What do computer simulations of many Scrabble games show about scores, bingos, game length, square usage...
competition/games/scrabble.simulation New
New entry, edited from material collected for the archive and not yet in a released version.
Problem
What do computer simulations of many Scrabble games show about scores, bingos, game length, square usage and the most commonly played words? [ Editor: problem statement reconstructed; the material is Mark Watkins's report of 500000 games played by the program BobBOT against itself, mailed to the sowpods mailing list in May 1999. In the boards a lower-case letter is a blank. ]
Show solution
Having a week off from consensus games, BobBOT was going to play 1
million games versus itself, but technical complications cut that number
to 500000. Here are various data from the ordeal:
The player going first wins 55.7% of the time.
The average score is 448-434 in favour of the first player.
About 1 in 250 games ends in a draw.
SCORES PER TURN:
This records the average score on turn one, turn two, etc., and also
the % of times the player exchanged or bingoed.
T# AVG XCH% BIN% T# AVG XCH% BIN%
1 30.8 4.7 14.8 2 38.5 1.1 20.5
3 42.8 1.0 23.1 4 43.2 0.8 22.1
5 43.9 0.7 22.2 6 43.8 0.6 21.5
7 43.8 0.6 21.2 8 43.5 0.6 20.7
9 43.4 0.6 20.4 10 43.1 0.6 20.0
11 42.8 0.6 19.6 12 42.4 0.6 19.0
13 42.1 0.6 18.6 14 41.5 0.6 18.0
15 40.9 0.6 17.4 16 40.3 0.6 16.8
17 39.6 0.6 15.9 18 38.8 0.5 15.1
19 37.6 0.3 14.0 20 35.2 0.2 12.3
etc.
BINGOS PLAYED:
2080673 bingos were played, an average of 4.16 per game.
There were 886589 7-letter bingos, 1143307 8-letter bingos,
and 50777 9+-letter bingos.
LENGTH OF GAMES:
This records what % of games lasted how long. A ply is one player's
turn, so in a 16-ply game, each player played 8 times.
Ply %gm Ply %gm
16 0.0 23 19.3
17 0.1 24 11.3
18 0.6 25 5.4
19 3.5 26 2.2
20 11.1 27 0.9
21 20.8 28 0.3
22 24.4 29+ 0.1
EARLY BLOCKOUTS:
a b c d e f g h i j k l m n o a b c d e f g h i j k l m n o
----------------------------- -----------------------------
1|= ' = ' W|1 1|= ' = ' =|1
2| - " " Z O|2 2| - " " - |2
3| - ' ' T I N|3 3| - ' ' - |3
4|' - ' C L O N K|4 4|' - ' - '|4
5| - R O T E |5 5| - - |5
6| " " F A A B A|6 6| " " " " |6
7| ' ' J I z L M|7 7| ' V ' B ' ' |7
8|= ' N A R I A L M|8 8|= C A D G E D ' L|8
9| ' ' P E E R Y O|9 9| ' R O U T E D R ' P I|9
10| " " H E R S " |10 10| " V E N A E " A N O A|10
11| - B O D T I C |11 11| P E T I T I U R|11
12|' - D A G R V A '|12 12|' Y A U D S ' I - I F '|12
13| - ' G E E Y A W N|13 13|B O W R E F M A T Z O S |13
14| - P L E S H F - I|14 14|A W S O X Y A G I - U|14
15|= Q U O I T S U N T A X|15 15|H K E I T l O A S C O O T|15
----------------------------- -----------------------------
21 unseen: DDEEEEEGIIINOORSTUUV? 22 unseen: EEEEEGHIIJLLLMNNNNQRR?
