tactics.c

   1 #include <assert.h>
   2 #include <stdio.h>
   3 #include <stdlib.h>
   4
   5 #define DEBUG
   6 #include "board.h"
   7 #include "debug.h"
   8
   9
  10 struct selfatari_state {
  11         int groupcts[S_MAX];
  12         group_t groupids[S_MAX][4];
  13
  14         /* This is set if this move puts a group out of _all_
  15          * liberties; we need to watch out for snapback then. */
  16         bool friend_has_no_libs;
  17         /* We may have one liberty, but be looking for one more.
  18          * In that case, @needs_more_lib is id of group
  19          * already providing one, don't consider it again. */
  20         group_t needs_more_lib;
  21         /* ID of the first liberty, providing it again is not
  22          * interesting. */
  23         coord_t needs_more_lib_except;
  24 };
  25
  26 static int
  27 examine_friendly_groups(struct board *b, enum stone color, coord_t to, struct selfatari_state *s)
  28 {
  29         for (int i = 0; i < s->groupcts[color]; i++) {
  30                 /* We can escape by connecting to this group if it's
  31                  * not in atari. */
  32                 group_t g = s->groupids[color][i];
  33
  34                 if (board_group_info(b, g).libs == 1) {
  35                         if (!s->needs_more_lib)
  36                                 s->friend_has_no_libs = true;
  37                         // or we already have a friend with 1 lib
  38                         continue;
  39                 }
  40
  41                 /* Could we self-atari the group here? */
  42                 if (board_group_info(b, g).libs > 2)
  43                         return false;
  44
  45                 /* We need to have another liberty, and
  46                  * it must not be the other liberty of
  47                  * the group. */
  48                 int lib2 = board_group_info(b, g).lib[0];
  49                 if (lib2 == to) lib2 = board_group_info(b, g).lib[1];
  50                 /* Maybe we already looked at another
  51                  * group providing one liberty? */
  52                 if (s->needs_more_lib && s->needs_more_lib != g
  53                     && s->needs_more_lib_except != lib2)
  54                         return false;
  55
  56                 /* Can we get the liberty locally? */
  57                 /* Yes if we are route to more liberties... */
  58                 if (s->groupcts[S_NONE] > 1)
  59                         return false;
  60                 /* ...or one liberty, but not lib2. */
  61                 if (s->groupcts[S_NONE] > 0
  62                     && !coord_is_adjecent(lib2, to, b))
  63                         return false;
  64
  65                 /* ...ok, then we can still contribute a liberty
  66                  * later by capturing something. */
  67                 s->needs_more_lib = g;
  68                 s->needs_more_lib_except = lib2;
  69                 s->friend_has_no_libs = false;
  70         }
  71
  72         return -1;
  73 }
  74
  75 static int
  76 examine_enemy_groups(struct board *b, enum stone color, coord_t to, struct selfatari_state *s)
  77 {
  78         /* We may be able to gain a liberty by capturing this group. */
  79         group_t can_capture = 0;
  80
  81         /* Examine enemy groups: */
  82         for (int i = 0; i < s->groupcts[stone_other(color)]; i++) {
  83                 /* We can escape by capturing this group if it's in atari. */
  84                 group_t g = s->groupids[stone_other(color)][i];
  85                 if (board_group_info(b, g).libs > 1)
  86                         continue;
  87
  88                 /* But we need to get to at least two liberties by this;
  89                  * we already have one outside liberty, or the group is
  90                  * more than 1 stone (in that case, capturing is always
  91                  * nice!). */
  92                 if (s->groupcts[S_NONE] > 0 || !group_is_onestone(b, g))
  93                         return false;
  94                 /* ...or, it's a ko stone, */
  95                 if (neighbor_count_at(b, g, color) + neighbor_count_at(b, g, S_OFFBOARD) == 3) {
  96                         /* and we don't have a group to save: then, just taking
  97                          * single stone means snapback! */
  98                         if (!s->friend_has_no_libs)
  99                                 return false;
 100                 }
 101                 /* ...or, we already have one indirect liberty provided
 102                  * by another group. */
 103                 if (s->needs_more_lib || (can_capture && can_capture != g))
 104                         return false;
 105                 can_capture = g;
 106
 107         }
 108
 109         if (DEBUGL(6))
 110                 fprintf(stderr, "no cap group\n");
 111
 112         if (!s->needs_more_lib && !can_capture && !s->groupcts[S_NONE]) {
 113                 /* We have no hope for more fancy tactics - this move is simply
 114                  * a suicide, not even a self-atari. */
 115                 if (DEBUGL(6))
 116                         fprintf(stderr, "suicide\n");
 117                 return true;
 118         }
 119         /* XXX: I wonder if it makes sense to continue if we actually
 120          * just !s->needs_more_lib. */
 121
 122         return -1;
 123 }
 124
 125 static int
 126 setup_nakade_or_snapback(struct board *b, enum stone color, coord_t to, struct selfatari_state *s)
 127 {
 128         /* There is another possibility - we can self-atari if it is
 129          * a nakade: we put an enemy group in atari from the inside. */
 130         /* This branch also allows eyes falsification:
 131          * O O O . .  (This is different from throw-in to false eye
 132          * X X O O .  checked below in that there is no X stone at the
 133          * X . X O .  right of the star point in this diagram.)
