We currently run SCG-Agent where the student-implemented agents compete.
I think, with minimal adjustments to our software, we can also
run SCG-Student where the students compete directly, optionally assisted by
a computer.

SCG-Student is a very slow running version of SCG where one round might take hours.
It has the flavor of correspondence chess where you might 
have days to do the next move.
SCG-Student is likely to use smaller upper bounds in the
configuration object than SCG-Agent.

Instead of full round-robin games, we will play Swiss-style tournaments,
drastically cutting down on the number of games.

Benefits of SCG-Student

1. Students grade themselves and give each other constructive feedback.
2. Great automated, interactive experience to learn about
   a computer-science-style scientific process. 
3. A very good introduction to SCG-Agent. Before the students implement their
   agent, they should play SCG-Student.
4. A semi-automated game allows to explore a much mider scientific space
   and can be applied to many topics.

Problems of SCG-Student

The administrator needs to run games in parallel.
When student 1 and 2 are playing, student 3 and 4 can play simultaneously.
We need to watch that the checking the administrator does is not too time consuming.

Sample challenges for SCG-Student:
Alice claims:
Any regular expression of size 10 can be translated into an equivalent DFA
with at most 80 states.

Bob strengthens it to:
Any regular expression of at most size 10 can be translated into an equivalent DFA
with at most 70 states.

Alice opposes:
Alice gives to Bob a regular expression  but Bob can only find an equivalent
DFA with 75 states. Bob loses reputation.

==========
Alice claims:
Any graph can be approximately colored with c=8 colors so that the fraction f=7/8
of the edges satisfy the coloring condition.

==========
Alice claims:
Any context-free grammar of size 10 can be translated into an
equivalent DFA with 100 states provided inputs are shorter than 10 characters.

Bob opposes:
Bob gives to Alice a CFG and she creates a DFA. 
Bob gives to Alice' DFA a string of 10 characters which the DFA accepts
but which is not accepted by the CFG.
Alice loses reputation.
===========
With SCG-student we are likely to have fewer niches and 
more kinds of challenges.