HIGH SCORE: 806
a b c d e f g h i j k l m n o
-----------------------------
1|V I E D A R R O W I N g|1 CAGOT 8d 22 22 MOMI 9e 27 27
2| - O O H " O - |2 GOGGLY f8 16 38 ITINERATE h7 80 107
3| J U B A ' Q N - |3 DITT 7g 16 54 TIVY k4 29 136
4|' R E D S H I F T S '|4 REDSHIFT 4d 88 142 QI i3 21 157
5| P A S E O I |5 FLUEY 13b 22 164 TREELaWN 14h 74 231
6| " E D " V " |6 TRIAZINE o8 293 457 JUBA 3c 35 266
7| ' D I T T Y ' |7 WONS l1 54 511 OOH 2d 37 303
8|= C A G O T ' T|8 ARROWINg 1h 140 651 VIED 1a 37 340
9| ' M O M I ' ' A R|9 CAULK l11 32 683 PASEO 5c 42 382
10| " G N " X I|10 NEBULISE 15a 83 766 AXE n9 55 437
11| - G E - C E A|11 ED 6e 28 794
12|' - L R A Z|12 +ANOP 12 806
13| F L U E Y ' A ' U - I|13
14| - " T R E E L a W N|14
15|N E B U L I S E K E|15
-----------------------------
HIGH LOSS: 599
a b c d e f g h i j k l m n o
-----------------------------
1|= V ' K R O N A J A N E|1 CUTTIER 8d 74 74 NOTARiZE i1 77 77
2| I " O Y E |2 YIN j2 31 105 KRONA 1f 34 111
3| V - ' T I - E |3 CISELURE d8 72 177 TOXEMIAS 15a 203 314
4|' A I A B A N G L E D '|4 WARED 14b 56 233 TOWNlIER 5b 70 384
5| T O W N l I E R - I |5 CHEROOTS 11b 76 309 SUB 10d 23 407
6| " " i " L |6 AIA 4b 20 329 HEINOUS 12g 82 489
7| ' ' Z ' Y |7 FUG 13c 46 375 BANGLE 4h 31 520
8|= C U T T I E R ' =|8 NEEDILY n1 87 462 VIVAT b1 22 542
9| ' I ' D E L O P E D|9 DELOPED 9i 88 550 JANE 1l 57 599
10| " S U B " " |10 ARGAN 14h 12 562
11| C H E R O O T S - |11 +FMPQ 40 602
12|' L H E I N O U S '|12
13| F U G ' ' - |13
14| W A R E D A R G A N - |14
15|T O X E M I A S ' =|15
-----------------------------
HIGH TOTAL: 1311
a b c d e f g h i j k l m n o
-----------------------------
1|= K A A L N A G E R V|1 JEED 8h 24 24 TOM 9g 25 25
2| B I L G Y " - I|2 cAUDRONS k5 82 106 REALLOT 10b 73 98
3| D A ' ' - E|3 SCUFT 12k 22 128 ADOPTIVE o8 176 274
4|' N E ' - W|4 OXIM n5 33 161 BIPARTED b6 69 343
5| E - c W O S|5 RISOLUTO e6 66 227 FINI c12 25 368
6| B Y R " " A A X |6 KIDNEYS c1 92 319 RHIZINEs 15a 311 679
7|H I S I ' ' U G I |7 HUT a7 38 357 BILGY 2b 38 717
8|U P ' S J E E D ' M A|8 WAG m5 28 385 VIEWS o1 51 768
9|T A ' O T O M R R D|9 ALNAGER 1f 82 467 ROQUE m9 30 798
10| R E A L L O T " O O " O|10 CAKE 1a 40 507
11| T U N Q P|11 +AEN 6 513
12|' E F - T ' S C U F T|12
13| D I O ' ' E I|13
14| - N " " - V|14
15|R H I Z I N E s ' E|15
-----------------------------
A 16-PLY GAME (one of 11 in the sample) WHICH HAS TEN BINGOS:
a b c d e f g h i j k l m n o
-----------------------------
1|= ' G A Q U A S|1 GaSTRAL 8d 68 68 LOGOTYPE d6 78 78
2| - G E N E R O U S - |2 BREAK c3 45 113 GRITTIER h1 80 158
3| B ' I ' O - U |3 HIM c9 30 143 VENNEL 13c 20 178
4|J I R D T V N '|4 UINTIATE 5e 82 225 CLOD h12 30 208
5| E U I N T A I T E I |5 ODOrIZED 15a 104 329 OVERSALE l3 74 282
6| " A L " I " R F |6 JIRD 4a 40 369 GENEROUS 2d 63 345
7| K O ' E ' S ' I |7 AQUAS 1k 74 443 YARDMEN m8 88 433
8|= G a S T R A L A Y E =|8 UNIFIER n3 77 520 WHITECOAT 10a 81 514
9| H O ' ' L A R |9 +ABFPWX 46 560
10|W H I T E C O A T " E R " |10
11| M Y - - D |11
12|' P C - M '|12
13| V E N N E L ' E |13
14| - " O " N - |14
15|O D O r I Z E D ' =|15
-----------------------------
SQUARE FREQUENCY:
Note that BobBOT always starts the game by playing horizontal.
