A critical debate has blossomed within the field of research policy, science and technology studies, and philosophy of science regarding the possible benefits and limitations of allocating extramural grants using a lottery system. The most common view among those supporting the lottery idea is that some form of modified lottery is acceptable, if properly combined with peer review. This means that partial randomization can be applied only after experts have screened the pursuit-worthiness of all submitted proposals and sorted out those of lowest quality. In the present paper, I will argue against the use of partial lotteries or partial randomization and instead promote use of a "pure lottery" in combination with a radical increase in block funding. The main reason for holding this position is that a partial lottery cannot solve the problems inherent in the current funding system, which is based on grant competitions and peer review. A partial lottery cannot decrease the enormous time-waste, reduce the uneven distribution of time between researchers, neutralize expert biases or mitigate academic power asymmetries. Instead, we need a stronger focus on improving general time management in academia by implementing a more holistic model for organizing research opportunities in the future.