From: jac@doe.carleton.ca (James A. Cherry)
Date: Thu, 25 Sep 1997 13:33:25 -0400 (EDT)
Subject: Stats for 10000 OSPD and SOWPODS games (long)
Message-id: <9709251733.AA09440@sarek.doe.carleton.ca>
Joel Sherman asked me a couple of days ago, "What fraction of OSPD games has the outcome determined by the Q or Z being stuck on a player's rack? How about for SOWPODS?" I made ACBot and DDBot each play 10,000 games against themselves in an attempt to answer that question. Here are some stats from those games.
These stats are how many of each tile per OSPD game were played, exchanged, and left on the rack for each player. The Q gets exchanged about 5 games in 100, it appears. The first player turns over 1.82 more tiles than the second.Total games processed: 10000 OSPD, 10000 SOWPODS Average OSPD tile usage by CPU0: A B C D E F G H I J K L M N Played: 4.47 0.99 1.01 2.01 6.02 1.02 1.50 1.02 4.43 0.51 0.51 1.98 1.01 2.97 Dumped: 0.01 0.01 0.01 0.01 0.00 0.00 0.02 0.00 0.07 0.00 0.00 0.02 0.00 0.02 Left: 0.04 0.01 0.02 0.02 0.10 0.01 0.04 0.01 0.14 0.00 0.00 0.06 0.01 0.11 O P Q R S T U V W X Y Z ? Tot Played: 4.01 1.02 0.44 2.92 2.00 2.96 1.93 0.99 1.01 0.51 1.02 0.50 1.0149.77 Dumped: 0.03 0.01 0.06 0.01 0.00 0.02 0.03 0.02 0.01 0.00 0.00 0.00 0.00 0.36 Left: 0.06 0.01 0.06 0.12 0.03 0.10 0.09 0.03 0.01 0.00 0.01 0.01 0.01 1.11 Average OSPD tile usage by CPU1: A B C D E F G H I J K L M N Played: 4.44 0.99 0.96 1.94 5.78 0.97 1.43 0.97 4.29 0.49 0.48 1.90 0.98 2.82 Dumped: 0.01 0.01 0.01 0.01 0.00 0.00 0.01 0.00 0.06 0.00 0.00 0.01 0.00 0.02 Left: 0.04 0.01 0.01 0.02 0.10 0.01 0.04 0.01 0.14 0.00 0.00 0.07 0.01 0.11 O P Q R S T U V W X Y Z ? Tot Played: 3.86 0.96 0.45 2.84 1.94 2.84 1.90 0.95 0.97 0.48 0.96 0.49 0.9748.05 Dumped: 0.03 0.00 0.04 0.01 0.00 0.01 0.02 0.01 0.00 0.00 0.00 0.00 0.00 0.26 Left: 0.07 0.01 0.06 0.12 0.03 0.10 0.08 0.03 0.01 0.00 0.01 0.01 0.01 1.11
Here are the same stats for SOWPODS games. The Q hardly ever gets exchanged now. And the first player turns over 1.80 more tiles than the second.Average SOWPODS tile usage by CPU0: A B C D E F G H I J K L M N Played: 4.52 1.02 0.99 2.00 6.02 1.01 1.49 1.00 4.46 0.51 0.49 1.96 1.00 2.92 Dumped: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.02 0.00 0.00 0.01 0.00 0.01 Left: 0.05 0.01 0.02 0.03 0.11 0.01 0.04 0.01 0.13 0.01 0.00 0.07 0.01 0.13 O P Q R S T U V W X Y Z ? Tot Played: 4.00 0.99 0.49 2.90 2.02 2.93 1.94 0.99 1.01 0.50 1.01 0.51 1.0449.72 Dumped: 0.00 0.00 0.01 0.00 0.00 0.01 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.08 Left: 0.07 0.01 0.02 0.14 0.04 0.11 0.09 0.03 0.01 0.00 0.01 0.00 0.01 1.17 Average SOWPODS tile usage by CPU1: A B C D E F G H I J K L M N Played: 4.38 0.96 0.96 1.95 5.76 0.97 1.43 0.98 4.28 0.48 0.50 1.90 0.98 2.82 Dumped: 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.02 0.00 0.00 0.01 0.00 0.01 Left: 0.05 0.01 0.02 0.03 0.11 0.01 0.04 0.01 0.13 0.01 0.00 0.07 0.01 0.13 O P Q R S T U V W X Y Z ? Tot Played: 3.87 0.98 0.47 2.81 1.91 2.84 1.89 0.95 0.97 0.49 0.97 0.48 0.9547.93 Dumped: 0.00 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.00 0.00 0.00 0.00 0.00 0.07 Left: 0.07 0.01 0.02 0.15 0.03 0.11 0.08 0.03 0.01 0.00 0.01 0.00 0.01 1.16
