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Originally micro-Max used the 'classical' piece values P=1, B=N=3, R=5 and Q=9. These piece values bring some undesirable effects, though. Although in theory an isolated Bishop should be considered the equal of a Knight, a pair of Bishops is worth nearly half a Pawn more than N+N or B+N. In other words, the first Bishop you lose is worth much more than the second.

Now the subtlety first Bishop vs second is too much for micro-Max to see, especially since it would have to be accounted for each side separately. But it is possible to discourage micro-Max to squander its Bishop pair all too easily by the simple trick of evaluating a Bishop slightly larger than a Knight. The drawback is that it will also avoid B vs N trades when the first Bishop was already gone, for no good reason. But this is much less damaging as letting his Bishops being traded for Knights early in the game. In addition, micro-Max' lack of end-game knowledge makes him really better with Bishops than with Knights in end games, as the latter require more long-range planning due to their slow gait.

A second problem with the classical piece values was that micro-Max often spontaneously sacrifices two pieces for a R+P. Most of the time this loses immediately, if the Pawn isn't a really good one. At the level where micro-Max plays, Pawns are dog-food if you have a numeric minority in Pieces. And a numeric minority is exactly what B+B vs R+P gives you. For the same reason, B or N vs 3P trades are usually losing dramatically.

To remedy all these bad habits, the piece values have been changed to P=2, N=7, B=8, R=12 and Q=23. Scaled to a more usual range, this would give P=0.8, N=2.8, B=3.2, R=4.8, Q=9.2. N+N against R+P is still considered equal, but as soon as Bishops are involved such trades are now taboo. A Knight is only traded voluntarily for 4 Pawns, and for a Bishop even that deal is considered neutral.

In the opening micro-Max plays reasonable with Pawns. His reluctance to create weak squares by moving a Pawn for which the second neighbor left or right is no longer covering the squares defended by this Pawn, leads to reasonably sound Pawn structures.

Unfortunately, the same rule leads to a great reluctance pushing Pawns in the end-game, when the Pawn structure has thinned so much that virtually every Pawn is isolated. For a Pawn that lacks both the left and the right second neighbor, pushing it actually receives a negative score. Increasing the general pawn-push bonus, which is nominally equal to one such 'missing-second-neighbor penalty' (9 centiPawn), leads to stormy Pawn play in the early middle game, completely exposing all pieces (and King), usually with fatal consequences.

As a solution, (suggested to me by Maarten Claessens), we included an extra Pawn-push bonus that slowly increases as the game progresses, as deduced from the amount of piece material already captured. This bonus is calculated from the captured-piece-material measure R as R/4. Since R starts at 0 and runs upto 40 for bare Kings, this means that the Pawn-push bonus increases by 10 cP in a Pawn ending. This is enough to cancel out the Pawn-push penalty of even an isolated Pawn, and at least makes advance of Pawns to half-way the board under the effect of the center-points table a dominant drive in such endings. This makes it a lot more likely that promotions get within the horizon.

The listing below highlights the evaluation improvements in micro-Max 4.5. They take only 9 extra charactes.

