they are my 5GG. Of my 128 fifth-great grandparents, thirty-two are through my paternal grandfather, and lived in Corleone.

Toto and I are also related through his father, Giovanni Riina. Michaele Giunta and Innocenza Papania, who married in 1729, are Toto’s 5GG and my 7GG. So in addition to being sixth cousins, once removed, on his mother’s side, we are also sixth cousins, twice removed, on his father’s side.

Giuseppe Sangiorgi and Filippa lo Munti, who married in 1683, are also Toto Riina’s direct ancestors and mine: they are his 6GG and my 7GG, which makes us fifth cousins, once removed. We’re also seventh cousins, twice removed, three different ways. Pietro Mannina and Gioachina Biscuso, who married in 1673, are his 6GG and my 8GG. So are Giuseppe Sciacchitano and Caterina Lanza, who married in 1703, and Giovanni Sciortino and Mattea Russo (of no known relation to Antonina), who married in 1689.

Giovanni Fruja and his wife, Giuseppa, who I estimate married sometime before 1650, are my 9GG and Toto Riina’s 7GG, making us 8th cousins, twice removed, through this pair of common ancestors. Another of our common ancestors is Tommaso Cimino (my 6GG, his 8GG), who married twice, first to Toto’s ancestor, and then to mine, making us half-seventh cousins, twice removed.

In population genetics, degree of consanguinity is measured as a percentage of one’s genetic inheritance held in common with another, called a coefficient of relationship (CoR). The more closely related you are to someone, the higher your CoR. Identical twins have a CoR of 100%. You and your mother have a coefficient of 50%, and so do you and any of your full siblings. Half siblings share a coefficient with aunt/uncle-nephew/niece relationships, of 25%.

In the same way the number of grains of rice grows exponentially larger, from one chessboard square to the next, the CoF gets exponentially smaller, the more distant the relationship. Fourth cousins share a coefficient of relationship of only 0.20%. Sixth cousins, once removed, have a CoR of 0.000061035156%

I have multiple ancestors in common with another Corleone Mafia boss, Michelangelo Gennaro. We’re second cousins, four times removed. My fifth-great grandparents, Leoluca Cascio and Emmanuela Todaro, are Michelangelo’s great grandparents.

Michelangelo and Toto are also multiply related. They’re third cousins, three times removed, both being descended from Giovanni Todaro and Antonina Russo. They are also fifth cousins, twice removed, through Domenico Saggio and Domenica Mondello, who married in 1651: they are Michelangelo Gennaro’s 4GG and Toto Riina’s 6GG. And all three of us are descended from my 9GG, Giovanni and Giuseppa Fruja, who are Gennaro’s 5GG and Riina’s 7GG.

Image credit: Giulio Campi, “The Chess Players”

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