 134          * X X X O O
 135          * X O * . . */
 136         /* TODO: Allow to only nakade if the created shape is dead
 137          * (http://senseis.xmp.net/?Nakade). */
 138
 139         /* This branch also covers snapback, which is kind of special
 140          * nakade case. ;-) */
 141         for (int i = 0; i < s->groupcts[stone_other(color)]; i++) {
 142                 group_t g = s->groupids[stone_other(color)][i];
 143                 if (board_group_info(b, g).libs != 2)
 144                         goto next_group;
 145                 /* Simple check not to re-examine the same group. */
 146                 if (i > 0 && s->groupids[stone_other(color)][i] == s->groupids[stone_other(color)][i - 1])
 147                         continue;
 148
 149                 /* We must make sure the other liberty of that group:
 150                  * (i) is an internal liberty
 151                  * (ii) filling it to capture our group will not gain
 152                  * safety */
 153
 154                 /* Let's look at the other liberty neighbors: */
 155                 int lib2 = board_group_info(b, g).lib[0];
 156                 if (lib2 == to) lib2 = board_group_info(b, g).lib[1];
 157                 foreach_neighbor(b, lib2, {
 158                         /* This neighbor of course does not contribute
 159                          * anything to the enemy. */
 160                         if (board_at(b, c) == S_OFFBOARD)
 161                                 continue;
 162
 163                         /* If the other liberty has empty neighbor,
 164                          * it must be the original liberty; otherwise,
 165                          * since the whole group has only 2 liberties,
 166                          * the other liberty may not be internal and
 167                          * we are nakade'ing eyeless group from outside,
 168                          * which is stupid. */
 169                         if (board_at(b, c) == S_NONE) {
 170                                 if (c == to)
 171                                         continue;
 172                                 else
 173                                         goto next_group;
 174                         }
 175
 176                         int g2 = group_at(b, c);
 177                         /* If the neighbor is of our color, it must
 178                          * be our group; if it is a different group,
 179                          * it must not be in atari. */
 180                         /* X X X X  We will not allow play on 'a',
 181                          * X X a X  because 'b' would capture two
 182                          * X O b X  different groups, forming two
 183                          * X X X X  eyes. */
 184                         if (board_at(b, c) == color) {
 185                                 if (board_group_info(b, group_at(b, c)).libs > 1)
 186                                         continue;
 187                                 /* Our group == one of the groups
 188                                  * we (@to) are connected to. */
 189                                 int j;
 190                                 for (j = 0; j < 4; j++)
 191                                         if (s->groupids[color][j] == g2)
 192                                                 break;
 193                                 if (j == 4)
 194                                         goto next_group;
 195                                 continue;
 196                         }
 197
 198                         /* The neighbor is enemy color. It's ok if
 199                          * it's still the same group or this is its
 200                          * only liberty. */
 201                         if (g == g2 || board_group_info(b, g2).libs == 1)
 202                                 continue;
 203                         /* Otherwise, it must have the exact same
 204                          * liberties as the original enemy group. */
 205                         if (board_group_info(b, g2).libs == 2
 206                             && (board_group_info(b, g2).lib[0] == to
 207                                 || board_group_info(b, g2).lib[1] == to))
 208                                 continue;
 209
 210                         goto next_group;
