"When he is thirsty, he drinks even water."
Translation:Když má žízeň, pije i vodu.
It would be better English to say 'when he is thirsty, he even drinks water'. So, in answer to Dillon below, the meaning is that he will resort to drinking water when he is thirsty but he doesn't usually drink it.
I can understand that. But I think the author wanted to stress that in the Czech sentence the "i" binds with "water", not with "pije". So he will resort to drinking even water and not some other drink. While in "he even drinks water" he will resort to drinking water instead of doing something else.
For the second half of this sentence, could you also say "..., pije ani vodu"? In other words substitute ani for i?