Many farmers do milk twice a day as you point out. Some however milk three times a day. It has two advantages. The yield is increased, and there is a drop in cases of mastitis by about 13 - 17%.
It is thought that milking three times a day creates milking conditions more similar to what would occur naturaly, as a calf left to it's own devices, will suckle from it's mother seven times a day.
Milking cows is bloody hard work, I know! I used to milk 250 of the things. When you're doing it seven days a week it doesn't take long for the novelty to wear off. For that reason many farmers don't milk three times a day, but stick with the traditional twice daily milking.
It's worth repeating that I was told the story 1st hand by the farmer concerned. I wasn't told it some bloke in a pub or a bus queue. I did express my astonishment about the outcome to him myself at the time.
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