11:09 AM
hi

Okay, so.
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

one minute
i move above my leftmost piece

leftmost piece

...whoops.

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

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...
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!

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