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Chicken genetics and probability.
I have blue gold rooster with 3 black silver and one Blue Silver hen. Only the blue hen should be capable of ever throwing splash chicks. (splash is white with black/grey mottling) This season I have set and hatched 22 of their eggs. (100% hatch on them so far is awesome but one died from its mom stomping it 😞) If the hens are all laying the same rate 1/4 should come from the Blue silver hen. (5.5) Yet 5 of the 22 chicks we have hatched are splash. The odds that 5 out of 5 chicks are all splash are kinda crazy. (.097%)
A Blue rooster over a Blue hen should result in 25% black 25% splash and 50% blue. The blue/black/splash coloring comes from genes that have 2 slots and 2 types. 2 copies of BL gives a black chicken 2 copies of bl+ give you a splash and one of each gene gives you a blue chicken. Each parent contributes 1 copy of one of their genes. So a black and a splash will give you blue chicks every time.
It is possible that I set more of the blue girls eggs but even doubling the number of her eggs (very unlikely) wouldn't make the odds reasonable.
The chance that it is some crazy mutation is also low because the mutation would have to be in the hen and be attached to both her BL and bl+ gene and it would have to over ride the male's color gene completely.
stuck between 2 highly unlikely realities.
Highly unlikely for an individual isn't the same as highly unlikely across a population. 0.1% is only one chance in 1000 - rolling the same number 3 times in a row on a 20 sided die has a probability of 1 in 8000, but you'll find loads of stories of it happening because there's a lot more than 8 thousand people who play D&D.
Your chooks are rolling along the edge of probability, but there's more than 1000 chickens in the world so the probability someone will hit that jackpot is close to 100%.