Square frequencies are in % of games in which the square was used.
------------------------------------------------------------------------------
| A1 B1 C1 D1 E1 F1 G1 H1 I1 J1 K1 L1 M1 N1 O1 |
| 33.4 25.5 26.3 34.9 27.8 29.4 33.9 68.6 34.5 31.0 30.0 43.3 37.3 36.8 54.2 |
| |
| A2 B2 C2 D2 E2 F2 G2 H2 I2 J2 K2 L2 M2 N2 O2 |
| 23.6 38.2 32.5 37.1 29.9 40.0 30.7 52.7 30.7 45.1 36.5 44.9 40.5 51.1 37.3 |
| |
| A3 B3 C3 D3 E3 F3 G3 H3 I3 J3 K3 L3 M3 N3 O3 |
| 24.5 31.7 47.5 42.1 32.7 32.0 34.9 50.2 38.0 35.7 37.4 48.7 57.2 39.7 37.9 |
| |
| A4 B4 C4 D4 E4 F4 G4 H4 I4 J4 K4 L4 M4 N4 O4 |
| 33.2 35.8 40.9 61.4 40.1 35.6 28.5 53.4 31.7 38.0 43.3 69.2 45.8 41.0 45.6 |
| |
| A5 B5 C5 D5 E5 F5 G5 H5 I5 J5 K5 L5 M5 N5 O5 |
| 27.6 29.4 33.1 41.6 62.1 40.2 33.9 43.7 35.9 42.4 68.3 48.5 39.1 36.9 39.1 |
| |
| A6 B6 C6 D6 E6 F6 G6 H6 I6 J6 K6 L6 M6 N6 O6 |
| 29.8 40.3 31.8 38.1 46.8 51.0 32.0 39.8 34.3 55.9 52.4 42.8 36.3 46.9 41.2 |
| |
| A7 B7 C7 D7 E7 F7 G7 H7 I7 J7 K7 L7 M7 N7 O7 |
| 35.8 29.6 34.1 30.4 47.8 38.6 50.2 47.1 55.6 46.8 49.6 36.6 40.8 36.0 46.6 |
| |
| A8 B8 C8 D8 E8 F8 G8 H8 I8 J8 K8 L8 M8 N8 O8 |
| 58.5 39.6 33.2 71.0 66.1 69.1 73.5 100% 67.3 58.0 55.9 62.0 47.5 49.1 74.4 |
| |
| A9 B9 C9 D9 E9 F9 G9 H9 I9 J9 K9 L9 M9 N9 O9 |
| 36.2 28.7 39.4 40.5 50.1 42.2 50.9 46.0 49.5 40.1 45.2 34.5 39.3 34.6 45.4 |
| |
| A10 B10 C10 D10 E10 F10 G10 H10 I10 J10 K10 L10 M10 N10 O10 |
| 31.9 46.5 38.4 47.3 51.3 55.7 37.5 42.1 35.0 52.5 49.3 40.8 36.9 48.5 40.2 |
| |
| A11 B11 C11 D11 E11 F11 G11 H11 I11 J11 K11 L11 M11 N11 O11 |
| 30.5 36.4 39.3 49.1 69.6 45.5 38.0 46.8 38.1 45.0 66.4 44.7 38.3 39.8 36.8 |
| |
| A12 B12 C12 D12 E12 F12 G12 H12 I12 J12 K12 L12 M12 N12 O12 |
| 42.6 44.1 49.0 70.4 45.0 36.2 29.2 57.0 32.7 39.1 44.2 64.9 45.1 42.9 44.4 |
| |
| A13 B13 C13 D13 E13 F13 G13 H13 I13 J13 K13 L13 M13 N13 O13 |
| 36.4 39.9 57.8 46.8 36.4 33.4 38.8 55.3 40.4 36.9 38.2 45.5 55.0 39.3 37.0 |
| |
| A14 B14 C14 D14 E14 F14 G14 H14 I14 J14 K14 L14 M14 N14 O14 |
| 35.5 51.6 41.1 42.3 36.9 46.9 36.3 58.2 36.1 48.9 40.5 43.6 40.0 51.2 33.8 |
| |
| A15 B15 C15 D15 E15 F15 G15 H15 I15 J15 K15 L15 M15 N15 O15 |
| 55.0 39.7 40.3 46.9 39.0 40.8 45.6 80.6 43.8 39.2 36.7 44.9 38.0 35.0 50.0 |
------------------------------------------------------------------------------
COMMONLY PLAYED WORDS:
This counts how many times a word was played as the "main" word, i.e.
not just hooking other tiles/words.
