Jurnal Ilmiah Komputer dan Informatika KOMPUTA
Edisi. .. Volume. .., Bulan 20.. ISSN : 2089-9033
Then look for the next step by using an algorithm MTDf to obtain an evaluation value of each step.
Each step has been sought can be seen in the following table:
Table 1 Left Step Search Results
Iteration G
Beta Lowerbound
Upperbound
1 -
∞ +∞
1170,5 1170,5
+∞ 2
1170,5 1171,5
1170,5 +∞
1172 1171,5
1172 +∞
3 1172
1172,5 1172
+∞ 1172
1172,5 1172,5
1172
Table 2 Right Step Search Results
Iteration G
Beta Lowerbound
Upperbound
1 -
∞ +∞
1170,5 1170,5
+∞ 2
1170,5 1171,5
1170,5 +∞
1172 1171,5
1172 +∞
3 1172
1172,5 1172
+∞ 1172
1172,5 1172,5
1172
Table 3 Up Step Search Results
Iteration G
Beta Lowerbound
Upperbound
1 -
∞ +∞
1184 1184
+∞ 2
1184 1185
1184 +∞
1184 1185
1184 1184
Table 4 Down Step Search Results
Iteration G
Beta Lowerbound
Upperbound
1 -
∞ +∞
1025 1025
+∞ 2
1025 1026
1025 +∞
1172 1026
1172 +∞
3 1172
1173 1172
+∞ 1172
1173 1172
1172
In the above table have been searching algorithms using MTDf. Variable G is the value of a function
call Alphabeta search, variable beta beta value at the MTD f to the value upperbound on the function
of the alphabet, while lowerbound and upperbound is the upper limit and lower limit of the algorithm
MTD f in the search. Then each displacement value obtained as follows: Left = 1172, 1172 =
Right, Up and Down = 1184 = 1172. From the results obtained that the next step is to up.
2.5 Testing System Testing algorithm is performed to test the accuracy
and speed of the algorithm MTD f which has been implemented in 2048. The game 2048 game will be
played by the algorithm MTD f as many as 10 times each search depth level. Then count the
number of games that could be reached in 2048 at each level of the depth of the search. So as to get the
accuracy of the algorithm MTD f by comparing the number of games that could be reached in 2048 with
the number of games that have been made. Search will be made until a greater degree of accuracy
equal to 50. As for the speed is calculated based on the time required to complete the game in 2048.
Table 5 Results of Testing Depth Level 0
Trial Status
Largest Tile
Time HH:mm:ss.SSS
Skor
1 Failed
256 00:00:05.627
3368 2
Failed 256
00:00:05.452 3236
3 Failed
128 00:00:04.053
1932 4
Failed 256
00:00:04.695 2632
5 Failed
512 00:00:07.212
5184 6
Failed 64
00:00:01.734 668
7 Failed
256 00:00:05.787
3472 8
Failed 256
00:00:05.761 3364
9 Failed
256 00:00:06.370
3884 10
Failed 128
00:00:03.698 1796
Table 6 Results of Testing Depth Level 1
Trial Status
Largest Tile
Time HH:mm:ss.SSS
Score
1 Failed
512 00:00:10.845
8548 2
Failed 256
00:00:04.725 2928
3 Failed
256 00:00:05.151
3140 4
Failed 512
00:00:09.751 7108
5 Failed
256 00:00:06.577
4200 6
Failed 512
00:00:08.955 6580
7 Failed
128 00:00:02.640
1292 8
Failed 512
00:00:08.136 5728
9 Failed
256 00:00:07.661
5012 10
Failed 128
00:00:02.824 1380
Table 7 Results of Testing Depth Level 2
Trial Status
Largest Tile
Time HH:mm:ss.SSS
Score
1 Failed
1024 00:07:50.290
16404 2
Failed 1024
00:06:03.666 12588
3 Failed
512 00:01:45.126
9352 4
Failed 1024
00:04:01.744 14824
5 Failed
512 00:00:46.471
7272 6
Failed 512
00:01:18.127 8092
7 Failed
1024 00:06:11.310
16848 8
Failed 1024
00:08:14.355 18380
9 Failed
512 00:01:49.780
9204 10
Failed 512
00:01:10.856 7464
Table 8 Results of Testing Depth Level 3
Trial Status
Largest Tile
Time HH:mm:ss.SSS
Score
