少ない棋譜からの将棋プレイヤ棋力推定システム

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1731125 50 10 AI 0 AI 4 168 132

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1

2

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4

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1

1.1

19 s±t± ho n e he ( - s he SRIRYI d u G H ± ( c s e e e u s G(H 1QT I 7SG)H 1QT I 7S FLUSG*H a s d 19 s 1QT I 7S FLUS z e e 19 k s e f 19 19 ci 19 c e G,H G-H e he ), h a(* e e G.H f h e z s d e ( s ue s e uiu ± io e ± e e d he s d ± d s h G/H k f he e i e 19 e h e G H 19 e e i k ei

1.2

e i i i

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e e i e d s ± u ks u e zu u G H e 19 19 f e e p u z

1.3

e e u e u e e z e e 19 s e e z e

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2

2.1

9

3

ho u 7 O d G H 7 O u e LIR SVV u f ± 01D5 175 19 ] se e d i e d u 19 3 16BE e s ( u ) u ± k u ± f u ( ( ( i ( he c c i s ± ( e he e d u d uiu e u d e s e i s he d e i u e e z he i ± he d uiu he e d e i f

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2.2

3

ho u d G (H s i u f u 01D5 175 u ] u 19 u c 19 c 19 c u f u * ( i .- he z 19 e 19 d e e d z e

2.3 AI

u u 2SRIRYI 19 u u G H ! "(!) d u "%(!) d "%(!) &−"(!), "(!) ≥ 0_{"(!), "(!) ≤ 0} (1) e e s ± e s e u k d o e e d z ei z 19 e he

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2SRIRYI 19 u he e e 19

( (cG )H 19 u

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3

e s u c c ± u k 19 u k 5 = e G/H h e ho 1 2 -. -/ k 2 1 0./ ( d 0./= 1 102347%% 8536 _{+ 1} (2) he 2 1 k -.< -/< ) * d -.< = -.− 16 × 0./ (3) -/< = -/+ 16 × 0./ (4) h / s * ± ) * AB%%5CB% 7A s e i * f u u f e e d ± s e ) ) ( u k e ) ) ) * f ) u e ) , he d i ) - he d i

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o ho u ( (G H e s u * u s u I L ( 2S 19 e I L k e i u he f 0 1D5 175 u ] u

3.1

4

3.1.1

ho ± ho e e k

3.1.2

i ± i ± k i /// ± u / o z u u k u / i u

3.1.3

k s e e ou

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)

3.1.4

he d k i e s e e - e ( u k * , k e i u ( i ( ± k e i k s i ( u f

3.2

3.2.1

d u k e e

3.2.2

o ho ( u u u z u i (*// ± u ou z ho u

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3.2.3

z k z ho s u k ) u k ) ( d ) u k ) ( u k ) ) ( i / he u -350 -300 -250 -200 -150 -100 -50 0 0 1000 2000 3000 4000 5000 6000 7000 8000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 -300 -250 -200 -150 -100 -50 0 0 200 400 600 800 1000 1200 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400

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3.2.4

u k u i ( he ,* d Z , d s u u k e * he / , ui i he , e d / ± u s s uiu ) ) ( u e e k e e i e d

3.3

4

3.3.1

) i he - d s z ho i f e i

3.3.2

o ho ) )/. u i /// ± u ou z ho e u

3.3.3

z ho s d d

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) ) ho ) )/. i u // / e u i f D E = D E × 0.23549 − 595.5 (5) , i e k D E = D E × 4.2464 + 2529 (6)

3.3.4

he i /// he hh z d he ) i ho ( (/ s ± e e ( ( s s ( (/ s -350 -300 -250 -200 -150 -100 -50 0 1150 1250 1350 1450 1550 1650 1750 1850 1950

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3.4

1

4

3.4.1

) ) i i ± z e d ±

3.4.2

e i u , u u

3.4.3

s ) ( I H A I d f e I . 0 1 2 3 4

3.4.4

* ) d d s

3.5

03

4

3.5.1

i ho

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3.5.2

) ) he M e

3.5.3

M u ) * d ) * M u ± z Z ± e

3.5.4

i he Z d s

3.6

3

2

3.6.1

o ho ± i s d i

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3.6.2

o ho * u i ± k d e ± i u

3.6.3

d ± ) f s ) d ± hh z i i ( u k d ± ( d

3.6.4

i ( u hh z ( u d i ± s d e 0 2 4 6 8 10 12 100 200 300 400 500 600 700 800 900 1000

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3.7

9

3

2

3.7.1

i u d z 19G H e d 19 e e i

3.7.2

e ( ( 19 u s u s u e u 19 u e e 19 ( ± e 19( 19 u e .-) d s o u z 19 s ) i ( u s o i d e i u

3.7.3

z 19 ho s ) ) 19 ho - -b A d f

3.7.4

-. d s s z * i f

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4

e * ) ± e 19 e * ( e * ) i u e

4.1

4.1.1

i s e i s ( u d s uiu ho he i ( ui ( s i k z e 19 e u e i u ) , i 19 ho d / s i 19 e ) * i s z 19 e

