Author |
Topic: First Move Advantage in DCR vs dcr (Read 1273 times) |
|
jdb
Forum Guru
Arimaa player #214
Gender: 
Posts: 682
|
 |
First Move Advantage in DCR vs dcr
« on: May 3rd, 2015, 7:52am » |
 Quote  Modify
|
Assuming gold and silver are only allowed to setup on the first rank, silver wins.
The columns of the following chart are, gold setup, number of gold wins, number of gold losses, number of repetitions, length of quickest silver win
g Da1 Cb1 Rc1 195 132 9 13
g Da1 Cb1 Rd1 176 148 12 13
g Da1 Cb1 Re1 178 136 22 13
g Da1 Cb1 Rf1 191 122 23 14
g Da1 Cb1 Rg1 201 120 15 14
g Da1 Cb1 Rh1 202 113 21 14
g Da1 Cc1 Rb1 218 111 7 13
g Da1 Cc1 Rd1 188 139 9 14
g Da1 Cc1 Re1 193 129 14 14
g Da1 Cc1 Rf1 205 108 23 14
g Da1 Cc1 Rg1 210 112 14 14
g Da1 Cc1 Rh1 222 101 13 14
g Da1 Cd1 Rb1 230 82 24 15
g Da1 Cd1 Rc1 217 105 14 14
g Da1 Cd1 Re1 206 111 19 14
g Da1 Cd1 Rf1 224 105 7 14
g Da1 Cd1 Rg1 238 93 5 15
g Da1 Cd1 Rh1 271 49 16 14
g Da1 Ce1 Rb1 229 63 44 15
g Da1 Ce1 Rc1 215 73 48 15
g Da1 Ce1 Rd1 214 89 33 15
g Da1 Ce1 Rf1 225 99 12 15
g Da1 Ce1 Rg1 258 72 6 15
g Da1 Ce1 Rh1 280 47 9 15
g Da1 Cf1 Rb1 240 56 40 16
g Da1 Cf1 Rc1 220 36 80 17
g Da1 Cf1 Rd1 211 58 67 15
g Da1 Cf1 Re1 206 93 37 15
g Da1 Cf1 Rg1 241 82 13 15
g Da1 Cf1 Rh1 260 67 9 14
g Da1 Cg1 Rb1 269 25 42 21
g Da1 Cg1 Rc1 258 23 55 21
g Da1 Cg1 Rd1 235 36 65 16
g Da1 Cg1 Re1 203 78 55 16
g Da1 Cg1 Rf1 201 94 41 15
g Da1 Cg1 Rh1 229 91 16 14
g Da1 Ch1 Rb1 255 45 36 17
g Da1 Ch1 Rc1 246 28 62 18
g Da1 Ch1 Rd1 225 49 62 16
g Da1 Ch1 Re1 180 92 64 16
g Da1 Ch1 Rf1 200 108 28 15
g Da1 Ch1 Rg1 204 111 21 15
g Db1 Ca1 Rc1 215 114 7 13
g Db1 Ca1 Rd1 221 107 8 13
g Db1 Ca1 Re1 216 112 8 13
g Db1 Ca1 Rf1 228 100 8 14
g Db1 Ca1 Rg1 229 98 9 14
g Db1 Ca1 Rh1 248 74 14 14
g Db1 Cc1 Ra1 259 52 25 16
g Db1 Cc1 Rd1 238 92 6 14
g Db1 Cc1 Re1 243 84 9 14
g Db1 Cc1 Rf1 233 90 13 14
g Db1 Cc1 Rg1 250 82 4 15
g Db1 Cc1 Rh1 291 42 3 14
g Db1 Cd1 Ra1 269 30 37 18
g Db1 Cd1 Rc1 251 57 28 15
g Db1 Cd1 Re1 249 79 8 15
g Db1 Cd1 Rf1 252 76 8 15
g Db1 Cd1 Rg1 285 44 7 15
g Db1 Cd1 Rh1 305 29 2 15
g Db1 Ce1 Ra1 292 16 28 20
g Db1 Ce1 Rc1 254 23 59 17
g Db1 Ce1 Rd1 255 47 34 16
g Db1 Ce1 Rf1 268 58 10 15
g Db1 Ce1 Rg1 286 46 4 15
g Db1 Ce1 Rh1 306 24 6 15
g Db1 Cf1 Ra1 288 15 33 20
g Db1 Cf1 Rc1 282 17 37 23
g Db1 Cf1 Rd1 265 29 42 18
g Db1 Cf1 Re1 246 49 41 16
g Db1 Cf1 Rg1 268 58 10 15
