Blunder cost in Go and Hex
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1 Fuego MoHex computing univ alberta 2011 november
2 Fuego MoHex 1 2 Fuego 3 MoHex 4
3 outline Fuego MoHex def n: to stumble blindly an ignorant move (bad when good available) a random move end game: usually fatal early game: maybe not
4 outline Fuego MoHex def n: to stumble blindly an ignorant move (bad when good available) a random move end game: usually fatal early game: maybe not
5 outline Fuego MoHex def n: to stumble blindly an ignorant move (bad when good available) a random move end game: usually fatal early game: maybe not
6 outline Fuego MoHex def n: to stumble blindly an ignorant move (bad when good available) a random move end game: usually fatal early game: maybe not
7 outline Fuego MoHex def n: to stumble blindly an ignorant move (bad when good available) a random move end game: usually fatal early game: maybe not
8 outline Fuego MoHex def n: to stumble blindly an ignorant move (bad when good available) a random move end game: usually fatal early game: maybe not
9 Fuego MoHex assume stochastic-player : random move what if one player always s on move k? Fuego vs Fuego- MoHex vs MoHex-
10 Fuego MoHex assume stochastic-player : random move what if one player always s on move k? Fuego vs Fuego- MoHex vs MoHex-
11 Fuego MoHex assume stochastic-player : random move what if one player always s on move k? Fuego vs Fuego- MoHex vs MoHex-
12 Fuego MoHex assume stochastic-player : random move what if one player always s on move k? Fuego vs Fuego- MoHex vs MoHex-
13 Fuego MoHex assume stochastic-player : random move what if one player always s on move k? Fuego vs Fuego- MoHex vs MoHex-
14 Fuego MoHex assume stochastic-player : random move what if one player always s on move k? Fuego vs Fuego- MoHex vs MoHex-
15 Fuego MoHex : parameters parameters 2-player alternate-move no-draw T: max moves per game t: move in {0,..., T} e t : solving ease after t moves w t : fraction winning moves w t < 0 means all moves lose after best move, w t+1 w T m t : score of move t r t : rank of move t s p : strength of player p 0 (hard)...1 (easy) -1 (all lose)...1 (all win) -1 (bad)...1 (good) 1 (worst)...k (best) -1 (anti-perfect)...1 (perfect)
16 Fuego MoHex : parameters parameters 2-player alternate-move no-draw T: max moves per game t: move in {0,..., T} e t : solving ease after t moves w t : fraction winning moves w t < 0 means all moves lose after best move, w t+1 w T m t : score of move t r t : rank of move t s p : strength of player p 0 (hard)...1 (easy) -1 (all lose)...1 (all win) -1 (bad)...1 (good) 1 (worst)...k (best) -1 (anti-perfect)...1 (perfect)
17 Fuego MoHex : parameters parameters 2-player alternate-move no-draw T: max moves per game t: move in {0,..., T} e t : solving ease after t moves w t : fraction winning moves w t < 0 means all moves lose after best move, w t+1 w T m t : score of move t r t : rank of move t s p : strength of player p 0 (hard)...1 (easy) -1 (all lose)...1 (all win) -1 (bad)...1 (good) 1 (worst)...k (best) -1 (anti-perfect)...1 (perfect)
18 Fuego MoHex : parameters parameters 2-player alternate-move no-draw T: max moves per game t: move in {0,..., T} e t : solving ease after t moves w t : fraction winning moves w t < 0 means all moves lose after best move, w t+1 w T m t : score of move t r t : rank of move t s p : strength of player p 0 (hard)...1 (easy) -1 (all lose)...1 (all win) -1 (bad)...1 (good) 1 (worst)...k (best) -1 (anti-perfect)...1 (perfect)
19 Fuego MoHex : parameters parameters 2-player alternate-move no-draw T: max moves per game t: move in {0,..., T} e t : solving ease after t moves w t : fraction winning moves w t < 0 means all moves lose after best move, w t+1 w T m t : score of move t r t : rank of move t s p : strength of player p 0 (hard)...1 (easy) -1 (all lose)...1 (all win) -1 (bad)...1 (good) 1 (worst)...k (best) -1 (anti-perfect)...1 (perfect)
20 Fuego MoHex : parameters parameters 2-player alternate-move no-draw T: max moves per game t: move in {0,..., T} e t : solving ease after t moves w t : fraction winning moves w t < 0 means all moves lose after best move, w t+1 w T m t : score of move t r t : rank of move t s p : strength of player p 0 (hard)...1 (easy) -1 (all lose)...1 (all win) -1 (bad)...1 (good) 1 (worst)...k (best) -1 (anti-perfect)...1 (perfect)
21 Fuego MoHex : parameters parameters 2-player alternate-move no-draw T: max moves per game t: move in {0,..., T} e t : solving ease after t moves w t : fraction winning moves w t < 0 means all moves lose after best move, w t+1 w T m t : score of move t r t : rank of move t s p : strength of player p 0 (hard)...1 (easy) -1 (all lose)...1 (all win) -1 (bad)...1 (good) 1 (worst)...k (best) -1 (anti-perfect)...1 (perfect)