1 Succeed
2048 00:15:20.262
24508 2
Failed 1024
00:10:42.021 17788
3 Failed
1024 00:11:36.187
16476 4
Failed 1024
00:15:19.595 9552
5 Succeed
2048 00:26:19.731
20176 6
Failed 1024
00:09:35.158 15620
7 Failed
512 00:07:35.641
8780 8
Failed 1024
00:12:23.831 12456
9 Failed
1024 00:12:21.244
12492 10
Failed 512
00:09:37.873 7968
Table 9 Results of Testing Depth Level 4
Trial Status
Largest Tile
Time HH:mm:ss.SSS
Score
1 Failed
1024 00:31:49.967
16160 2
Failed 1024
00:28:05.387 17748
3 Failed
1024 00:39:40.811
12252 4
Succeed 2048
00:43:53.370 20168
5 Failed
1024 00:36:10.246
14040 6
Succeed 2048
00:33:54.834 20256
Jurnal Ilmiah Komputer dan Informatika KOMPUTA
Edisi. .. Volume. .., Bulan 20.. ISSN : 2089-9033
7 Succeed
2048 00:29:55.392
21124 8
Failed 1024
00:34:29.883 15448
9 Failed
1024 00:37:18.236
15640 10
Failed 1024
00:42:23.269 10260
Table 10 Results of Testing Depth Level 5
Trial Status
Largest Tile
Time HH:mm:ss.SSS
Score
1 Succeed
2048 00:57:05.272
20472 2
Succeed 2048
01:11:45.322 21220
3 Failed
1024 01:08:59.489
15804 4
Succeed 2048
01:27:40.496 20516
5 Succeed
2048 01:13:29.821
20304 6
Failed 1024
01:19:01.814 18708
7 Failed
1024 01:25:12.240
19948 8
Failed 1024
01:23:10.546 18412
9 Succeed
2048 01:32:27.933
20572 10
Succeed 2048
01:21:23.320 20344
2.6 Testing Result
The results of testing that was done ten times at each depth level can be seen in the picture.
Figure 8 Testing Results Based on Max Tile
Figure 9 Testing Results Based on Score Figure 10 Testing Results Based on Time
3. FINAL
3.1 Conclusion
Based on the results of the study, analysis of system design and implementation as well as tests
performed on the algorithms MTD f to finish the game in 2048, it could be concluded that the
algorithm MTD f can be applied to the game in 2048, but to get the tile in 2048 in order to win the
game in 2048 requires level searches search depth of at least three and takes about 13 minutes 59
seconds. The level of accuracy of the algorithm MTD f on a quest with a depth of level zero, one
and two is 0, whereas on level three is 20, a level four was 30 and the level of five is 60.
3.2
Suggestion
In the algorithm implementation MTDf on the game in 2048 is still far from perfect and there are still
many shortcomings. Therefore it is necessary to do a deeper analysis. The advice can be given by the
researchers in this study is to apply other algorithms that can be applied to the game in 2048 in order to
more quickly and accurately to complete the game in 2048.
REFERENCES
[1] K. Lu, Game Theory of 2048, Math 89s: Game Theory and Democracy, 2014.
[2] Stepen, Perbandingan Algoritma Greedy Bactracking Dalam Penyelesaian Permainan
2048, Makalah IF2211 Strategi Algoritma , 2014.
[3] V. Vryniotis, Using Artificial Intelligence to solve the 2048 Game JAVA code |
Datumbox, 14 November 2014. [Online]. Available:
http:blog.datumbox.comusing- artificial-intelligence-to-solve-the-2048-game-
java-code. [Accessed 20 September 2015]. [4] A. Plaat, MTD f A Minimax Algorithm
faster than NegaScout, Erasmus University, Rotterdam, 1997.
500 1000
1500 2000
2500
1 2
3 4
5 6
7 8
9 10
MAX TILE
LEVEL 0 LEVEL 1
LEVEL 2 LEVEL 3
LEVEL 4 LEVEL 5
5000 10000
15000 20000
25000 30000
1 2
3 4
5 6
7 8
9 10
Score
LEVEL 0 LEVEL 1
LEVEL 2 LEVEL 3
LEVEL 4 LEVEL 5
1000 2000
3000 4000
5000 6000
1 2
3 4
5 6
7 8
9 10
Time
LEVEL 0 LEVEL 1
LEVEL 2 LEVEL 3
LEVEL 4 LEVEL 5
s
