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BGonline.org Forums
Inconceivable!
Posted By: Nack Ballard In Response To: Inconceivable! (happyjuggler0)
Date: Sunday, 25 July 2010, at 2:05 a.m.
Well, it is clear if both players play as well as the bot does. But with only a 0.006 difference, +/-0.002, then it is not inconceivable that the practical best play might be splitting.
Right, it is not inconceivable. There are several factors that might tip the scale, though each by itself is fairly unlikely. The least unlikely of these, IMO, is that bots do not yet play well enough (or there is a systemic bug that rears its head) and some results will be overturned in the future. It should be noted, though that GnuBG, while only 5k, is g[S D10.4]. That is, XG 4-ply's closer result of g[S D6] 32k is not the only one we see.
The next most likely possible-overturn factor is that D leads to more complex games on average; against a weaker player some vig is regained in long term complications. (This is a counter-factor against stronger players.) However, in terms of leeway .006 at GG translates to about .009 for money. It is difficult to estimate the value of complexity.
Misresponse vig is another factor (for example, after 61P-54S, Opp might immediately hit with 62 or 53, an error at her GS score). I don't know which play induces greater misresponse, though, and the net difference is unlikely to exceed .002 in any case.
Complexity and misresponse (see the previous two paragraphs) are often confused. There is overlap, so for purposes of counting the effect of the very next roll/play should be excluded from the complexity factor.
As you say, variance is a wild card. It should be noted that +/- .002 CI for each play translates to about +/- .0028 for the margin between two plays. (There's a square route factor involved.) With rounding possibilities (as Miran mentioned), it might be as little as .0015*sqrt2 = .0021 or as much as .0025*sqrt2 = .0035. (It would be nice to be able to see the fourth decimal point.) Chances are only 1/15 or so, though, that it hits the extreme high end of the range. Say it's above average at .003; that would still mean 4 s.d. in the right direction (about 1/32000) in order for .006 to actually be zero (let alone cross over). That said, I suspect bots underestimate CIs/variance, so who knows.
As an example from a different opening, 52 at [money] is mildly better with splitting than coming down if memory serves, but if you think your opponent will misplay 21 41 and 51 in response then you don't want to split.
Whether anything like that is going on here or not I don't know, but it is food for thought.
Regarding your example: For opening 52, we have Snowie [S D6] 46k, GnuBG [S D15] 92k, XG3 [S D14] and XG4 [S D15]. Let's call agg [S D12].
Here are agg (bot aggregates) for the replies to opening 52D:
52D-21 [$ S57]
52D-41 [$ S46]
52D-51 [$ S41]Adding the splitting misreply errors of .057, .046 and .041, and dividing by 18 yields .008, which is less than the .012 gambited away. So, even if one is 100% certain that the opponent will actually make all three of these huge mistakes, that is insufficient justification by itself to play opening 52D. (Moreover, existing misreponses are empirically only 70% as large in EMG terms at GS/GG compared to money.)
I bring this final point up only to emphasize that misresponse vig is typically smaller than people imagine.
Nack
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