22 Fuego MoHex : parameters parameters 2-player alternate-move no-draw T: max moves per game t: move in {0,..., T} e t : solving ease after t moves w t : fraction winning moves w t < 0 means all moves lose after best move, w t+1 w T m t : score of move t r t : rank of move t s p : strength of player p 0 (hard)...1 (easy) -1 (all lose)...1 (all win) -1 (bad)...1 (good) 1 (worst)...k (best) -1 (anti-perfect)...1 (perfect)
23 Fuego MoHex : parameters parameters 2-player alternate-move no-draw T: max moves per game t: move in {0,..., T} e t : solving ease after t moves w t : fraction winning moves w t < 0 means all moves lose after best move, w t+1 w T m t : score of move t r t : rank of move t s p : strength of player p 0 (hard)...1 (easy) -1 (all lose)...1 (all win) -1 (bad)...1 (good) 1 (worst)...k (best) -1 (anti-perfect)...1 (perfect)
24 Fuego MoHex : parameters parameters 2-player alternate-move no-draw T: max moves per game t: move in {0,..., T} e t : solving ease after t moves w t : fraction winning moves w t < 0 means all moves lose after best move, w t+1 w T m t : score of move t r t : rank of move t s p : strength of player p 0 (hard)...1 (easy) -1 (all lose)...1 (all win) -1 (bad)...1 (good) 1 (worst)...k (best) -1 (anti-perfect)...1 (perfect)
25 Fuego MoHex : game simulation game simulation assume games non-pathological for each t sample m t with E[m t ] = s p e t compute r t from m t using w t, make move with rank r t sample w t+1 using w t and r t (strongest move from winning position leaves no opponent winning moves)
26 Fuego MoHex : game simulation game simulation assume games non-pathological for each t sample m t with E[m t ] = s p e t compute r t from m t using w t, make move with rank r t sample w t+1 using w t and r t (strongest move from winning position leaves no opponent winning moves)
27 Fuego MoHex : game simulation game simulation assume games non-pathological for each t sample m t with E[m t ] = s p e t compute r t from m t using w t, make move with rank r t sample w t+1 using w t and r t (strongest move from winning position leaves no opponent winning moves)
28 Fuego MoHex : game simulation game simulation assume games non-pathological for each t sample m t with E[m t ] = s p e t compute r t from m t using w t, make move with rank r t sample w t+1 using w t and r t (strongest move from winning position leaves no opponent winning moves)
29 Fuego MoHex : game simulation game simulation assume games non-pathological for each t sample m t with E[m t ] = s p e t compute r t from m t using w t, make move with rank r t sample w t+1 using w t and r t (strongest move from winning position leaves no opponent winning moves)
30 Fuego MoHex : game simulation game simulation assume games non-pathological for each t sample m t with E[m t ] = s p e t compute r t from m t using w t, make move with rank r t sample w t+1 using w t and r t (strongest move from winning position leaves no opponent winning moves)
31 Fuego MoHex : game simulation game simulation assume games non-pathological for each t sample m t with E[m t ] = s p e t compute r t from m t using w t, make move with rank r t sample w t+1 using w t and r t (strongest move from winning position leaves no opponent winning moves)
32 Fuego MoHex : cost E[m t ] s p e t assume s p > 0 E[m t ] = 0 (s p 0) cost: resulting drop in expected win rate indirectly measures s p e t w t
33 Fuego MoHex : cost E[m t ] s p e t assume s p > 0 E[m t ] = 0 (s p 0) cost: resulting drop in expected win rate indirectly measures s p e t w t
34 Fuego MoHex : cost E[m t ] s p e t assume s p > 0 E[m t ] = 0 (s p 0) cost: resulting drop in expected win rate indirectly measures s p e t w t
35 Fuego MoHex : cost E[m t ] s p e t assume s p > 0 E[m t ] = 0 (s p 0) cost: resulting drop in expected win rate indirectly measures s p e t w t
36 Fuego MoHex : cost E[m t ] s p e t assume s p > 0 E[m t ] = 0 (s p 0) cost: resulting drop in expected win rate indirectly measures s p e t w t
37 Fuego MoHex : cost E[m t ] s p e t assume s p > 0 E[m t ] = 0 (s p 0) cost: resulting drop in expected win rate indirectly measures s p e t w t
38 settings outline Fuego MoHex settings experiments Fuego vs Fuego- board 7 7, 9 9, for each move t, 500 games for each game, 10K MCTS simulations / move resign threshold 0.05 white komi 7.5
39 settings outline Fuego MoHex settings experiments Fuego vs Fuego- board 7 7, 9 9, for each move t, 500 games for each game, 10K MCTS simulations / move resign threshold 0.05 white komi 7.5
40 settings outline Fuego MoHex settings experiments Fuego vs Fuego- board 7 7, 9 9, for each move t, 500 games for each game, 10K MCTS simulations / move resign threshold 0.05 white komi 7.5
