If now you have a 1000-sided die, which has a higher expectation under best strategy compared to rolling 10 100-sided die?
I'm thinking about an analytical way to solve it but the case for 10 100-side die is so complicated since the sum of 10-sided dice can have different combination. That's why I want to turn to an intuitive method since we only need to compare which one is larger. The sum of 10 100-sided die has higher expectation(505>500.5) and a thinner distribution(can't reach 1 to 9).