The first class was a public class & anybody could join in at any time. The second class had reserved early seats based on the initial supply of the dices; without investment in the initial dices the game doesnt start, whereas sudoku generation is free.
With PoS you have to buy coins before you can stake. There's no way to bootstrap your stake without spending money.
The best random oracle we know is of course, Proof-of-Work.
You, a mathematician, walk into the class to purchase a brick to label.
The first class has solved sudokus with deterministic difficulty to prove they did work to build the structure, whereas in the second class you have just dice sums & have to trust them telling you they rolled the diced only every fixed interval etc. It's distributed but not decentralized.