Room for Emrakul and xnor

xnor

11:09 AM

hi

user61230

Okay, so.

user61230

Let's start with the board clear.

user61230

Hmm. Let's juts type in our moves, then?

xnor

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?

user61230

I'd want to look at it again before saying there's a hole in it, but probably, yeah.

xnor

11:10 AM

ok, cool

user61230

It definitely indicates I didn't know what I was talking about.

xnor

let's use number coordinates, OK?

user61230

(oh, the anxiety)

xnor

haha

user61230

I have a screenshot of the grid from the game... mind if we use the letter coords?

xnor

11:11 AM

i move at (0,2)

user61230

Waaaait, one sec.

xnor

ok

user61230

What size grid are you using / would it be too much of an issue to open a screenshot in paint?

user61230

Just for convenience

xnor

i don't know the grid size yet

i was just going to expand it

user61230

11:12 AM

...we could be here all day :P

xnor

unless the grid limitation is part of your argument?

i think i can win within 15 moves

is that ok?

user61230

xnor

oh, nice

user61230

It's not part of my argument, but I'd rather not play out an infinite grid

user61230

And sure!

xnor

11:13 AM

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)

user61230

xnor

great!

user61230

...I'll shrink the image next time, sorry.

xnor

next, I move in one of the four center squares

it's your move

user61230

xnor

11:15 AM

one minute

i move above my leftmost piece

user61230

xnor

leftmost piece

user61230

...whoops.

user61230

My bad.

xnor

no problem!

user61230

11:17 AM

xnor

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

user61230

For clarity, your new squares are orange and mine are light blue.

xnor

i get four in a row by moving below your leftmost square

Sp3000

(don't worry, I was thinking of the knights-move thing as well)

user61230

11:19 AM

...shiny

xnor

i got the knight's move idea from playing the AI

Sp3000

Same, though the AI sort of surrounds you first-made blocks if you place them randomly

user61230

Okay

user61230

hmm

xnor

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

user61230

11:21 AM

I'm... not sure.

Sp3000

I thought Emkraul assumed that red moves adjacent to a previous move

Which is why I asked

user61230

Adjacency shouldn't be a requirement

user61230

In generating the second chain of two, the first should have been blocked out

user61230

But it wasn't

xnor

is the fact that i made four threats for three-in-a-rows after my five moves accounted for?

user61230

11:22 AM

ah

user61230

I see what happened

Sp3000

Also: " In order to create a 4-chain, we need to create a linked 3-chain" isn't true

user61230

In creating the 3-chain, you also created a linked 2-chain.

user61230

@Sp3000 It definitely is.

user61230

Because if it weren't, then the chain would have at most two degrees of movement.

user61230

11:23 AM

That would be killed on the next blue move.

user61230

@xnor Hmm... it's confusing me. Linking 3-chains and 2-chains now...

user61230

Maybe I'm thinking about this wrong.

user61230

It's not degrees of freedom for particular chains, it's degrees of freedom among adjacent cycles.

user61230

Hrrrrng. Your move created two DoM among 3-cycles, and two DoM among 2-cycles.

user61230

Gahhhhhh. Thank you, @xnor!

xnor

11:26 AM

sure!

good luck with your proof

user61230

It's 3:30 AM, so I'm uh, going to go sleep, actually. But I'll ponder this.

xnor

good night!

Sp3000

Hmm

user61230

G'night, and thanks again!

user61230

@xnor I know why my proof fails

user61230

11:36 AM

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.

user61230

What you did was a totally different d) expand two chains.

user61230

If you restrict movement to the first three, the proof holds. If you try and do the fourth thing, it fails.

user61230

3-chains can't become linked to 2-chains in my model

Transcript for

Room for Emrakul and xnor