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 Post subject: Re: Hoen Shinpo--Are historical handicap openings still good
Post #21 Posted: Tue Aug 17, 2021 5:12 am 
Lives with ko

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John Fairbairn wrote:
Ohashi says that, by the endgame, in modern komi go, if a player is leading by half a point, that may represent about 90% win rate. OK, but then he says, "If he loses 1 point, this will drop 80% and may become 10%." Forget the mix-up between % and percentage points - Japanese are as prone to grocer's mathematics as we are. But in my grocer's head, I say "losing a point in a half-point game means the lead switches" so I expect the win rate now to be 90% for the other guy. I assume Ohashi may have been a bit sloppy and omitted some detail about the 1-point mistake (sente/gote?), but I also assume that I have probably missed something. What?

I think what you are missing, actually you don't seem to be missing anything because it is a case that you are adding sente / gote considerations were there is none. The predicted points and point differences are estimates of the final result of the game. If you had a choice of gote moves x and y, where x > y, but choice y your point loss is approximately y - x. If you instead make a mistake of sente or gote, then the estimate is still of the final result of the game, but one one component of the point difference will be an estimate of the value of sente. Basically, you can speak of 1 point mistake without specifying sente or gote, it could have been that you played a move in sente that is just 1 point less than it could have been or you could have played a really big move in gote and this 1 point is the difference compared to playing some sente moves first.

The "point difference" and "percentages" are both estimates that are
1. affected by uncertainty
2. are mapping win-loss (or 0-1 result of the game) in two different ways that introduces ambiguity of presentation

The uncertainty is less toward the end of the game and in quiet positions, it also depends on the quality of the analysis. The percentages should get closer and closer to 0% or 100% as the game moves closer to the end, even if the game is quite close.

The ambiguity of mapping a win-loss result to a point difference can lead to values that are difficult to interpret. For example the swing between who wins a capturing race can be heavily biased in terms of points, as was mentioned by Ohashi, basically what does it really mean to say that the average of x and y is (x + y) / 2, and that this is the outcome of the game, if that is not a likely outcome of the game and only x or y are plausible outcomes. This is just a simple example to show that the point estimate can be almost meaningless.

We probably shouldn't discuss "percentages" or "point differences" very much when reviewing games. I sometimes feel one can just as well say "I checked it with a computer" or "computer approved" than say "a is 16.4% better than b" or "a is 3.4 pts better than b".

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