Early game is defined as fewer than 34 tiles on the board. SOWPODS turns average 2.2 or 2.3 more points than OSPD turns, and the second player is more often ahead than behind after the first couple of moves.OSPD SOWPODS CPU0 CPU1 CPU0 CPU1 EARLY GAME Turns 4.3 3.8 4.2 3.7 Average turn score 36.2 38.0 39.4 41.3
Middle game is defined as between 34 and 66 tiles on the board. Now, each player scores the same per turn. SOWPODS turns are still worth 2.2 or 2.3 more points.MIDDLE GAME OSPD SOWPODS Turns 4.0 4.0 3.9 3.9 Average turn score 37.4 37.4 40.7 40.6
SOWPODS games average 24 more points for each side than OSPD games, despite lasting half a turn less. While the second player averages more points per turn than the first player, the first player has the advantage of having an extra half turn per game. Thus, the first player has a whopping 9% (or 4.5%, depending on how you look at it) advantage at OSPD and 10% (or 5%) at SOWPODS. In both lexica, 0.5% of games end in ties.COMPLETE GAME OSPD SOWPODS Turns 12.5 12.0 12.0 11.5 Average turn score 33.9 34.4 37.2 37.7 Average final score 427.8 416.9 451.8 438.8 Winning %age 54.2% 45.3% 54.9% 44.6% PassWins (807/405) 386 419 184 220 QZWins 46 53 26 24
A "PassWin" is a game that ended with six passes. 807 such games occurred at OSPD, which seems really damn high to me. 386 were won by CPU0, 419 were won by CPU1, and I guess 2 of them ended in ties. Only 405 such games happened at SOWPODS. I think with proper endgame playing, these numbers would drop. A "QZWin" is what Joel was interested in. 99 OSPD games were won by a player that (a) played out, (b) was losing after they played out, (c) was winning after the end-of-game rack adjustment, and (d) got points for the Q or Z being on the opponent's rack. 50 SOWPODS games were won that way. Again, it's hard to say how these numbers would change with proper endgame play.
Joel and Larry felt that many more than 1% of tourney OSPD games end with a stuck Q or Z. They might be right: humans treat the Q differently than the robots do, fer sure. The robots tend to hang onto it longer.
At OSPD, there were 14954 7lw played and 19586 8lw played, for a 4/3 ratio. At SOWPODS, 17600 7lw and 21260 8lw give closer to a 6/5 ratio. These OSPD computer players average 3.45 bingos per game, while their SOWPODS counterparts average 3.89 per game. 13.2% of OSPD games featured the first player bingoing immediately, while 16.3% of SOWPODS games had the same thing happen.NICE PLAYS OSPD SOWPODS 7lw bingos 8042 6912 9475 8125 7lw opening bingos 1318 100 1625 66 8lw bingos 9562 10024 10453 10807 Double-Doubles 1292 1325 1587 1598 Triple-triples 243 277 328 272 9lw+ 573 576 654 608 9lw+ bingos 340 336 450 402
One player plays a nine or longer main word every ninth game at OSPD and every eighth game at SOWPODS. Anyone who's interested in seeing a list of the long words played can email me. For a lark, here are the 9s that were played more than once (and the pair of 10s) at OSPD. Letters in brackets were already on the board, and asterisks denote bingos.
