Q1 Why is a UT, of any type, called a UT?
Q2 So I started looking at the UT, type 1. I was trying to convince myself that the first move into it would produce a switch. But there are so many spots! So many spots! It's like a whole pack of rabid Dalmations are running around Macbeth's castle and the Lady is going mad, mad, mad, I tell you, alternatively trying to sweep them out with a broom and a dagger! There's no hope for her, and less for me! So I have to build a comprehensive tree to see this? I started several times, but it's like one of those moving trees from Birnam Wood headed toward Dunsinane!
Q3 I can't even get past the initial move into a type 1 UT, to be honest. So are there two or three fundamental first moves?
Q4 I count to three if I show, without loss of generality, one spot connecting to itself without encircling the other (and sprouting a new spot in the process, of course), one spot connecting to itself but encircling the other in the process, and one spot connecting to the other. But the first two are really the same, even though they look real different?
Q5 Because you have an empty spot ("encircled" or not) which is accessible to either of the 2/3 full spots in the next move, or which can be cut off from or left accessible to the offspring of the two 2/3 full spots if the next move connects them?
Q6 I'm not smart enough to think about that! First am I right?
Q7 Second, is there some way to recognize "equivalent configurations" without me having to try to think?
Q8 I realize that the term "equivalent configurations" is loaded (for example if the second player for n spots, for some n, were "known" to always win with correct play, then all of the possible configurations after the first move are in some sense equivalent), but that's not what I mean (I don't think!). I mean, is there some neat little simplification for me to prune my trees of irrelevent encirclement distractions?
Q9 I realize that encirclement can be profound since it has the capacity to cut off space so I guess there's not much pruning capacity here?
Q10 Are there other devices?
Q11 Do my questions even seem sane?
Q12 Or am I mad, mad, mad, I tell you?
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