2-Letter Words:
QI 126273 AX 12801 OI 6073 HI 4840 YO 4415
XI 19762 JO 11621 IO 5594 OO 4819 OY 4381
OX 17329 ZO 10718 OW 5291 FY 4671 UH 4352
EX 14575 IF 6728 YU 5127 OE 4614 EE 4332
XU 13276 OF 6560 WO 4895 AI 4468 WE 4300
3-Letter Words:
QAT 52314 AXE 9046 OYE 7231 WOX 6379 JET 6018
QIS 30802 JOE 8772 WOO 6860 VOW 6146 ZEE 6003
AIA 13393 QUA 8404 TAJ 6859 GOX 6129 VAW 5970
EAU 9775 SUQ 7886 OAF 6580 VEX 6115 OOF 5879
OXO 9050 VOX 7597 YOU 6487 UEY 6029 JEW 5799
4-Letter Words:
EUOI 18975 AJEE 5466 ANOA 4872 INIA 4461 AQUA 4074
QAID 15804 JIVE 5286 QUOD 4861 QUAG 4436 ZOEA 4070
QADI 12413 IXIA 4946 IOTA 4829 OGEE 4434 ODEA 3971
JIAO 7843 OHIA 4928 WAQF 4612 AGIO 4283 QOPH 3900
QATS 7541 QUAI 4884 FIVE 4482 JUVE 4202 JEFE 3864
5-Letter Words:
TRANQ 7240 OORIE 3604 OIDIA 2988 QUERN 2502 AULOI 2313
QANAT 5211 ZOEAE 3542 ZOOEA 2822 ADIEU 2428 AQUAE 2309
FAQIR 5003 QIBLA 3346 AUDIO 2818 AERIE 2366 COOEE 2307
TALAQ 4301 AIOLI 3110 ROQUE 2622 ZAIRE 2361 QUEEN 2284
AINEE 3697 OUIJA 3055 QUOIF 2534 QUOIT 2333 EERIE 2277
[ Editor: QUERN was "AUERN" in the original posting; Watkins corrected
it in a follow-up message the same day. ]
6-Letter Words:
QINTAR 2166 OUTVIE 939 QIVIUT 838 FOOTIE 752 AGOUTI 680
EUOUAE 1737 ZOOEAE 891 ZOUAVE 834 QUIVER 751 TOEIER 671
QINDAR 1691 WIENIE 852 ZOARIA 815 AVIATE 698 TOITOI 666
FEIJOA 989 HEINIE 852 AZIONE 807 IOLITE 687 VOIDEE 665
YAQONA 944 QUINOA 842 HOAGIE 806 EQUATE 687 FOVEAE 665
7-Letter Words: (number of bingos, not # of times played)
ETAERIO 1197 TAENIAE 477 ANISOLE 409 AERATES 347 AERIEST 330
ERASION 695 INERTIA 470 SOUTANE 395 ANISEED 345 ALINERS 329
OTARINE 692 AEROSAT 452 ORDINEE 391 AENEOUS 343 AIRIEST 327
ATONIES 684 ISATINE 442 ORIGANE 389 AROINTS 342 URINOSE 326
ETESIAN 587 SERIATE 438 OLEARIA 371 OREADES 339 ENOLASE 326
AIERIES 575 ANEROID 436 OARIEST 365 IRISATE 337 ROUTINE 324
ROSEATE 542 INOSITE 431 SEALINE 363 AEOLIAN 337 ANESTRA 324
OTARIES 506 ISOLATE 422 ESTRONE 360 SIENITE 336 AEONIAN 324
SENARII 487 SOREDIA 418 RETINOL 359 TORNADE 333 ARENITE 321
ARENOSE 478 RIOTISE 409 IODATES 347 OLEATES 333 SUETIER 311
8-Letter Words: (number of bingos, not # of times played)
AERATION 682 DETAINEE 406 RETINOID 348 RITORNEL 321 TRIENNIA 294
ETAERIOS 672 INAURATE 391 TAENIOID 347 RETAILOR 321 TAILERON 294
ERIONITE 624 ORIENTED 387 TENORITE 346 EULOGIAE 321 TONALITE 292
AEROLITE 592 AEGIRITE 387 OLEARIAS 346 RETAINER 320 ENTAILER 291
INERTIAE 526 ALIENATE 368 REORIENT 339 INERTIAL 319 EATERIES 288
DOUANIER 471 TENTORIA 365 AEGIRINE 337 RETAINED 318 OEDIPEAN 287
ANTERIOR 442 AERONAUT 362 OUTRAISE 333 FOEDARIE 316 ELOIGNER 286
AREOLATE 430 INTERIOR 361 ABOITEAU 324 ALEURONE 316 UREDINIA 285
UNEASIER 418 ETIOLATE 358 ERGATOID 322 IODINATE 313 TAENIATE 285
ERADIATE 416 ETOURDIE 356 DAINTIER 322 ADROITER 300 ANTIHERO 284
9-Letter Words: (number of bingos, not # of times played)
NEOTEINIA 27 REEDITION 23 INTERLAID 22 ETIOLATED 21
OUTEARNED 25 ORIENTATE 23 ARSENIATE 22 DENITRATE 21
ARENATION 25 ALIENATOR 23 PERITONEA 21 DEANERIES 21
ITERATION 24 ITINERATE 22 NEURATION 21 ANOREXIES 21
OUTWAITED and OUTVOICED are more common, but aren't bingos very often.