/***************************************************************************/ /* micro-Max, */ /* A chess program smaller than 2KB (of non-blank source), by H.G. Muller */ /***************************************************************************/ /*version 4.5 (1868 characters)features: */ /* - recursive negamax search */ /* - all-capture MVV/LVA quiescence search */ /* - (internal) iterative deepening */ /* - best-move-first 'sorting' */ /* - a hash table storing score and best move */ /* - futility pruning */ /* - king safety through magnetic, frozen king in middle-game */ /* - R=2 null-move pruning */ /* -keep hash and repetition-draw recognition at game level*/ /* - full FIDE rules (expt under-promotion) and move-legality checking */ #define W while #define K(A,B) *(int*)(T+A+(B&8)+S*(B&7)) #define J(A) K(y+A,b[y])-K(x+A,u)-K(H+A,t) #define U (1<<24) struct _ {int K,V;char X,Y,D;} A[U]; /* hash table, 16M entries */ int M=136,S=128,I=8e3,C=799,Q,O,K,N,R,J,Z,k=16,*p,c[9]; /* M=0x88 */ char L, w[]={0,2,2,7,-1,8,12,23}, /* relative piece values */ o[]={-16,-15,-17,0,1,16,0,1,16,15,17,0,14,18,31,33,0, /* step-vector lists */ 7,-1,11,6,8,3,6, /* 1st dir. in o[] per piece*/ 6,3,5,7,4,5,3,6}, /* initial piece setup */ b[129], /* board: half of 16x8+dummy*/ T[1035]; /* hash translation table */ D(q,l,e,E,z,n) /* recursive minimax search, k=moving side, n=depth*/ int q,l,e,E,z,n; /* (q,l)=window, e=current eval. score, E=e.p. sqr.*/ { /* e=score, z=prev.dest; J,Z=hashkeys; return score*/ int j,r,m,v,d,h,i,F,G,V,P,f=J,g=Z; char t,p,u,x,y,X,Y,H,B; struct _*a=A+(J+k*E&U-1); /* lookup pos. in hash table*/ q--; /* adj. window: delay bonus */ k^=24; /* change sides */ d=a->D;m=a->V;X=a->X;Y=a->Y; /* resume at stored depth */ if(a->K-Z|z| /* miss: other pos. or empty*/ !(m<=q|X&8&&m>=l|X&S)) /* or window incompatible */ d=Y=0; /* start iter. from scratch */ X&=~M; /* start at best-move hint */ W(d++<n||d<3|| /* iterative deepening loop */ z&K==I&&(N<1e6&d<98|| /* root: deepen upto time */ (K=X,L=Y&~M,d=3))) /* time's up: go do best */ {x=B=X; /* start scan at prev. best */ h=Y&S; /* request try noncastl. 1st*/ P=d<3?-I:D(-l,1-l,-e,S,0,d-3); /* Search null move */ m=-P<l|R>35?d-2?-I:e:-P; /* Prune or stand-pat */ N++; /* node count (for timing) */ do{u=b[x]; /* scan board looking for */ if(u&k) /* own piece (inefficient!)*/ {r=p=u&7; /* p = piece type (set r>0) */ j=o[p+16]; /* first step vector f.piece*/ W(r=p>2&r<0?-r:-o[++j]) /* loop over directions o[] */ {A: /* resume normal after best */ y=x;F=G=S; /* (x,y)=move, (F,G)=castl.R*/ do{ /* y traverses ray, or: */ H=y=h?Y^h:y+r; /* sneak in prev. best move */ if(y&M)break; /* board edge hit */ m=E-S&b[E]&&y-E<2&E-y<2?I:m; /* bad castling */ if(p<3&y==E)H^=16; /* shift capt.sqr. H if e.p.*/ t=b[H];if(t&k|p<3&!(y-x&7)-!t)break; /* capt. own, bad pawn mode */ i=37*w[t&7]; /* value of capt. piece t */ m=i<0?I:m; /* K capture */ if(m>=l&d>1)goto C; /* abort on fail high */ v=d-1?e:i-p; /* MVV/LVA scoring */ if(d-!t>1) /* remaining depth */ {v=p<6?b[x+8]-b[y+8]:0; /* center positional pts. */ b[G]=b[H]=b[x]=0;b[y]=u|32; /* do move, set non-virgin */ if(!(G&M))b[F]=k+6,v+=50; /* castling: put R & score */ v-=p-4|R>29?0:20; /* penalize mid-game K move */ if(p<3) /* pawns: */ {v-=9*((x-2&M||b[x-2]-u)+ /* structure, undefended */ (x+2&M||b[x+2]-u)-1 /* squares plus bias */ +(b[x^16]==k+36)) /* kling to non-virgin King */-(R>>2); /*Pawn-push bonus in ending*/ if(y+r+1&S)b[y]|=7,i+=C; /* promote p to Q, add score*/ } J+=J(0);Z+=J(8)+G-S; /* update hash key(s) */ v+=e+i;V=m>q?m:q; /* new eval and alpha */ v=d>3|v>V?-D(-l,-V,-v, /* recursive eval. of reply */ F,0,d-1):v; /* or fail low if futile */ if(K-I&&v+I&&z&x==K&y==L) /* move pending. if legal, */ {Q=-e-i;O=F; /* in root & found, exit D */R+=i>>7;return I; /*captured non-P material*/ } J=f;Z=g; /* restore hash key(s) */ b[G]=k+6;b[F]=b[y]=0;b[x]=u;b[H]=t; /* undo move,G can be dummy */ } if(v>m) /* new best, update max,best*/ m=v,X=x,Y=y|S&F; /* mark double move with S */ if(h){h=0;goto A;} /* redo after doing old best*/ if(x+r-y|u&32| /* not 1st step,moved before*/ p>2&(p-4|j-7|| /* no P & no lateral K move,*/ b[G=x+3^r>>1&7]-k-6 /* no virgin R in corner G, */ ||b[G^1]|b[G^2]) /* no 2 empty sq. next to R */ )t+=p<5; /* fake capt. for nonsliding*/ else F=y; /* enable e.p. */ }W(!t); /* if not capt. continue ray*/ }}}W((x=x+9&~M)-B); /* next sqr. of board, wrap */ C:if(m>I-M|m<M-I)d=98; /* mate holds to any depth */ m=m+I|P==I?m:0; /* best loses K: (stale)mate*/ if(a->D<99) /* protect game history */ a->K=Z,a->V=m,a->D=d, /* always store in hash tab */ a->X=X|8*(m>q)|S*(m<l),a->Y=Y; /* move, type (bound/exact),*/ /*if(l>I)printf("%2d ply, %9d searched, score=%6d by %c%c%c%c\n",d-2,N-S,m, 'a'+(X&7),'8'-(X>>4),'a'+(Y&7),'8'-(Y>>4&7)); /* uncomment for Kibitz */ } /* encoded in X S,8 bits */ k^=24; /* change sides back */ return m+=m<e; /* delayed-loss bonus */ } main() { K=8;W(K--) {b[K]=(b[K+112]=o[K+24]+8)+8;b[K+16]=18;b[K+96]=9; /* initial board setup*/ L=8;W(L--)b[16*L+K+8]=(K-4)*(K-4)+(L-3.5)*(L-3.5); /* center-pts table */ } /*(in unused half b[])*/ N=1035;W(N-->M)T[N]=rand()>>9; W(1) /* play loop */ {N=-1;W(++N<121) printf("%c",N&8&&(N+=7)?10:".?+nkbrq?*?NKBRQ"[b[N]&15]); /* print board */ p=c;W((*p++=getchar())>10); /* read input line */ K=I; /* invalid move */ if(*c-10)K=*c-16*c[1]+C,L=c[2]-16*c[3]+C; /* parse entered move */ D(-I,I,Q,O,1,3); /* think or check & do*/ } }

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