simplification (the prob of

mc_sample(survives_action(a,[a,b,c],0,c),1000,P). is 0.312, too high, it
should be 17/63=0.26984126984)

examples/inference/truel.pl

@@ -4,6 +4,7 @@
 The firing order is a, b and c. Each truelist can shoot at another truelist
 or at the sky (deliberate miss). The truelist have these probabilities of 
 hitting the target (if they are not aiming at the sky): a 1/3, b 2/3 and c 1.
+The aim for each truelist is kill all the other truelists.
 The question is: what should a do to maximize his probability of living? 
 Aim at b, c or the sky?
 Note that the best strategy for the other truelists and situations is
@@ -14,18 +15,18 @@
 */
 
 /** <examples>
-?- best_strategy(a,[b,c],[a,b,c],S).
+?- best_strategy(a,[a,b,c],S).
 % What is the best action for a?
-% S= ($).
-?- mc_sample(survives_action(a,[b,c],0,[a,b,c],b),1000,P).
+% S= sky
+?- mc_sample(survives_action(a,[a,b,c],0,b),1000,P).
 % What is the probability that a survives if it aims at b?
-% P = 0.256
-?- mc_sample(survives_action(a,[b,c],0,[a,b,c],c),1000,P).
+% P = 0.267
+?- mc_sample(survives_action(a,[a,b,c],0,c),1000,P).
 % What is the probability that a survives if it aims at c?
-% P = 0.292
-?- mc_sample(survives_action(a,[b,c],0,[a,b,c],'$'),1000,P).
+% P =  0.312 
+?- mc_sample(survives_action(a,[a,b,c],0,sky),1000,P).
 % What is the probability that a survives if it aims at the sky?
-% P = 0.383
+% P = 0.39682539682
 */
 :- use_module(library(mcintyre)).
 
@@ -39,58 +40,56 @@
 
 :- begin_lpad.
 /**
- * best_strategy(+A:atom,+Rest:list,+L:list,-S:atom).
+ * best_strategy(+A:atom,+L:list,-S:atom).
  *
- * The best strategy for truelist A with Rest remaining to shoot and
- * L still alive is to aim at S (with '$' for the sky).
+ * The best strategy for truelist A with 
+ * L still alive is to aim at S (with sky for the sky).
  *
  */
-best_strategy(A,Rest,L,S):-
+best_strategy(A,L,S):-
     delete(L,A,L1),
-    append(L1,['$'],L2),
-    maplist(ev_action(A,Rest,L),L2,LP),
+    append(L1,[sky],L2),
+    maplist(ev_action(A,L,0),L2,LP),
     sort(LP,LP1),
     reverse(LP1,[_P-S|_]).
 
 
 /**
- * ev_action(+A:atom,+Rest:list,+L:list,+S:atom,-C:couple).
+ * ev_action(+A:atom,+L:list,+T:term,+S:atom,-C:couple).
  *
- * Tuelist A with Rest to shoot, L still alive performing action S survives
+ * Tuelist A with L still alive performing action S in turn T survives
  * with probability P in C=P-S.
  *
  */
-ev_action(A,Rest,L,S,P-S):-
-    mc_sample(survives_action(A,Rest,0,L,S),1000,P).
+ev_action(A,L,T,S,P-S):-
+  mc_sample(survives_action(A,L,T,S),1000,P).
 
 /**
- * survives_action(+A:atom,+Rest0:list,+T:term,+L0:list,+S:atom)
+ * survives_action(+A:atom,+L0:list,+T:term,+S:atom)
  *
- * A survives truel performing action S at round T with Rest0 to shoot in
- * the round and L0 still alive
+ * A survives truel performing action S with L0 still alive in turn T
  *
  */
-survives_action(A,Rest0,T,L0,S):-
-    shoot(A,S,Rest0,L0,T,Rest,L1),
-    survives_round(Rest,L1,A,T).
+survives_action(A,L0,T,S):-
+  shoot(A,S,L0,T,L1),
+  remaining(L1,A,Rest),
+  survives_round(Rest,L1,A,T).
+
 /**
- * shoot(+H:atom,+S:atom,+Rest0:list,+L0:list,+T:term,-Rest:list,-L:list).
+ * shoot(+H:atom,+S:atom,+L0:list,+T:term,-L:list).
  *
  * When H shoots at S with Rest0 to shoot in round T and L0 still alive,
  * the truelist to shoot in the round become Rest and the truelist still
  * alive L
  */
-shoot(H,S,Rest0,L0,T,Rest,L):-
-    (S='$' ->  
-      L=L0,
-      Rest=Rest0
+shoot(H,S,L0,T,L):-
+    (S=sky ->  
+      L=L0
     ;
       (hit(T,H) ->
-        delete(L0,S,L),
-        delete(Rest0,S,Rest)
+        delete(L0,S,L)
       ;   
-        L=L0,
-        Rest=Rest0
+        L=L0
       )
     ).
 
@@ -124,31 +123,36 @@
 survives_round([],L,A,T):-
   survives(L,A,s(T)).
 
-survives_round([H|Rest],L0,A,T):-
-    base_best_strategy(H,Rest,L0,S),
-    shoot(H,S,Rest,L0,T,Rest1,L1),
+survives_round([H|_Rest],L0,A,T):-
+    base_best_strategy(H,L0,S),
+    shoot(H,S,L0,T,L1),
+    remaining(L1,H,Rest1),
     member(A,L1),
     survives_round(Rest1,L1,A,T).
 
 
 /** 
- * base_best_strategy(+A:atom,+Rest:list,+T:list,-S:atom).
+ * base_best_strategy(+A:atom,+T:list,-S:atom).
  *  
- *  the best action for A when Rest follow him in the round and
- *  T is the list of surviving truelist, is S (with '$' for the sky)
+ *  the best action for A when 
+ *  T is the list of surviving truelist, is S 
  *
  *  These are the strategies that are easy to find (most intuitive)
  *
  */
-base_best_strategy(b,[c],[b,c],c).
-base_best_strategy(c,[],[b,c],b).
-base_best_strategy(a,[c],[a,c],c).
-base_best_strategy(c,[],[a,c],a).
-base_best_strategy(a,[b],[a,b],b).
-base_best_strategy(b,[],[a,b],a).
-base_best_strategy(b,[c],[a,b,c],c).
-base_best_strategy(c,[],[a,b,c],b).
+base_best_strategy(b,[b,c],c).
+base_best_strategy(c,[b,c],b).
+base_best_strategy(a,[a,c],c).
+base_best_strategy(c,[a,c],a).
+base_best_strategy(a,[a,b],b).
+base_best_strategy(b,[a,b],a).
+base_best_strategy(b,[a,b,c],c).
+base_best_strategy(c,[a,b,c],b).
 
+remaining([A|Rest],A,Rest):-!.
+
+remaining([_|Rest0],A,Rest):-
+  remaining(Rest0,A,Rest).
 
 :- end_lpad.