-- Mark Watkins <mwatkins@math.uga.edu> (May 1999)
[ Editor: an earlier simulation, 5000 games, reported by Steve Thomas to
the crossword-games-pro and word-game-programmers mailing lists in
December 1994 under "The word QI". His second message, which repeated
the tables with explanations, is merged here; Larry Sherman
<icenine@panix.com> had asked what the column headings mean. ]
Some time ago, I built a Scrabble-playing computer program with the
third edition of OSW. Casual inspection of the logs of half a dozen
games revealed that the program played the word "QI" twice. This datum
has made it into the literature (the latest Onwords and the Dec 24
edition of the Daily Telegraph (a British national daily newspaper)) as
"extensive computer simulation" and either "one third of all games" and
"30% of all games". Both versions of the tale, naturally, have all
correct attribution stripped off.
While I was away from my desk over the holidays, "my" workstation has
been contemplating Scrabble, and played 5000 games against itself. The
results are interesting. In 111532 plays, the program played a total
of 234697 words, of which 41501 were unique. The single commonest word
was "QI", played in 2619 moves, with the word occurring 3017 times;
there were 520 "QIS" plays, the word occurring 547 times in all. It is
of course possible for the word "QI" to be played up to twice in a
single game, but the figures suggest that "QI" occurs in 50-60% of all
games, not 30-33%.
U-less Q words.
1 INQILABS
1 QWERTIES
2 INQILAB
2 QASIDAS
2 QIVIUTS
3 QIGONGS
3 YAQONAS
4 BURQAS
5 QIVIUT
5 QWERTY
6 QIBLAS
7 QASIDA
7 QINTARS
10 TALAQS
11 QIGONG
11 YAQONA
15 BURQA
15 QANATS
18 WAQFS
19 QOPHS
19 SUQS
23 QINTAR
30 QIBLA
34 QOPH
40 WAQF
47 TALAQ
60 QANAT
67 QADIS
92 SUQ
125 QATS
199 QADI
547 QIS
548 QAT
3017 QI
Here are the stats collected. "Full" employs some rack-leave
heuristics plus some tree-searching. "RackMan" just uses the
rack-leave heuristics.
These are stats overall, and broken down by games in which Full
starts/replies and has 0, 1, or 2 blanks. Win, draw, and loss are
numbers of games in the appropriate category. Score is average (mean)
game score, and oscore is average game score of RackMan. Spread is
average spread (absolute difference in scores).
Start: Full Start: RackMan
Total 0# 1# 2# 0# 1# 2#
total: 5000 611 1252 637 681 1227 592
win: 2525 172 719 523 145 553 413
draw: 24 7 2 2 3 6 4
loss: 2451 432 531 112 533 668 175
score: 410 382 418 449 375 405 433
oscore: 412 435 405 375 444 419 389
spread: 78 83 72 92 91 69 77
This section gives the minimum, maximum, and average of the various
quantities for Full and RackMan. Single play is the score for a single
turn. Single game is the score for a full game. Tiles seen is the
number of tiles that appeared on the rack at some point during the
game. Moves used is the number of turns the game lasted. "Using ..."
are move scores using the relevant letter, '#' being the blank, and
DWS, Wx4, TWS, and Wx9 being plays using a double word score, two DWSs,
triple word score, and two TWSs. Bonus score the move score for bonus
(bingo) plays. Turns w/ Q and # are the number of turns the players
hold on to the Q and blank, per game. Racks exch is the number of
racks exchanged, per game.
