go game

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go

learn

  • interactive way to go point, stone, liberty, string (or chain), atari, ko, komi, byoyomi (AlphaGo-Lee Sedol match, for each match, each player had 2 hr + 3x 60s byoyomi), positional superko, situational superko, live group, dead group, eye, life and death problem, semiai, seki

  • browser opponent

rules

  • tromp-taylor rules

  • in practice

    • after 2 consecutive passes, players agree on which groups are dead/captured

    • if no agreement, play continues

    • then game is scored

  • computer implementations often based on TT rules

    • situational superko

    • no suicide

    • algorithm to recognize dead/captured groups at end of game

    • TT scoring

    • result is close to Chinese rules

solving go

small boards
  • proof tree for 2x2 go

  • in theory (with enough time/memory), any go state can be solved by minimax

  • in practice, search space infeasible for boards 8x8 or bigger

  • up to 5x5 (does not use psk) erik van der werf

  • up to 30-cells (does not use psk) erik van der werf

  • open problems

    • solve all 6x6 go openings   (msc/ugrad: theory there, just needs coding)

    • solve 1xn opening for n ≥ 13 (msc/ugrad: theory + coding)

    • needed linear go theory: move pruning, move ordering

linear go

solving
  • small boards

  • solving 1xn go open for n over 12: why ?

  • many early-win-detection observations do not apply in linear go

  • eg. linear go blocks have no interior region, so blocks have no true eyes

  • eg. there are no local safe linear go patterns

  • need linear go early-win-detection/pruning observations

some linear go proof trees

1x3
 - - -

   |

 - x -
1x4
     - - - -

        |

     - x - -

   /         \

 - x o -   - x - o

    |         |

 - x * x   - x x -      o cannot play at *: ko

some linear go exercises

x-to-move
find minimax value and principal variation for each

 x - o - -

 o - x - -

 x - - o -

 o - - x -

 o - - - -

 - o - - -

 - - o - -
answers
 1 2 3 4 5
 x - o - -  val 0     pv x:4 o:2 x:1 o:2 pass pass

 o - x - -  val x+5   pv x:4 p x:2

 x - - o -  val x-5   pv x:2 o:3 x:2 o:1

 o - - x -  val x+5   pv x:2

 o - - - -  val x+5   pv x:4 ... (use 3rd result above)

 - o - - -  val 0     pv x:4

 - - o - -  val 0     pv x:2 o:4 (o:1 loses) x:5 o:4

some safe linear go positions

unconditionally safe whole-board positions

- x -

- x x -

- x - x -
- x x x -

- x x x x -
- x - x x -

- x x x x x -
- x - x x x -
- x x - x x -
- x - x - x -

...

not necessarily safe
x -

x - -
x - x
x x -

x - - -
x - x -
x - - x
x x - -
x - x x
x x x -

...
some conditionally safe whole-board positions
** if x has never played at each ! cell ** then whole board for x

- x ! ! x -

- x ! ! x x -

- x ! ! x x - x -
- x ! ! x - x x -
- x ! ! x ! ! x -

...

not necessarily safe (why?)
- x ! ! ! x -