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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.

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

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.

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

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.

                             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

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.

MIDDLE GAME                  OSPD             SOWPODS
Turns                   4.0      4.0      3.9      3.9
Average turn score     37.4     37.4     40.7     40.6

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.

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
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.

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.

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
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.

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)*

APOEN(ZYMES) APO(ENZYME)S

Same thing for SOWPODS:

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)

(PROVEN)DErS PRo(VENDERS)

James.