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BGonline.org Forums
Mochy's blunder 05
Posted By: Timothy Chow In Response To: Mochy's blunder 05 (Colin Owen)
Date: Saturday, 14 February 2015, at 12:23 a.m.
Colin Owen wrote:
but does every bg position have an explanation as to the best play?
This depends on what you mean by an "explanation."
In theory there is always the trivial "explanation" that if there a cap on the cube value then the minimax theorem guarantees the existence of an equilibrium strategy, and a brute-force computation (that is never carried out in practice except for non-contact races) shows that play X is an equilibrium play. This is not what any sane person would call an "explanation" that play X is the best play, so your question might be rephrased, is there always an explanation other than this trivial one?
At the other extreme, you might say that an "explanation" is any vaguely plausible argument whose conclusion is "play X is the best play." This might sound silly, but it's what passes for an "explanation" the vast majority of the time. A person sees that the computer plays X, invents a vaguely plausible argument whose conclusion is, "play X is best," and calls that an "explanation." Explanations of this type also always exist. In particular, you can take any play, regardless of whether it's actually best, and "explain" why it's best. You can see this phenomenon in action whenever a bot verdict gets overturned. People confidently provide explanations of why the original bot play is best, and then when the verdict is overturned, without missing a beat, they come up with explanations of why the new play is best.
Although the above discussion might lead one to be skeptical about the existence of meaningful explanations in most cases, I think that the opposite is true. In virtually any position, you can generate vaguely plausible arguments for all the candidate plays, and then declare that the factors in favor of play X outweigh the factors in favor of the other plays. Implicitly, what you're doing is using your judgment and experience to assign weights to various factors, and then picking the play with the highest weight. Bots do this explicitly whereas humans assign explicit numbers for only a small number of factors (wins, gammons, shots, etc.), but the principle is the same. This, I believe, counts as an explanation as long as the weights are approximately correct and therefore yield the right verdict most of the time.
For example, let's consider a position in which you're tempted to say that the "explanation" is that making the 5pt is right because it's right. If phrased in exactly this way, and taken at face value, it's not really an explanation, but I would claim that implicitly, what is being asserted is this: Making the 5pt is a strong play in most positions because it is a permanent asset and is often a key part of a strong board and/or prime; in the present position, the arguments in favor of other plays do not outweigh the merits of making the 5pt. This is closer to being a real explanation; it would be even closer if one were to flesh out exactly what the merits of the other plays are, and assign weights to them in a way that usually arrives at the right answer. I claim that fleshing out the statement in this way can almost always be done. One standard tool is to modify the position until some other play comes out on top, thereby giving you some sense of how much weight other factors carry.
The more you attempt to construct explanations in this fashion, and adjust your weights of various factors, the more you will learn and the better you will play. So not only is there almost always an explanation, but seeking such an explanation, and testing whether your judgment of the various factors is accurate, rather than just being satisfied with your current set of weights because they happened to deliver the right verdict in a particular instance, is the best way to improve.
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