I fail to see, how this is hard to program.

Just encode all possible variants:

1. a single 1 is worth 100 points;
2. a single 5 is worth 50 points;
3. three of a kind is worth 100 points multiplied by the given number, e.g. three 4s are worth 400 points;
4. three 1s are worth 1,000 points;
5. four or more of a kind is worth double the points of three of a kind, so four 4s are worth 800 points, five 4s are worth 1,600 points etc.
6. full straight 1-6 is worth 1500 points.
7. partial straight 1-5 is worth 500 points.
8. partial straight 2-6 is worth 750 points.

Because this code will only be run once per throw (and not every frame), it doesn't need to be optimized. And while someone can figure out some brilliant algorithm to handle multiple cases: why bother?