Bold conjectures

Because what's the point of making a conjecture if it isn't provocative? After a short but extremely fruitful with Chris and Jesse this afternoon, and bolstered up on the basis of a whole two examples that I've worked through, I have the following two bold conjectures:

• [In a D strategy] The first time that the E rule is violated, the reference of that round has already appeared as the reference of an earlier round.
• (Corollary of the first) The first time that the E rule is violated, if you chop the branch off at the previous move (i.e., P's move), the result of doing so for all branches in a winning D-strategy will be a winning E-strategy.

So: The hunt for counterexamples is on!