 211                 });
 212
 213                 /* Now, we must distinguish between nakade and eye
 214                  * falsification; we must not falsify an eye by more
 215                  * than two stones. */
 216                 if (s->groupcts[color] < 1 ||
 217                     (s->groupcts[color] == 1 && group_is_onestone(b, s->groupids[color][0])))
 218                         return false;
 219
 220                 /* We would create more than 2-stone group; in that
 221                  * case, the liberty of our result must be lib2,
 222                  * indicating this really is a nakade. */
 223                 for (int j = 0; j < s->groupcts[color]; j++) {
 224                         group_t g2 = s->groupids[color][j];
 225                         assert(board_group_info(b, g2).libs <= 2);
 226                         if (board_group_info(b, g2).libs == 2) {
 227                                 if (board_group_info(b, g2).lib[0] != lib2
 228                                     && board_group_info(b, g2).lib[1] != lib2)
 229                                         goto next_group;
 230                         } else {
 231                                 assert(board_group_info(b, g2).lib[0] == to);
 232                         }
 233                 }
 234
 235                 return false;
 236 next_group:
 237                 /* Unless we are dealing with snapback setup, we don't need to look
 238                  * further. */
 239                 if (!s->groupcts[color])
 240                         return -1;
 241         }
 242
 243         return -1;
 244 }
 245
 246 static int
 247 check_throwin(struct board *b, enum stone color, coord_t to, struct selfatari_state *s)
 248 {
 249         /* We can be throwing-in to false eye:
 250          * X X X O X X X O X X X X X
 251          * X . * X * O . X * O O . X
 252          * # # # # # # # # # # # # # */
 253         /* We cannot sensibly throw-in into a corner. */
 254         if (neighbor_count_at(b, to, S_OFFBOARD) < 2
 255             && neighbor_count_at(b, to, stone_other(color))
 256                + neighbor_count_at(b, to, S_OFFBOARD) == 3
 257             && board_is_false_eyelike(b, &to, stone_other(color))) {
 258                 assert(s->groupcts[color] <= 1);
 259                 /* Single-stone throw-in may be ok... */
 260                 if (s->groupcts[color] == 0) {
 261                         /* O X .  There is one problem - when it's
 262                          * . * X  actually not a throw-in!
 263                          * # # #  */
 264                         foreach_neighbor(b, to, {
 265                                 if (board_at(b, c) == S_NONE) {
 266                                         /* Is the empty neighbor an escape path? */
 267                                         /* (Note that one S_NONE neighbor is already @to.) */
 268                                         if (neighbor_count_at(b, c, stone_other(color))
 269                                             + neighbor_count_at(b, c, S_OFFBOARD) < 2)
 270                                                 return -1;
 271                                 }
 272                         });
 273                         return false;
 274                 }
 275
 276                 /* Multi-stone throwin...? */
 277                 assert(s->groupcts[color] == 1);
 278                 group_t g = s->groupids[color][0];
 279
 280                 assert(board_group_info(b, g).libs <= 2);
 281                 /* Suicide is definitely NOT ok, no matter what else
 282                  * we could test. */
 283                 if (board_group_info(b, g).libs == 1)
 284                         return true;
 285
 286                 /* In that case, we must be connected to at most one stone,
 287                  * or throwin will not destroy any eyes. */
 288                 if (group_is_onestone(b, g))
 289                         return false;
 290         }
 291         return -1;
 292 }
 293
 294 bool
 295 is_bad_selfatari_slow(struct board *b, enum stone color, coord_t to)
 296 {
 297         if (DEBUGL(5))
 298                 fprintf(stderr, "sar check %s %s\n", stone2str(color), coord2sstr(to, b));
 299         /* Assess if we actually gain any liberties by this escape route.
