As interesting as this game is, it also opens another question: Can you describe a general strategy that will guarantee the highest (or lowest) score for any given roll?
The great vos Savant problem that left egg on the faces of so many academics. This is an awesome problem to pose for initial theoretical probabilities from students before following up with empirical results.
I quickly figured out how to play that game successfully – success in that case being measured by my being able to solve under exam conditions, problems like the ones the teacher had shown us and we had practiced in class and done for homework.
In fact, you can’t separate real teaching from learning. They are simply two perspectives of the same human interactive process.
For whereas technology can provide instruction and can provide teachers and students with resources to assist them, what is cannot do on its own is teach them.