3x3 and long chain puzzle---a real surprise (to me) Dots and Boxes
8 replies. Last post: 2007-09-04
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8 replies. Last post: 2007-09-04
Reply to this topic Return to forumRed is three up but is going to lose that long chain, and it's got
eleven boxes in!
6 + + +-+-+-+ |r|r|r|5 +-+-+-+-+-+ | 4 +-+-+-+ + + | | |3 + + + + + + | | |2 + + + + + + | |1 + + + +-+-+ a b c d e f
I am *amazed* that red can win this one. If and when a second chain
forms in the bottom left, red will find he's lost the chain battle
and in particular is going to lose all 11 of those boxes in the 11-chain.
He has to struggle out of the position ensuring that, if blue keeps
control, he manages to land *one* measly box out of the nine in the
corner! On the other hand, my feeling for this one is that the best
play line is rather natural—I've certainly seen a part of it in
an actual game, and I actually fancy that I would have had *some*
chance of finding it over the board.
wcc
Aah, I see why we get those funny indentations now: it's spaces at the end of lines. Try again.
6 + + +-+-+-+ |r|r|r|5 +-+-+-+-+-+ |4 +-+-+-+ + + | | |3 + + + + + + | | |2 + + + + + + | |1 + + + +-+-+ a b c d e f
So just to keep this topic alive, do you now know how to play this one :
6 + +-+ + + +
\| \|
5 +-+-+-+-+-+
\|
4 +-+-+-+ + +
\| \| \|
3 + + + + + +
\| \| \|
2 + + + + + +
\| \|
1 + + + +-+-+
a b c d e f
and win ?
Hum same problem with spaces:
6 + +-+ + + + | |5 +-+-+-+-+-+ |4 +-+-+-+ + + | | |3 + + + + + + | | |2 + + + + + + | |1 + + + +-+-+ a b c d e f
I don't, but I have some tables that might tell me! The nim-value of the 3x3 icelandic corner is 0, and the nim-value of the chain is also 0 of course, so if I want to keep control I should sacrifice 2 in the top left. In fact, surely this wins. I will then win the long chain battle, which will give me *at least* 1 in the icelandic corner, and that and the top left hand corner which I get whilst losing the short chain battle, and the 11-chain, wins me the game.
wcc
[looks in tables] Right. I computed the value of 3x3 icelandic + 11-chain + 1-chain + 2-chain, and it's 3 to the player whose move it isn't, so the move I suggest does win (13-12), although I don't know if it's optimal.
wcc
Yes congrats you are right.
So after c5-c6 Red get two boxes and is faced with similar puzzle as yours : give you only 1 box in the icelandic corner by playing b3-b4.
Yes, so that brings us back to the original question: how does red (in the initial position) keep blue down to 1 box in the 3x3 corner? :-) The point is that blue must keep control: red already has 3 boxes so if blue loses control then red gets the 11-chain and wins. What surprised me was that he couldn't both keep control and get two boxes! If red plays it well, at least :-)