Full RackMan
Min Max Ave Min Max Ave
Single play: 1 284 36.73 2 221 37.07
Single game: 236 740 410.80 246 624 412.28
Tiles seen: 38 71 51.15 39 70 51.17
Moves used: 8 17 11.37 9 17 11.33
Using 'J': 9 126 39.94 9 130 40.49
Using 'K': 8 167 38.56 9 185 38.17
Using 'Q': 11 284 35.69 11 139 35.61
Using 'S': 2 194 52.71 6 221 53.53
Using 'X': 8 131 44.44 13 126 44.74
Using 'Z': 11 221 44.81 11 203 45.33
Using '#': 1 284 70.81 5 221 72.12
Using DWS: 2 122 36.22 4 126 36.17
Using Wx4: 24 131 67.14 24 130 68.33
Using TWS: 6 137 43.59 6 147 43.49
Using Wx9: 75 284 147.58 81 221 147.29
Bonus score: 58 284 78.33 57 221 78.59
Turns w/ Q: 0 6 1.41 0 8 1.36
Turns w/ #: 0 12 2.15 0 12 2.12
Racks exch: 0 4 0.18 0 3 0.18
These are the minimum, maximum, and average spreads (absolute
differences in scores) and aggregates (sum of scores), together with
the individual game scores for games in which they happened. (Pretty
impressive, winning a game by over 400 points!)
Spread: 0 418 78.85 (379+379) (740+322)
Aggregate: 623 1078 823.08 (342+281) (571+507)
These are the percentages of times the program find itself with a rack
of tiles repeating letters the indicated number of tiles. I don't
print a line if there were no instances, so there was at least one case
of a rack with a letter repeated 6 times, but no clean sweeps.
%age racks repeating a letter at most n times
n Full RackMan
1 35.81 36.56
2 55.86 55.18
3 7.71 7.73
4 0.60 0.51
5 0.02 0.01
6 0.00 0.00
These represent occasions when the racks suffered from acute vowelitis
and consonantitis.
%age racks with: Full RackMan
6+ vowels: 1.64 1.62
6+ consonants: 11.10 11.10
These are bonus (bingo) statistics. The first line is the number
played per game, and the rest the percentages of games with the
indicated number of bonuses.
Bonuses: Full RackMan
Per game: 1.65 1.65
% with 0: 11.44 10.78
% with 1: 34.78 35.32
% with 2: 35.16 35.86
% with 3: 15.14 14.24
% with 4: 3.08 3.42
% with 5: 0.40 0.36
% with 6: 0.00 0.02
These are the longest words for Full and RackMan.
Longest words: CANTONIZES and THICKENINGS
These are per-game percentages. Most of the time goes in the end-game
stuff for Full. Without this, essentially all games take 2-4 seconds.
The end-game analysis has an arbitrary cut-off of 5 minutes per move,
although in practice this is only needed in one move per game. As a
result, there would be few games which take much over 300s.
Cpu time usage:
% using 1-2s: 0.42
% using 2-4s: 9.22
% using 4-8s: 15.28
% using 8-16s: 15.86
% using 16-32s: 14.22
% using 32-64s: 14.92
% using 64-128s: 13.16
% using 128-256s: 8.08
% using 256-512s: 8.84
=>Finally, just curious, is QI being played more often than ZO? I suppose
=>it figures to be considering how much easier it is to use the Z in other
=>words, and the fact that there is one more I than O in the bag.
ZO is played 1256 times in all. QI is, as I said earlier, the
commonest single word. The commonest few words are:
1168 IF
1169 EE
1172 EX
1178 JO
1243 AD
1256 ZO
1314 AT
1331 AR
1352 EF
1353 NE
1392 EL
1438 IN
1447 EN
1451 TE
1456 ID
1505 WE
1513 IT
1637 ER
1941 RE
3017 QI
=>And
=>what in hell is WAQF?!? I dare you to pronounce this abomination without
=>biting your tongue or the inside of your mouth!
I believe it's a provision in Moslem law in respect of religious
bequests.
-- Steve Thomas <sthomas@specialix.co.uk>, Specialix Research Limited,
December 1994