 300          * Note that this is not 100% as we cannot check whether we are
 301          * connecting out or just to ourselves. */
 302
 303         struct selfatari_state s;
 304         memset(&s, 0, sizeof(s));
 305         int d;
 306
 307         foreach_neighbor(b, to, {
 308                 enum stone color = board_at(b, c);
 309                 s.groupids[color][s.groupcts[color]++] = group_at(b, c);
 310         });
 311
 312         /* We have shortage of liberties; that's the point. */
 313         assert(s.groupcts[S_NONE] <= 1);
 314
 315         d = examine_friendly_groups(b, color, to, &s);
 316         if (d >= 0)
 317                 return d;
 318
 319         if (DEBUGL(6))
 320                 fprintf(stderr, "no friendly group\n");
 321
 322         d = examine_enemy_groups(b, color, to, &s);
 323         if (d >= 0)
 324                 return d;
 325
 326         if (DEBUGL(6))
 327                 fprintf(stderr, "no escape\n");
 328
 329         d = setup_nakade_or_snapback(b, color, to, &s);
 330         if (d >= 0)
 331                 return d;
 332
 333         if (DEBUGL(6))
 334                 fprintf(stderr, "no nakade group\n");
 335
 336         d = check_throwin(b, color, to, &s);
 337         if (d >= 0)
 338                 return d;
 339
 340         if (DEBUGL(6))
 341                 fprintf(stderr, "no throw-in group\n");
 342
 343         /* No way to pull out, no way to connect out. This really
 344          * is a bad self-atari! */
 345         return true;
 346 }
 347
 348
 349 /* Is this ladder breaker friendly for the one who catches ladder. */
 350 static bool
 351 ladder_catcher(struct board *b, int x, int y, enum stone laddered)
 352 {
 353         enum stone breaker = board_atxy(b, x, y);
 354         return breaker == stone_other(laddered) || breaker == S_OFFBOARD;
 355 }
 356
 357 bool
 358 is_border_ladder(struct board *b, coord_t coord, enum stone lcolor)
 359 {
 360         int x = coord_x(coord, b), y = coord_y(coord, b);
 361
 362         if (DEBUGL(5))
 363                 fprintf(stderr, "border ladder\n");
 364         /* Direction along border; xd is horiz. border, yd vertical. */
 365         int xd = 0, yd = 0;
 366         if (board_atxy(b, x + 1, y) == S_OFFBOARD || board_atxy(b, x - 1, y) == S_OFFBOARD)
 367                 yd = 1;
 368         else
 369                 xd = 1;
 370         /* Direction from the border; -1 is above/left, 1 is below/right. */
 371         int dd = (board_atxy(b, x + yd, y + xd) == S_OFFBOARD) ? 1 : -1;
 372         if (DEBUGL(6))
 373                 fprintf(stderr, "xd %d yd %d dd %d\n", xd, yd, dd);
 374         /* | ? ?
 375          * | . O #
 376          * | c X #
 377          * | . O #
 378          * | ? ?   */
 379         /* This is normally caught, unless we have friends both above
 380          * and below... */
 381         if (board_atxy(b, x + xd * 2, y + yd * 2) == lcolor
 382             && board_atxy(b, x - xd * 2, y - yd * 2) == lcolor)
 383                 return false;
 384         /* ...or can't block where we need because of shortage
 385          * of liberties. */
 386         int libs1 = board_group_info(b, group_atxy(b, x + xd - yd * dd, y + yd - xd * dd)).libs;
 387         int libs2 = board_group_info(b, group_atxy(b, x - xd - yd * dd, y - yd - xd * dd)).libs;
 388         if (DEBUGL(6))
 389                 fprintf(stderr, "libs1 %d libs2 %d\n", libs1, libs2);
 390         if (libs1 < 2 && libs2 < 2)
 391                 return false;
 392         if (board_atxy(b, x + xd * 2, y + yd * 2) == lcolor && libs1 < 3)
 393                 return false;
 394         if (board_atxy(b, x - xd * 2, y - yd * 2) == lcolor && libs2 < 3)
 395                 return false;
 396         return true;
 397 }
 398
 399 /* This is very trivial and gets a lot of corner cases wrong.
