What is the probability that a child of siblings would inherit identical alleles from a grandparent?

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consanguinity (Left) Absence of inbreeding: horizontal lines connect mates, vertical lines connect parents with their child; (right) an inbreeding loop: horizontal bar at top of loop connects brother and sister, all other lines and bars as above

The probability that a child of siblings would inherit a pair of identical alleles from a grandparent is 1 in 4.1

In the study of consanguinity, the coefficient of inbreeding (F) defines the probability that two alleles are identical by descent from a common ancestor. Because siblings share approximately half of their chromosomal constitution, a mating between them results in a higher likelihood of their offspring being homozygous for alleles derived from their shared grandparents. As the degree of consanguinity decreases, this probability is halved; for example, the likelihood is 1 in 8 for the child of an aunt and nephew, and 1 in 16 for the child of first cousins.123