We have to distinguish two issues here: search and eval strategies. Search just figures out how you should force your way to the best achievable position in a turn-based game. But the task to tell you what is best rests purely on eval.
Indeed. That is what has been confusing me a bit. I think we can divide maxn/parnoid as follows.The search strategy is always maxn (or min-max) in which each player maximizes its own score and only that.What differentiates the strategies is how that eval score is formed at the leaves. There are many maxn like mixed strategies with different social oriented evaluation SOE. A clear distinction between maxn and paranoid can be made by noting paranoid as a two player game where the tuple is (x,-x,-x,...). With individual material score's of (a,b,c) paranoid can be for example (x=a,-x,-x) OR (x=a-(b+c),-x,-x) OR (x=3a-(b+c),-x,-x) OR (x=a-max(b,c),-x,-x) etc...Maxn oth contains distinct eval tuples.
a - max(b,c) is significantly less paranoid than a - (b+c). It assumes the strongest opponent will turn against you, while the weakest will remain neutral. Nevertheless, I think scores like a/(a+b+c) would be more natural.
Maybe, but I am not sure as to the real difference. if we take out the same amount from evals the "relaive degree of parnoia" remains the same i.e (x,-x,-x) is still same as ((x+a),-(x+a),-(x+a)). Those are functionally equivalent since the relative order of nodes remain the same according to Korf paper. Paranoid_sum=a-(b+c) is one magnitude less than paranoid_max=a-max(b,c) if we assume a,b,c are roughly of the same magnitude. So to have a comparison it may be appropriate to define paranoid_sum = a-(b+c)/2 instead. I think that a - max(b,c) is more suited to games where there is no prize for second place, and a - (b+c) when 2nd place matters. Say a is far ahead and guranteed first place, the paranoic scores when b is the root player will be paranoid_sum = b - (MAX_SCORE + c) and paranoid_max= b - max(MAX_SCORE + c) = b - MAX_SCORE, so clearly paranoid_max to not compare its score against c sorta of not caring for second place ??
In multi-player games the eval is highly effected by the higher-order strategy of alliance formation. In a multi-player Chess game each player has two assets: its material, and the right to move. Even if player A has more material than B and C together, he would still lose if B and C teamed up against him, because B and C can make two moves per turn-cycle, which is a devastating advantage. So alliances are a domininant factor.
Yes, I think that if two week humans make an alliance against a strong computer always, then there is pretty much nothing we can do about it! That takes away some of the fun from multi-player games I think. But if the humans are "rational" and make and break alliances with whomever is weaker/stronger then we have a chance to be smart by changing the social orientation (SO) as the game goes on. For linear SOs, a dynamic matrix representing the SO of each player has been successfully used. Other methods may be used for paranoid_max and others that can not be represented by matrix.
Team up against the weakest as long as the others are balanced might be a better strategy (a cheap way to up your chances from 33% to 50%). And because engagement in Chess is likely to weaken both sides, even unbalanced strongest might cooperate such that the losses of their skirmish with the weakest benefits the middle one, because the strongest takes the unavoidable losses.
It makes sense. I haven't yet implemented a way to handle when one player gets taken but that is definitely the incentive i.e upping your chance to 50%.