 400  * We need this to be just very fast. One important point is
 401  * that we sometimes might not notice a ladder but if we do,
 402  * it should always work; thus we can use this for strong
 403  * negative hinting safely. */
 404 bool
 405 is_middle_ladder(struct board *b, coord_t coord, enum stone lcolor)
 406 {
 407         int x = coord_x(coord, b), y = coord_y(coord, b);
 408
 409         /* Figure out the ladder direction */
 410         int xd, yd;
 411         xd = board_atxy(b, x + 1, y) == S_NONE ? 1 : board_atxy(b, x - 1, y) == S_NONE ? -1 : 0;
 412         yd = board_atxy(b, x, y + 1) == S_NONE ? 1 : board_atxy(b, x, y - 1) == S_NONE ? -1 : 0;
 413
 414         if (!xd || !yd) {
 415                 if (DEBUGL(5))
 416                         fprintf(stderr, "no ladder, too little space; self-atari?\n");
 417                 return false;
 418         }
 419
 420         /* For given (xd,yd), we have two possibilities where to move
 421          * next. Consider (-1,-1):
 422          * n X .   n c X
 423          * c O X   X O #
 424          * X # #   . X #
 425          */
 426         bool horiz_first = ladder_catcher(b, x, y - yd, lcolor); // left case
 427         bool vert_first = ladder_catcher(b, x - xd, y, lcolor); // right case
 428
 429         /* We don't have to look at the other 'X' in the position - if it
 430          * wouldn't be there, the group wouldn't be in atari. */
 431
 432         /* We do only tight ladders, not loose ladders. Furthermore,
 433          * the ladders need to be simple:
 434          * . X .             . . X
 435          * c O X supported   . c O unsupported
 436          * X # #             X O #
 437          */
 438         assert(!(horiz_first && vert_first));
 439         if (!horiz_first && !vert_first) {
 440                 /* TODO: In case of basic non-simple ladder, play out both variants. */
 441                 if (DEBUGL(5))
 442                         fprintf(stderr, "non-simple ladder\n");
 443                 return false;
 444         }
 445
 446         /* We do that below for further moves, but now initially - check
 447          * that at 'c', we aren't putting any of the catching stones
 448          * in atari. */
 449 #if 1 // this might be broken?
 450 #define check_catcher_danger(b, x_, y_) do { \
 451         if (board_atxy(b, (x_), (y_)) != S_OFFBOARD \
 452             && board_group_info(b, group_atxy(b, (x_), (y_))).libs <= 2) { \
 453                 if (DEBUGL(5)) \
 454                         fprintf(stderr, "ladder failed - atari at the beginning\n"); \
 455                 return false; \
 456         } } while (0)
 457
 458         if (horiz_first) {
 459                 check_catcher_danger(b, x, y - yd);
 460                 check_catcher_danger(b, x - xd, y + yd);
 461         } else {
 462                 check_catcher_danger(b, x - xd, y);
 463                 check_catcher_danger(b, x + xd, y - yd);
 464         }
 465 #undef check_catcher_danger
 466 #endif
 467
 468 #define ladder_check(xd1_, yd1_, xd2_, yd2_, xd3_, yd3_)        \
 469         if (board_atxy(b, x, y) != S_NONE) { \
 470                 /* Did we hit a stone when playing out ladder? */ \
 471                 if (ladder_catcher(b, x, y, lcolor)) \
 472                         return true; /* ladder works */ \
 473                 if (board_group_info(b, group_atxy(b, x, y)).lib[0] > 0) \
 474                         return false; /* friend that's not in atari himself */ \
 475         } else { \
 476                 /* No. So we are at new position. \
 477                  * We need to check indirect ladder breakers. */ \
 478                 /* . 2 x 3 . \
 479                  * . x o O 1 <- only at O we can check for o at 2 \
 480                  * x o o x .    otherwise x at O would be still deadly \
 481                  * o o x . . \
 482                  * We check for o and x at 1, these are vital. \
 483                  * We check only for o at 2; x at 2 would mean we \
 484                  * need to fork (one step earlier). */ \
 485                 coord_t c1 = coord_xy(b, x + (xd1_), y + (yd1_)); \
 486                 enum stone s1 = board_at(b, c1); \
 487                 if (s1 == lcolor) return false; \
 488                 if (s1 == stone_other(lcolor)) { \
 489                         /* One more thing - if the position at 3 is \
 490                          * friendly and safe, we escaped anyway! */ \
 491                         coord_t c3 = coord_xy(b, x + (xd3_), y + (yd3_)); \
 492                         return board_at(b, c3) != lcolor \
 493                                || board_group_info(b, group_at(b, c3)).libs < 2; \
