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Its a function called a Binary combinatorial distribution function, I combined all of the possibilities from 6 to all female (with a 50% probability of any individual being female). It was fun.

The 4 foot per bird rule is for birds who don;t get out during the day, since you are letting them out for the day time they really only need enough room that they will not fight ferociously for perch space.

The beak clipping is the only "cruel" part of the process and its done so that the chickens wont kill each other under factory farm conditions, short of actually improving those conditions that's the most humane thing to do, just like docking a tail from a dog breed that is prone to tail breakage.

Just saying hi, I found this forum on google and had to join in order to do some math. Serius problems I know...

Assuming that you get a straight run and not scammed your chances of getting at least 6 of any given gender are as follows (Number of birds:% chance of 6 hens) (6:1.563%) (11:50.0%) (16:89.5%) (21:98.7%) (7:6.250%) (12:61.3%) (17:92.8%) (22:99.2%) (8:14.45%) (13:70.9%) (18:95.2%) (23:99.5%)...