Your description of EVGOO is incorrect; you describe a Causal Decision Theory algorithm, but (assuming the opponent also knows your strategy ‘cause otherwise you’re cheating) what you want is LDT. (Assuming they only see each others’ policy for that game, so an agent acting as eg CDT is indistinguishable from real CDT, then LDT is optimal even against such fantastic pathological opponents as “Minimax if my opponent looks like it’s following the algorithm that you the reader are hoping is optimal, otherwise resign” (or, if they can see each others’ policy for the whole universe of agents you’re testing, then LDT at least gets the maximum aggregate score).)
I’ll note that CDT and FDT prescribe identical actions against Stockfish, which is the frame of mind I had when writing.
More to your point—I’m not sure that I am describing CDT: ”always choose the move that maximises your expected value (that is, p(win) + 0.5 * p(draw)), taking into account your opponent’s behaviour” sounds like a decision rule that necessitates a logical decision theory, rather than excluding it?
Your point about pathological robustness is valid but I’m not sure how much this matters in the setting of chess.
Lastly, if we’re using the formalisms of CDT or FDT or whatever, I think this question ceases to be particularly interesting, as these are logically omniscient formalisms—so I presume you have some point that I’m missing about logically relaxed variants thereof.
I agree none of this is relevant to anything, I was just looking for intrinsically interesting thoughts about optimal chess.
I thought at least CDT could be approximated pretty well with a bounded variant; causal reasoning is a normal thing to do. FDT is harder, but some humans seem to find it a useful perspective, so presumably you can have algorithms meaningfully closer or further, and that is a useful proxy for something. Actually never mind, I have no experience with the formalisms.
I guess “choose the move that maximises your expected value” is technically compatible with FDT, you’re right. It seems like the obvious way to describe what CDT does, and a really unnatural way to describe what FDT does, so I got confused.
Your description of EVGOO is incorrect; you describe a Causal Decision Theory algorithm, but (assuming the opponent also knows your strategy ‘cause otherwise you’re cheating) what you want is LDT.
(Assuming they only see each others’ policy for that game, so an agent acting as eg CDT is indistinguishable from real CDT, then LDT is optimal even against such fantastic pathological opponents as “Minimax if my opponent looks like it’s following the algorithm that you the reader are hoping is optimal, otherwise resign” (or, if they can see each others’ policy for the whole universe of agents you’re testing, then LDT at least gets the maximum aggregate score).)
I’ll note that CDT and FDT prescribe identical actions against Stockfish, which is the frame of mind I had when writing.
More to your point—I’m not sure that I am describing CDT:
”always choose the move that maximises your expected value (that is, p(win) + 0.5 * p(draw)), taking into account your opponent’s behaviour” sounds like a decision rule that necessitates a logical decision theory, rather than excluding it?
Your point about pathological robustness is valid but I’m not sure how much this matters in the setting of chess.
Lastly, if we’re using the formalisms of CDT or FDT or whatever, I think this question ceases to be particularly interesting, as these are logically omniscient formalisms—so I presume you have some point that I’m missing about logically relaxed variants thereof.
I agree none of this is relevant to anything, I was just looking for intrinsically interesting thoughts about optimal chess.
I thought at least CDT could be approximated pretty well with a bounded variant; causal reasoning is a normal thing to do. FDT is harder, but some humans seem to find it a useful perspective, so presumably you can have algorithms meaningfully closer or further, and that is a useful proxy for something.
Actually never mind, I have no experience with the formalisms.
I guess “choose the move that maximises your expected value” is technically compatible with FDT, you’re right.
It seems like the obvious way to describe what CDT does, and a really unnatural way to describe what FDT does, so I got confused.