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More data to support making the 2 pt with opening 64
Posted By: David Rockwell In Response To: More data to support making the 2 pt with opening 64 (Tom Keith)
Date: Tuesday, 9 February 2010, at 4:46 p.m.
Let's keep in mind that the significance of a margin relates to the size and depth of the rollout. The one at the top of this post was very large and deep.
Your suggestion has not been done. Similar research has done. A couple of things may be stated.
1. All one ply errors and errors of odd ply reduce equity.
2. All even ply errors increase equity.
3. systemic errors are more likely to occur at low ply. Positions diverge as ply increases.
In the work I have done, most (that means > 50%) of the cumulative net error in play can be found in the 1st ply. If you visualize the sequence implied by the three points above it is alternating decreasing. If you can identify the mistakes made in the 1st ply, there's a good chance you have captured most (that means > 50%) of the picture. There's no reason to go 10 ply deep. And, in fact there isn't good reason to go 2 ply deep. 1 ply can be worthwhile.
I have investigated the errors in play for the 1st ply on GNU for the three plays 64P, 64S and 64R. 64S has the fewest (measured by equity) with 64P close behind. 64R lost more equity than the other two due to errors in play. So, for GNU, the rollout appears to be close to accurate through the 1st ply for S & P, but overstates the relative value of R by something like .002 (going by memory).
To put some numbers around the analysis, the largest error I have ever seen in the 1st ply is something on the order of .005. The mode is .000. And, the mean or median is around .001.
Let's take a fictional example. Assume that P has errors of .002 in the 1st ply while S has errors of .000. Since systemic errors become less likely as ply increases, the absolute value of the difference in errors is likely to decline. (Here, please understand that by likely, I mean something like 95%+. It would be very odd to see otherwise out of the opening.) It is difficult to construct a fictional sequence of errors that makes any sense at all that adds to .004 given the 1st ply errors listed above. It would have to look something like this.
P / .002 .000 .001 .000 .0005 .000
S / .000 -.001 .000 -.0005 .000 -.0025
The sequence would have to break in just the right way at every turn. The bot would have to make errors only for the opener on P every time and make errors only for the responder for S. That just isn't going to happen very often. it is far more likely that errors will be largely offsetting at later plys.
If errors in play are causing opening rollout inaccuracies, they will be found in the 1st few plys. If 64P is overturned at some point by S or R, it will likely happen because several of the immediate responses to 64P are being played wrong by the bot.
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