Give one’s left ball/nut (for something)
Vulgar, men only, and deliberately perverse version of ‘give one’s right arm for something’ where ‘ball’ is preferred in Britain and elsewhere, while ‘nut’ is preferred in North America. Testicles as part of the ‘crown jewels’ are most certainly precious. If a man is prepared to give one of them up in order to gain or achieve something, the end goal must indeed be worth it. The expression dates from the late 20th century.