I think it's a very neat idea to divide the reward into the current and the next block! (1)
But this random "dice roll" thing (2) might be a bit tricky to implement and could be exploit.
Continuing your line of thought (of reward block separation),
I have much more simple solution to this random thing. Why not use the nonce itself as a "dice roll"?
Take the given nonce of a previous block and use it as a base to calculate the bonus of the block finder (3).
For example if the nonce is 368234 you can calculate by simple module the extra reward (34 coins)!
One can argue that since the nonce is given by the miner, he might choose not to announce his block
if the reward is too low for him (like: 5801103, only 3 coins bonus at the next block).
I would disagree with that argument. Since he already invested the work to find the block,
he can choose to take the basic reward + small bonus, or try to find another block with larger
bonus but risking someone else announcing a block and leave him with nothing.
I would take the money and go…
https://i.imgur.com/RvgyNTy.pngPM me for a bounty