 494                 } \
 495                 enum stone s2 = board_atxy(b, x + (xd2_), y + (yd2_)); \
 496                 if (s2 == lcolor) return false; \
 497                 /* Then, can X actually "play" 1 in the ladder? */ \
 498                 if (neighbor_count_at(b, c1, lcolor) + neighbor_count_at(b, c1, S_OFFBOARD) >= 2) \
 499                         return false; /* It would be self-atari! */ \
 500         }
 501 #define ladder_horiz    do { if (DEBUGL(6)) fprintf(stderr, "%d,%d horiz step (%d,%d)\n", x, y, xd, yd); x += xd; ladder_check(xd, 0, -2 * xd, yd, 0, yd); } while (0)
 502 #define ladder_vert     do { if (DEBUGL(6)) fprintf(stderr, "%d,%d vert step of (%d,%d)\n", x, y, xd, yd); y += yd; ladder_check(0, yd, xd, -2 * yd, xd, 0); } while (0)
 503
 504         if (ladder_catcher(b, x - xd, y, lcolor))
 505                 ladder_horiz;
 506         do {
 507                 ladder_vert;
 508                 ladder_horiz;
 509         } while (1);
 510 }
 511
 512
 513 bool
 514 board_stone_radar(struct board *b, coord_t coord, int distance)
 515 {
 516         int bounds[4] = {
 517                 coord_x(coord, b) - distance,
 518                 coord_y(coord, b) - distance,
 519                 coord_x(coord, b) + distance,
 520                 coord_y(coord, b) + distance
 521         };
 522         for (int i = 0; i < 4; i++)
 523                 if (bounds[i] < 1)
 524                         bounds[i] = 1;
 525                 else if (bounds[i] > board_size(b) - 2)
 526                         bounds[i] = board_size(b) - 2;
 527         for (int x = bounds[0]; x <= bounds[2]; x++)
 528                 for (int y = bounds[1]; y <= bounds[3]; y++)
 529                         if (board_atxy(b, x, y) != S_NONE) {
 530                                 /* fprintf(stderr, "radar %d,%d,%d: %d,%d (%d)\n",
 531                                         coord_x(coord, b), coord_y(coord, b),
 532                                         distance, x, y, board_atxy(b, x, y)); */
 533                                 return true;
 534                         }
 535         return false;
 536 }
 537
 538 void
 539 cfg_distances(struct board *b, coord_t start, int *distances, int maxdist)
 540 {
 541         /* Queue for d+1 spots; no two spots of the same group
 542          * should appear in the queue. */
 543 #define qinc(x) (x = ((x + 1) >= board_size2(b) ? ((x) + 1 - board_size2(b)) : (x) + 1))
 544         coord_t queue[board_size2(b)]; int qstart = 0, qstop = 0;
 545
 546         foreach_point(b) {
 547                 distances[c] = board_at(b, c) == S_OFFBOARD ? maxdist + 1 : -1;
 548         } foreach_point_end;
 549
 550         queue[qstop++] = start;
 551         for (int d = 0; d <= maxdist; d++) {
 552                 /* Process queued moves, while setting the queue
 553                  * for new wave. */
 554                 int qa = qstart, qb = qstop;
 555                 qstart = qstop;
 556                 for (int q = qa; q < qb; qinc(q)) {
 557 #define cfg_one(coord, grp) do {\
 558         distances[coord] = d; \
 559         foreach_neighbor (b, coord, { \
 560                 if (distances[c] < 0 && (!grp || group_at(b, coord) != grp)) { \
 561                         queue[qstop] = c; \
 562                         qinc(qstop); \
 563                 } \
 564         }); \
 565 } while (0)
 566                         coord_t cq = queue[q];
 567                         if (distances[cq] >= 0)
 568                                 continue; /* We already looked here. */
 569                         if (board_at(b, cq) == S_NONE) {
 570                                 cfg_one(cq, 0);
 571                         } else {
 572                                 group_t g = group_at(b, cq);
 573                                 foreach_in_group(b, g) {
 574                                         cfg_one(c, g);
 575                                 } foreach_in_group_end;
 576                         }
 577 #undef cfg_one
 578                 }
 579         }
 580
 581         foreach_point(b) {
 582                 if (distances[c] < 0)
 583                         distances[c] = maxdist + 1;
 584         } foreach_point_end;
 585 }
 586
 587 float
 588 board_effective_handicap(struct board *b)
 589 {
 590         /* For very small/very large boards, we might want
 591          * to account for different "base komi". */
 592         float first_move = 7.5; // point value of move on empty board
 593         assert(b->handicap != 1);
 594         return (b->handicap ? b->handicap : 1) * first_move - b->komi;
 595 }