In the next game I was blue and, having one long chain and seeing that at two spots we could break them are make them with a single move, I thought I would have the choice. I didn't count moves. Why was I wrong?

[game;id:1425395;move:20]

The shown move was the move with which I thought I won the game but which seems to have lost me the game.

At that point you want NOT to choose the number of chains in either the left or the bottom region as mario_p can then decide what to do in the other one and thus win control. Thus you want to keep playing waiting moves, including opening short chains as this will be less costly than losing control. I see 0 free move in the left, 2 at the bottom and either 7 or 8 in the right, but mario_p can force 7 (thus forcing you to make the first choice) by playing the vertical move on the top right of the “6-loop” (just to give it a name) (at least I believe so).

I misthought that when there was 1 chain blue would have the last free move…

Yes but here it could end up with 1, 2 or 3 chains, right?

@Hjallti: this is a good question! To really understand the answer you have to learn about nim-values for dots and boxes regions. In short, you are perhaps thinking that every region is either “some number of chains” or “undecided”. But the problem is that mathematically there is more than one kind of “undecided” region. The one in the top left is a very common one, but the one at the bottom of your game above is a rather rarer one and has a different “parity” to the one in the top left. Here is a way I can explain the difference not using nim language at all. In the top left, we have the most common situation: when the move is made which decides the number of chains, if we make the move for which there are an even number of “waiting around” moves afterwards, then we will get a chain. But in the bottom we have the rarer situation that when the decision is finally made about whether that region is a chain or not, the move that gives an even number of waiting moves is the sacrifice, which makes 0 chains. So in some sense, putting those two regions together, you can think of the resulting region as 1 chain. So in short everything is consistent. I agree it's surprising; the region you've discovered is as far as I know pretty much the simplest region where the “zero move” makes 0 chains rather than 1 chain: you can sacrifice the top left hand box and then you get the simplest region I know. If you really want to know what's going on then read the nim stuff at wccanard.wetpaint.com .

Thx for this. I read this night.

This chapter one to three I read quite easy and I understood reasons (proofs as math.) quite fast. I did not get chapter 4 yet. May be it makes sense to be a bit less quick there.

U will do me playing more games of d&b as this stuff really is fun. I learned everthing about XOR and the Euler formula while my study - really nice to c it used here!

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