tygxc wrote:
@12742
"blame tromp's data" ++ No, I do not blame the data.
Tromp found (4.82 +- 0.03) * 10^44 legal positions, but as the 3 random samples show the vast majority of those legal positions have multiple promotions from both sides and thus cannot result from optimal play by both sides
Right. Silly me, I was thinking promotions to queens and knights are a perfectly normal aspect of chess (with large numbers of multiple promotions in the tiny less than 10^7 games master chess dataset) and often optimal (proponent ) or legal (opponent) regardless of any previous promotions. But I now see you have taken the tygxc-logical move to generalize bishops and rooks to queens and knights.
Masterful!
@tygxc would do well to discuss things with one of the best AIs (Claude 3.5 Sonnet, ChatGPT 4o / Bing AI Chat) to clarify some points, since he does not believe humans who have more knowledge than him. Remember, these models are trained on a large subset of all human knowledge. While they are not 100% reliable supplementary questions usually resolve any initial inaccuracies (for full disclosure, there were examples of this in the raw output for this query). Don't use AIs as encyclopedias, use them for intellectual stimulation!
Here is the sort of thing I mean (edited for compactness and quality)
Me >: Hallo Claude. Is it necessary for a weak solution of a game to deal with every legal opponent move or just some subset of these?
Claude >: A weak solution of a game refers to a strategy that guarantees a player the best possible outcome
A weak solution must deal with every legal opponent move, not just a subset. Here's why:
1. Completeness requirement: The weak solution must provide a strategy that works against any possible sequence of opponent moves, as long as the player following the solution plays optimally. If it only covered a subset of opponent moves, it wouldn't be a true solution.
2.Tree structure: Conceptually, a weak solution can be thought of as a decision tree that covers all possible game paths resulting from optimal play. Each node in this tree must account for all legal opponent moves at that point.
3. It's important to note that while a weak solution must account for all legal opponent moves, it doesn't necessarily provide the optimal counter for every possible game state - only those that can arise from optimal play by both sides. This is what makes it "weak" compared to a strong solution, which would provide optimal moves for every possible game state, including those arising from suboptimal play.
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The point at the end is an interesting nicety. A drawing strategy in a weak solution does not have to play accurately against bad opponent moves because it only has the objective of achieving a draw. For example, the opponent can blunder mate in 1 and the strategy can just play to achieve a draw and still meet the definition. But to have no way of finding out what move to play is NOT compatible with the definition.