There are 166 numbered boxes. You have a set amount of points that increases with time at a fixed rate. You can use 100 points to use a fair RNG to generate 10 numbers and the numbered boxes are uncovered. You can use 30 points to generate 3 numbers to do the same. If the RNG chooses a box already uncovered, you regain 5 points. You can use 300 points to uncover any single box of your choosing
What is the optimal strategy to uncover all boxes in the least amount of time? How many boxes should you have uncovered before you start using the single box uncover at 300 points?