(AL)ImENTED* ALIMENT(ED)* (ANTIDOTE)D ANtI(DO)TeD* BEPAINT(ED)* B(E)PaIN(T)ED* (C)OALI(F)IED* COAL(IF)IED* c(O)RA(L)LINE* c(OR)ALLINE* CRINO(LI)Ne* CRINO(LI)NE* DEA(NE)RIES* (DE)ANERIES* (DE)ANERIES* DE(FEATURE) DE(FEATURE) DE(ORBITED) DEOrB(IT)ED* ENERGE(TI)C* (EN)ERGETIc* ETERNIZ(ED)* (ETERNIZE)D EU(G)LENOI(D)* E(U)G(L)ENOID* FALcONI(NE)* FAlCON(IN)E* G(LO)RIFIED* gLOR(I)F(I)Ed* iNANI(MA)TE* I(N)ANIMAt(E)* (IN)ANiMATE* (LI)NEArItY* (LI)NeARITY* mETE(OR)ITE* ME(T)EORIT(E)* (ME)TEORITE* NECTAR(I)N(E)* NEC(TA)RINE* NEUTrI(NO)S* NEuTRI(NO)s* (OUTJINX)ED OUT(JINXED) OUT(QUOTED) OUT(QUOTED) O(U)T(R)AISED* (OUTRAISE)D (OVEN)WARES (OVENWARE)S (QUARTZ)ITE (QUARTZ)ITE (QUEENS)IDE (QUEENS)IDE (QUOTA)tION (QUOTA)T(I)ON RE(AWAKENS) (REAWAKEN)S REImAGI(NE)* REImAGI(NE)* RETAIL(ER)S* R(ET)AILERS* R(ETA)RDANT RETaR(DA)NT* RET(EN)TION* RETEnTI(ON)* TOLERAT(ED)* TOlERAT(ED)*Same thing for SOWPODS:APOEN(ZYMES) APO(ENZYME)S
ACIER(AG)ES* ACI(E)R(A)GES* A(GO)NISTIC* (A)GOnI(S)TIC* ANAERO(BE)S* AN(A)E(R)OBES* BR(OM)INATE* BR(OM)INATE* DEaERAT(OR)* DEAERA(TO)R* DENtATI(ON)* DEN(TA)TION* DE(OXIDISE) DE(OXIDISE) DoUGH(I)ES(T)* DOuGHIE(ST)* (D)R(A)GOnETS* DRAG(ON)ETS* ELU(T)R(I)AtE* EL(U)T(R)IAtE* EPiFA(UN)AE* EpIFA(UN)AE* ESCAL(A)dE(R)* (ESCALADE)R E(V)AgA(T)ION* EV(AGA)TION FA(R)ANDI(N)E* (FARAND)INE F(AS)TENING* (FASTEN)ING f(IF)TEENTH* fIF(T)E(E)NTH* FOLI(AT)U(RE) FO(LI)AtURE* (FRUITION)S FRUI(TI)ONS* GARNITU(RE)* GA(R)NIT(U)RE* GL(AIRIEST) G(L)AIR(I)EsT* (IO)DINATES* IODIN(AT)ES* IRoNCL(AD)S* IRONC(LA)DS* (LACERATE)D L(ACERATED) L(ON)G(I)TUDE LONGIt(U)D(E)* MaD(DE)NING* (MA)dDEnING* RAC(EM)IZES* (RACEMIZE)S REEN(JOYED) REEN(JOYED) (REFLEX)ION REfLEXI(ON)* RE(GREETE)D RE(GREETED) (RE)GULISED* (RE)GULISED* (RELIGHT)ED (R)El(I)GHTED* RELOCA(TE)E* (RE)LOCATEE* S(E)RRANOI(D)* SERRANO(ID)* (ST)UtTERER* sTUTT(ER)ER* TENOR(IT)ES* T(EN)ORITEs* T(E)R(A)TOGeN* TERA(TO)gEN* T(ET)ANISED* TET(A)NI(S)ED* UNDERTO(NE)* UNDER(TONE)James.(PROVEN)DErS PRo(VENDERS)