Before I'm bogged down by the changes let me

return to the snortGO

puzzle. Recall that in **snortGO** black and white take

turns in placing a Go-stone on the board respecting the rule that no

stones of opposite colour may be adjacent. Javier is right that snortGo

with an empty starting board having an odd number of rows and columns is

a first player's win (place your first stone on the central spot and

respond to your opponent's moves by reflecting them along the

center).

Still, one can compose realistic end-game problems (as

in the previous snortGo post where the problem was : prove that the position is a first

player's win and indicate a winning move for both black and white).

To start the analysis let us remove all spots which are unavailable for

both players (as depicted in the top picture). Some of the remaining

spots are available to just one player (the central free spots and the

two in the top left corner). One counts that black has 5 such central

spots and white 4 (including the top left corner). So, all the genuine

action is happening in the three remaining corner regions for which one

can calculate the exact value following the rules of combinatorial game

theory where bLack is playing Left and white Right (so the free

spots for black add up to +5 whereas those for white add up to -4). It

is pretty easy to work out the exact values of the corner subgames

To find the value of the total game we have to sum up these

values which can either be done by hand (use this and this to get

started and use the inductive rule $G+H = \\{ G^L+H,G+H^L \\vert

G^R+H,G+H^R \\}$) or using combinatorial game suite to

verify that this sum is equal to $\\{ \\{ 3 \\vert 2 \\} \\vert -1 \\}$

which is a fuzzy game (that is, confused with zero or a first

player's win). To find the actual winning moves just try out the

Left (bLack) and Right (white) options in the corner games to find out

that there is a unique winning move for white and there are just 2

winning moves for bLack, all indicated in the pictures below.

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