4.1.2

4

19 G H 19 ( ( e e 19 u 19 ( ) u "%(!) &−"(!), "(!) ≥ 0_{"(!), "(!) ≤ 0} (1) "(!) k io "(!) k z ±± e 19 "(!) u e 19 e * ± 19 * u 19 d e ( i zu u i u ) ) ) u , e

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4.2

4.2.1

z e e ± o s d s e G/H ± u s c h o ( ± ± u e e s s f u

4.2.2

) , o 19 s f ho ( s ) 19 * 19 19( , 19( d o

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4.2.3

19 he s )78Y 9R LQ 3SUL O .72 .,- 8Y 44 ) 7C9 IJ2SSP he ft cG *H ef 7C9 e * ( * ( ft

4.2.4

u d u e he d i ± e ho o * * ( ) * , - . / * . , (,- )/. ( - /-) ( )* . ( // .**

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/ e ii u u o ) o (( ( o s e k ± c s e G/H z e * e d d

4.2.5

4

( ( e s u I L u ( u ) ) ) , u f

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5

he * ( e k i ± c k c e he * u e ( he i ) he c * he c e i u u k f he i f

5.1

5.1.1

* e f ± e e ki * ki fi

5.1.2

* ( u 19 i u ( u i u e e e ki * ki fi z i u * 19 i i 1 2 * i u d 3 4 19 i i u d ± 1 3 2 4 i u d

5.1.3

z ho s

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1 2 3 4 5 6 7 8 9 10 1 1530 795 1458 1742 1840 1844 2129 1881 1976 1980 187 2 1484 1028 1412 1824 2143 1879 2175 1921 2072 1977 168 3 1604 1097 1748 1935 2001 1978 2207 2101 2112 2111 277 4 1572 1226 1757 1991 2196 2009 2238 2170 2193 2115 305 ± z ho ( 1 2 3 4 5 6 7 8 9 10 1 56 36 56 46 57 93 73 69 98 54 2 55 33 46 41 41 87 68 49 74 50 3 78 70 92 82 93 132 117 114 151 103 4 77 66 82 77 77 126 112 94 127 99 * i u 2 e

5.1.4

i u e i o he e i ± * u 7 O u e s cG H * 1 2 * u e 3 4 e e he s k u e k e ± 1 3 i 2 4 e e he u f e d

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5.2

03

5.2.1

f i

5.2.2

* f u ( ( * ) i u e c c f 0 ( i ± u u

5.2.3

s d ( he i i u

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ho ± i io e i

5.2.4

u o e f d f k - ( he e k c ,( ,/ ( he e c d ± ,/ ,, /, he d l e u e i c u e e e i e i u k

5.3

03

5.3.1

u e ± i

5.3.2

19 i f u 0 20 40 60 80 100 120 140 0 500 1000 1500 2000 2500 3000 20 30 40 50 60 70 80 90 (%)

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( ( * ) s u i ± u i u e

5.3.3

s i e ) u k a c A g A

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* u k a c A g A e s ( u k e e e u z z k ± 150 160 170 180 190 200 210 100 90 80 70

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u k a c A g A

5.3.4

u k e ± 2 i k i i / p k e d / u k * d e e z e u s u e k

5.4

03

5.4.1

e u s u k 2 e i

5.4.2

19 i f u ( ( * )

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e u s i ± u i u e

5.4.3

e i s u k s e i u , e i u a d f s

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) e i u u k ,

5.4.4

k u ) * c u i ( e c d

5.5

03

5.5.1

* e i u d i e

5.5.2

19 i f u ( ( 150 200 250 300 350 400 450 500 5 ₁₀ ₁₅ ₂₀ ₂₅ ₃₀ ₃₅ ₄₀ ₄₅ ₅₀ ₅₅ ₆₀ ₆₅ ₇₀ ₇₅ ₈₀ ₈₅ ₉₀ ₉₅ 100

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s z ho u i . ± * u u ho i u i u e

5.5.3

i u k z s - u k a d f s

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* u k ** u k *, ± , u k * c e * he e e s e s z u u k 150 350 550 750 950 1150 1350 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80

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he ** k /, ± z ho s . 1 2 3 4 5 6 7 8 9 10 ( ) * 10.4

5.5.4

7 O u e c s 19 d e ( i i ** s h d * i , u k ( u * G (H d

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6

6.1

± i z f± e -u e e e i d d u ( u k i Z( d u s i /// ) u e u / e u i z e i ho e u o ( ( d u e 19 e u ± e c 19 u 19 s e zu 19 d u ) * i u i e ef d i ± 19 s i u ( u i u e ho u o u e d z i u e e i ± e e e z c u se i

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e s ** i e u *, ef e d u

6.2

s e u e i e k

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u r e e u p± ± u u e e u p± i u e k ho e u e e u p± s r e u p± h A A .8 ))*- o

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Silver, David, et al. "Mastering the game of Go with deep neural networks and tree

search." Nature, Vol. 529, No. 7587 pp.484-489, (2016).

[4]

Silver, David,

et al., ‘‘Mastering the game of go without human knowledge,’’ Nature,

Vol. 550, No. 7676, pp.354-359, (2017).

[5]

,

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, (2017).

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Guid, M. and Bratko, I. COMPUTER ANALYSIS OF WORLD CHESS

CHAMPIONS. ICGA Journal, Vol. 29, No. 2, pp. 65-73 (2006).

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