136 7. AUTOMATIC GENERAL GAME TUNING
f .x/ D 150
1
1 Cexp
x
30
C K
3
!
f .x/ D L log
2
x
f .x/ D 2
x
70
:
Fitness Calculation
Os
1 n Oy
Loss
.
Os; Oy
/
D NRMSE
.
Os; Oy
/
D
q
P
n
iD1
.
Oy
i
Os
i
/
2
n
.
Oy
max
Oy
min
/
:
1 Loss.Os; Oy/
7.4.2 EVOLVING GAMES FOR PLAYER EXPERIENCE
Experimental Setup
Defender Waves Seaquest
20
21 7
m D 0:2
m D 0:4
m D 1:0
7.4. MODELING PLAYER EXPERIENCE 137
K
3
D 3
K
3
D 12
20
l D 10 1=l C
p
2 d D 10
V .s/ D
8
ˆ
<
ˆ
:
score.s/;
1000; s
1000; s:
C
p
2
100
Evolving for a Linear Score Progression
y D 0:2x
x y x
1 0
10
1
y D 0:2x
Seaquest 200
Waves 500 Defender
800
138 7. AUTOMATIC GENERAL GAME TUNING
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
Fitness
1.25
1.00
0.75
0.50
0.25
0.00
-0.25
Fitness
2
1
0
-1
-2
Fitness
0 200 400 600 800 1000
Generation
0 200 400 600 800 1000
Generation
0 200 400 600 800 1000
Generation
Average Fitness over all Generations
Defender_Lin_0.2
Average Fitness over all Generations
Waves_Lin_0.2
Average Fitness over all Generations
Seaquest_Lin_0.2
Fitness
Fitness Fitness
y D 0:2x
Defender Waves Seaquest
N
N
N
y D 0:2x
100
80
60
40
20
0
Average Score for Each Step
100
80
60
40
20
0
Average Score for Each Step
175
150
125
100
75
50
25
0
Average Score for Each Step
0 100 200 300 400 500
Steps
0 100 200 300 400 500
Steps
0 100 200 300 400 500
Steps
Average Score over all Generations
Defender_Lin_0.2
Average Score over all Generations
Waves_Lin_0.2
Average Score over all Generations
Seaquest_Lin_0.2
gen = 0-200
gen = 200-400
gen = 400-600
gen = 600-800
gen = 800-1000
wanted
gen = 0-100
gen = 100-200
gen = 200-300
gen = 300-400
gen = 400-500
wanted
gen = 0-50
gen = 50-100
gen = 100-150
gen = 150-200
gen = 200-250
wanted
y D 0:2x
Defender Waves Seaquest
Waves
Defender
7.4. MODELING PLAYER EXPERIENCE 139
10
y D x
500
400
300
200
100
0
Score
Score
700
600
500
400
300
200
100
0
0 100 200 300 400 500
Steps
0 100 200 300 400 500
Steps
Validation Results for Defender,
Played by MCTS
Validation Results for Waves,
Played by MCTS
Setting 1
Setting 2
Setting 3
Setting 4
Setting 5
Setting 6
Setting 7
Setting 8
Setting 9
Setting 10
wanted
Setting 1
Setting 2
Setting 3
Setting 4
Setting 5
Setting 6
Setting 7
Setting 8
Setting 9
Setting 10
wanted
Score
500
400
300
200
100
0
0 100 200 300 400 500
Steps
Validation Results for Seaquest,
Played by MCTS
Setting 1
Setting 2
Setting 3
Setting 4
Setting 5
Setting 6
Setting 7
Setting 8
Setting 9
Setting 10
wanted
y D x
Defender
Waves
Seaquest
Defender
y D mx m D 1
Waves Seaquest
Fitting Advanced Score Trends
140 7. AUTOMATIC GENERAL GAME TUNING
0.8
0.6
0.4
0.2
0.0
Fitness
140
120
100
80
60
40
20
0
Average Score for Each Step
0 200 400 600 800 1000
Generation
0 100 200 300 400 500
Steps
Average Fitness Over All Generations
Waves_Sig
Average Score Over All Generations
Waves_Sig
gen = 0-100
gen = 100-200
gen = 200-300
gen = 300-400
gen = 400-500
wanted
Fitness
y D
150
1Cexp.
x
20
C3/
Waves
0.8
0.6
0.4
0.2
Fitness
140
120
100
80
60
40
20
0
Average Score for Each Step
0 200 400 600 800 1000
Generation
0 100 200 300 400 500
Steps
Average Fitness Over All Generations
Waves_Sig
Average Score Over All Generations
Waves_Sig
gen = 0-100
gen = 100-200
gen = 200-300
gen = 300-400
gen = 400-500
wanted
y D
150
1Cexp.
x
20
C12/
Waves
0:5 1:0
0:8
250
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