Sometimes we should persist to succeed. But other times it might be wiser to give up on the task at hand and focus our energy on something new. Knowing whether a task is worth the effort potentially requires multiple capacities, including sensitivity to one's own likelihood to succeed on the current problem, the associated costs with continuing to pursue it, and evaluation of opportunities for reward from the success. But these capacities may be particularly challenging for young children. Here we ask how young children are sensitive to cognitive cost (one's capacity and the opportunity cost of persisting) and reward probability (how likely they are to receive a reward when succeeding) when making decisions. Using a simple counting task, we showed that 4- to 5-year-old children in the US (N = 40, pre-registered) chose to give up more when the task was more difficult (and therefore cognitively more costly), especially when the probability of reward was low. These results extend previous findings and suggest the ability to consider and evaluate cognitive cost and reward probability may be in place by 4 years of age.