Does greed help a forager survive?

We investigate the role of greed on the lifetime of a random-walking forager on an initially resource-rich lattice. Whenever the forager lands on a food-containing site, all the food there is eaten and the forager can hop S more steps without food before starving. Upon reaching an empty site, the forager comes one time unit closer to starvation. The forager is also greedy-given a choice to move to an empty or to a food-containing site in its local neighborhood, the forager moves preferentially toward food. Surprisingly, the forager lifetime varies nonmonotonically with greed, with different senses of the nonmonotonicity in one and two dimensions. Also unexpectedly, the forager lifetime in one dimension has a huge peak for very negative greed where the forager is food averse.