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Is chess fundamentally harder to "effectively" solve than Go?
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[QUOTE="PAllen, post: 6852414, member: 275028"] Tablebase is a precisely defined term in game theory, and that is not what it is. In some sense, access to tree is needed to construct it (but shortcuts are possible, so less than the whole tree is needed; also, retrograde analysis from terminal positions is used in contruction while a game tree typically uses forward analysis). In chess, it is a list of (position descriptor, resolution). Resolution in Nalimov tables is simply (white wins in x moves with mutual perfect play, draw, or black wins in x move with mutual perfect play). Its size is exceedingly small compared to a complete game tree. For Go, one would typically use some choice of "area rules" e.g. Chinese, because these require no knowledge of game history (i.e. captured stones) to score a position (relying on the fact that there are theorems characterizing the scoring difference between Japanese rules and Chinese assuming no handicap - thus the Japanese case could be reconstructed without recourse to game history for a normal, non-handicap game). Note that all the landmark AIs like alphago, alphazero etc. used Chinese rules. Then, a table base is a list of (position, final "black score - white score" with mutual perfect play). You need only one table for all komi, since that komi just means subtracting the komi from the recorded difference. I don't think this is a meaningful definition. Consider, for a simple specific, the case of a position K+P vs K. Consider a case where the side with P wins. Then, a huge part of the drawn result tree is nonsense where both kings meander away from the pawn for no reason, potentially resulting in draws. This has nothing to do with human or machine play. Instead, drawish is a characteristic of human (or machine) player knowledge - how reliably a skilled player can find the drawing moves in a theoretically drawn position. If it is easy/reliable, then the position is drawish. Note that this is function of human (or specific program type) playing "algorithm". So far, I agree completely. A key point is the assumption of engine equivalence. Here is where I disagree substantially. The issue is that the engines position scoring (or win probability scoring in the case of neural nets) causes the engine to effectively seek positions in which broadly similar - but not identical - engines are likely to err. As a result, the likely result is that the winning engine would typically have significant winning advantage over some other engines (e.g. 60/40), while tablebase player would be e.g. 52/48 over all the other engines. Then, such an engine would easily win the tournament over the table base player. The only way out of this for the tablebase player is to also include a model of imperfect player error profile. Note, that in chess analysis, one often speaks of a position "pressuring" the opponent, even if drawn. This simply means that an opponent of some type (human, engine category) is more likely to err. And, as I keep repeating, this is not derivable from the rules of chess. Instead, it requires modeling classes of imperfect opponent algorithms. For Go, none of this problem exists. A tablebase player would win 100% of the time against any existing AI, while the AIs win 100% against humans. [/QUOTE]
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