g Db1 Cf1 Rh1 290 33 13 15
g Db1 Cg1 Ra1 311 10 15 22
g Db1 Cg1 Rc1 319 2 15 29
g Db1 Cg1 Rd1 282 19 35 17
g Db1 Cg1 Re1 258 26 52 18
g Db1 Cg1 Rf1 248 52 36 17
g Db1 Cg1 Rh1 293 41 2 14
g Db1 Ch1 Ra1 297 15 24 18
g Db1 Ch1 Rc1 315 3 18 21
g Db1 Ch1 Rd1 281 25 30 17
g Db1 Ch1 Re1 263 39 34 17
g Db1 Ch1 Rf1 235 58 43 16
g Db1 Ch1 Rg1 237 78 21 15
g Dc1 Ca1 Rb1 233 93 10 14
g Dc1 Ca1 Rd1 240 83 13 14
g Dc1 Ca1 Re1 239 72 25 14
g Dc1 Ca1 Rf1 249 71 16 14
g Dc1 Ca1 Rg1 260 57 19 14
g Dc1 Ca1 Rh1 261 46 29 14
g Dc1 Cb1 Ra1 285 43 8 16
g Dc1 Cb1 Rd1 250 77 9 14
g Dc1 Cb1 Re1 251 71 14 14
g Dc1 Cb1 Rf1 260 60 16 15
g Dc1 Cb1 Rg1 282 40 14 15
g Dc1 Cb1 Rh1 279 39 18 14
g Dc1 Cd1 Ra1 288 17 31 19
g Dc1 Cd1 Rb1 285 30 21 20
g Dc1 Cd1 Re1 275 54 7 15
g Dc1 Cd1 Rf1 296 34 6 15
g Dc1 Cd1 Rg1 305 28 3 15
g Dc1 Cd1 Rh1 308 25 3 15
g Dc1 Ce1 Ra1 284 9 43 20
g Dc1 Ce1 Rb1 280 9 47 19
g Dc1 Ce1 Rd1 270 40 26 16
g Dc1 Ce1 Rf1 285 43 8 16
g Dc1 Ce1 Rg1 306 23 7 15
g Dc1 Ce1 Rh1 314 21 1 15
g Dc1 Cf1 Ra1 300 5 31 21
g Dc1 Cf1 Rb1 276 13 47 18
g Dc1 Cf1 Rd1 263 31 42 17
g Dc1 Cf1 Re1 270 41 25 17
g Dc1 Cf1 Rg1 297 29 10 16
g Dc1 Cf1 Rh1 315 20 1 15
g Dc1 Cg1 Ra1 313 4 19 22
g Dc1 Cg1 Rb1 316 9 11 17
g Dc1 Cg1 Rd1 281 6 49 17
g Dc1 Cg1 Re1 268 32 36 16
g Dc1 Cg1 Rf1 267 49 20 16
g Dc1 Cg1 Rh1 303 22 11 15
g Dc1 Ch1 Ra1 298 12 26 15
g Dc1 Ch1 Rb1 298 20 18 17
g Dc1 Ch1 Rd1 289 11 36 16
g Dc1 Ch1 Re1 260 24 52 15
g Dc1 Ch1 Rf1 264 47 25 15
g Dc1 Ch1 Rg1 251 52 33 16
g Dd1 Ca1 Rb1 291 34 11 16
g Dd1 Ca1 Rc1 278 48 10 15
g Dd1 Ca1 Re1 277 52 7 15
g Dd1 Ca1 Rf1 295 27 14 15
g Dd1 Ca1 Rg1 295 31 10 15
g Dd1 Ca1 Rh1 293 34 9 14
g Dd1 Cb1 Ra1 308 23 5 16
g Dd1 Cb1 Rc1 286 38 12 16
g Dd1 Cb1 Re1 278 46 12 15
g Dd1 Cb1 Rf1 299 22 15 15
g Dd1 Cb1 Rg1 300 24 12 15
g Dd1 Cb1 Rh1 295 26 15 15
g Dd1 Cc1 Ra1 310 19 7 18
g Dd1 Cc1 Rb1 312 19 5 16
g Dd1 Cc1 Re1 283 36 17 16
g Dd1 Cc1 Rf1 305 19 12 15
g Dd1 Cc1 Rg1 297 22 17 15
g Dd1 Cc1 Rh1 303 21 12 15
g Dd1 Ce1 Ra1 315 1 20 27
g Dd1 Ce1 Rb1 311 10 15 16
g Dd1 Ce1 Rc1 317 6 13 16
g Dd1 Ce1 Rf1 311 11 14 16
g Dd1 Ce1 Rg1 321 12 3 16
g Dd1 Ce1 Rh1 330 4 2 19
g Dd1 Cf1 Ra1 299 11 26 15
g Dd1 Cf1 Rb1 306 12 18 16
g Dd1 Cf1 Rc1 311 7 18 16
g Dd1 Cf1 Re1 288 28 20 18
g Dd1 Cf1 Rg1 312 16 8 16
g Dd1 Cf1 Rh1 321 12 3 16
g Dd1 Cg1 Ra1 307 16 13 15
g Dd1 Cg1 Rb1 315 11 10 15
g Dd1 Cg1 Rc1 325 7 4 15
g Dd1 Cg1 Re1 271 31 34 17
