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11:09 AM
hi
 
Okay, so.
Let's start with the board clear.
Hmm. Let's juts type in our moves, then?
 
so are we on the same page that if I can win a game under these conditions, that means there's a hole in the proof somewhere?
 
I'd want to look at it again before saying there's a hole in it, but probably, yeah.
 
ok, cool
 
It definitely indicates I didn't know what I was talking about.
 
11:11 AM
let's use number coordinates, OK?
 
(oh, the anxiety)
 
haha
 
I have a screenshot of the grid from the game... mind if we use the letter coords?
 
i move at (0,2)
 
Waaaait, one sec.
 
11:11 AM
ok
 
What size grid are you using / would it be too much of an issue to open a screenshot in paint?
Just for convenience
 
i don't know the grid size yet
i was just going to expand it
 
...we could be here all day :P
 
unless the grid limitation is part of your argument?
i think i can win within 15 moves
is that ok?
 
11:12 AM
oh, nice
 
It's not part of my argument, but I'd rather not play out an infinite grid
And sure!
 
I move at four spaces that form a square each a knight's move apart
does that make sense?
(I make these four moves in a row with the understanding that you pass each time because I never threaten a line of 3)
 
great!
 
...I'll shrink the image next time, sorry.
 
11:14 AM
next, I move in one of the four center squares
it's your move
 
one minute
i move above my leftmost piece
 
leftmost piece
 
...whoops.
My bad.
 
11:17 AM
no problem!
 
i move to one space below and one space to the left of the space i just moved in
(sp3000: we're playing a game where Emrakul gives me the handicap of passing unless i threaten three or more in a row)
Emrakul is blue
 
For clarity, your new squares are orange and mine are light blue.
 
i get four in a row by moving below your leftmost square
 
(don't worry, I was thinking of the knights-move thing as well)
 
11:19 AM
...shiny
 
i got the knight's move idea from playing the AI
 
Same, though the AI sort of surrounds you first-made blocks if you place them randomly
 
Okay
hmm
 
i think it's a forced win no matter how you respond to the knight's move, but I haven't tried all the possibilities
@Emrakul so where does your proof go wrong on this example?
i can't put my finger on it
 
I'm... not sure.
 
11:21 AM
I thought Emkraul assumed that red moves adjacent to a previous move
Which is why I asked
 
Adjacency shouldn't be a requirement
In generating the second chain of two, the first should have been blocked out
But it wasn't
 
is the fact that i made four threats for three-in-a-rows after my five moves accounted for?
 
ah
I see what happened
 
Also: " In order to create a 4-chain, we need to create a linked 3-chain" isn't true
 
In creating the 3-chain, you also created a linked 2-chain.
@Sp3000 It definitely is.
Because if it weren't, then the chain would have at most two degrees of movement.
That would be killed on the next blue move.
@xnor Hmm... it's confusing me. Linking 3-chains and 2-chains now...
Maybe I'm thinking about this wrong.
It's not degrees of freedom for particular chains, it's degrees of freedom among adjacent cycles.
Hrrrrng. Your move created two DoM among 3-cycles, and two DoM among 2-cycles.
Gahhhhhh. Thank you, @xnor!
 
11:26 AM
sure!
good luck with your proof
 
It's 3:30 AM, so I'm uh, going to go sleep, actually. But I'll ponder this.
 
good night!
 
Hmm
 
G'night, and thanks again!
@xnor I know why my proof fails
I made a rather complicated implicit assumption that a move either a) starts a new chain, b) expands a chain, or c) links two chains.
What you did was a totally different d) expand two chains.
If you restrict movement to the first three, the proof holds. If you try and do the fourth thing, it fails.
3-chains can't become linked to 2-chains in my model
 

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