41 settings outline Fuego MoHex settings experiments Fuego vs Fuego- board 7 7, 9 9, for each move t, 500 games for each game, 10K MCTS simulations / move resign threshold 0.05 white komi 7.5
42 settings outline Fuego MoHex settings experiments Fuego vs Fuego- board 7 7, 9 9, for each move t, 500 games for each game, 10K MCTS simulations / move resign threshold 0.05 white komi 7.5
43 settings outline Fuego MoHex settings experiments Fuego vs Fuego- board 7 7, 9 9, for each move t, 500 games for each game, 10K MCTS simulations / move resign threshold 0.05 white komi 7.5
44 Fuego MoHex settings experiments black white active games black baseline white baseline Fuego vs. Fuego- (7x7) player win rate move #
45 Fuego MoHex settings experiments Fuego vs. Fuego- (9x9) black white active games black baseline white baseline player win rate move #
46 Fuego MoHex settings experiments black white active games black baseline white baseline Fuego vs. Fuego- (13x13) player win rate move #
47 Hex outline Fuego MoHex Hex all winning moves settings experiments
48 Fuego MoHex all winning moves Hex all winning moves settings experiments
49 settings outline Fuego MoHex Hex all winning moves settings experiments MoHex vs MoHex- board 7 7, 9 9, for each move t, 500 games for each game, 1K MCTS simulations / move 7 7: after, use solver to find winning moves
50 settings outline Fuego MoHex Hex all winning moves settings experiments MoHex vs MoHex- board 7 7, 9 9, for each move t, 500 games for each game, 1K MCTS simulations / move 7 7: after, use solver to find winning moves
51 settings outline Fuego MoHex Hex all winning moves settings experiments MoHex vs MoHex- board 7 7, 9 9, for each move t, 500 games for each game, 1K MCTS simulations / move 7 7: after, use solver to find winning moves
52 settings outline Fuego MoHex Hex all winning moves settings experiments MoHex vs MoHex- board 7 7, 9 9, for each move t, 500 games for each game, 1K MCTS simulations / move 7 7: after, use solver to find winning moves
53 settings outline Fuego MoHex Hex all winning moves settings experiments MoHex vs MoHex- board 7 7, 9 9, for each move t, 500 games for each game, 1K MCTS simulations / move 7 7: after, use solver to find winning moves
54 Fuego MoHex Hex all winning moves settings experiments Mohex vs. Mohex- (7x7) black white active games black baseline white baseline player win rate move #
55 Fuego MoHex Hex all winning moves settings experiments Mohex vs. Mohex- (7x7) black white active games black baseline white baseline available wins player win rate move #
56 Fuego MoHex Hex all winning moves settings experiments Mohex vs. Mohex- (9x9) black white active games black baseline white baseline player win rate move #
57 Fuego MoHex Hex all winning moves settings experiments Mohex vs. Mohex- (9x9) 250 sim./move black white active games black baseline white baseline player win rate move #
58 Fuego MoHex Hex all winning moves settings experiments Mohex vs. Mohex- (11x11) black white active games black baseline white baseline player win rate move #
59 outline Fuego MoHex future work start: low cost after few moves: more costly after: cost smooth time management? not yet...
60 outline Fuego MoHex future work start: low cost after few moves: more costly after: cost smooth time management? not yet...
61 outline Fuego MoHex future work start: low cost after few moves: more costly after: cost smooth time management? not yet...
62 outline Fuego MoHex future work start: low cost after few moves: more costly after: cost smooth time management? not yet...
63 outline Fuego MoHex future work start: low cost after few moves: more costly after: cost smooth time management? not yet...
64 future work outline Fuego MoHex future work smarter s eg: sample only from reasonable moves? (Hex: stay in mustplay Go: no eye fill-in) eg: player less time (ponder player more time)?
65 future work outline Fuego MoHex future work smarter s eg: sample only from reasonable moves? (Hex: stay in mustplay Go: no eye fill-in) eg: player less time (ponder player more time)?
66 future work outline Fuego MoHex future work smarter s eg: sample only from reasonable moves? (Hex: stay in mustplay Go: no eye fill-in) eg: player less time (ponder player more time)?
67 future work outline Fuego MoHex future work smarter s eg: sample only from reasonable moves? (Hex: stay in mustplay Go: no eye fill-in) eg: player less time (ponder player more time)?
68 future work outline Fuego MoHex future work smarter s eg: sample only from reasonable moves? (Hex: stay in mustplay Go: no eye fill-in) eg: player less time (ponder player more time)?
69 dank u outline Fuego MoHex thank you future work UofA GAMES, Schaeffer Natural Sciences and Engineering Research Council of Canada
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