g Dd1 Cg1 Rf1 288 28 20 16
g Dd1 Cg1 Rh1 306 21 9 15
g Dd1 Ch1 Ra1 303 18 15 15
g Dd1 Ch1 Rb1 314 12 10 15
g Dd1 Ch1 Rc1 324 9 3 15
g Dd1 Ch1 Re1 273 35 28 16
g Dd1 Ch1 Rf1 286 21 29 16
g Dd1 Ch1 Rg1 292 27 17 16
This is a histogram showing the length of wins.
For silver wins in X, count in from the start.
There are 12 positions that are win in 13 for silver.
There are 121 positions that are win in 14 for silver, etc.
For gold wins in X,count backwards from the end.
There are 2688 positions that are win in 2 for gold.
There are 168 positions that are win in 3 for gold, etc.
There are 3498 positions that involve repetition.
0 0 0 0 0 0 0 0 0 0 0 0 0 12 121 1075 1478 1199 787 558 487 620 488 185 104 92 90 96 136 230 127 131 67 25 36 15 25 5 1 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3498 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 3 0 0 7 28 7 20 66 96 107 95 114 118 127 191 221 403 609 877 1044 1500 4112 8117 10967 6200 2740 1604 928 645 385 270 173 68 31 22 3 168 2688 0 0
|
| « Last Edit: May 3rd, 2015, 5:49pm by jdb » |
 IP Logged |
|
|
|
deep_blue
Forum Guru
Arimaa player #9854
Posts: 212
|
|
Re: First Move Advantage in DCR vs dcr
« Reply #1 on: May 3rd, 2015, 8:19am » |
Quote Modify
|
Do I read this statistics correctly, if gold sets up g Dd1 Ce1 Ra1 theres only one silver setup that wins?
|
|
IP Logged |
|
|
|
clyring
Forum Guru
Arimaa player #6218
Gender: 
Posts: 362
|
|
Re: First Move Advantage in DCR vs dcr
« Reply #2 on: May 3rd, 2015, 11:51am » |
Quote Modify
|
I was more curious about the 2-rank case when I asked in the chatroom but this is nice as well.
Multi-linear least squares regression estimates every step centralizing the dog refutes a net +29.5 silver setups, counting repetitions as half-refutations, every step centralizing the cat +11.6, the rabbit -8.3, but each step bringing the dog and cat further apart as +10.2, when these are the only parameters.
Like deep_blue I am curious about the one refutation to Dd1 Ce1 Ra1. Maybe that can be used for a future Oracle puzzle.
Also, how deep is the longest silver win from setup? EDIT: 29 moves, thanks! 
Can we see a sample line?
|
| « Last Edit: May 3rd, 2015, 7:35pm by clyring » |
IP Logged |
I administer the Endless Endgame Event (EEE). Players welcome!
|
|
|
|
Home
Help
Search
Members
Login
Register
Reply
Notify of replies
Send Topic
Print