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Opening 32Z: reply errors

Posted By: Nack Ballard
Date: Friday, 8 January 2010, at 1:58 a.m.

In Response To: Opening 32Z: reply errors (Daniel Murphy)

I almost overlooked your reply. I hope you find mine before it drops the bottom of your first page.

Yes, that was clearer, thanks -- in other words, in part, in money games, future cube action affects the size of checker play errors, both the error one is contemplating making and the error one hopes one's opponent will make in reply -- an effect that cannot, obviously, be included in calculating the net effect of those errors at DMP. Right? There's the additional point that in a money game one might make a checker play error in order to induce a mistaken cube action, a strategy which, obviously, won't work at DMP.

Right. You probably summed up my point better than I did.

Let me just note that the 20:9 ratio (20/9=2.22) you found in comparing the loss caused by like errors in 2nd/3rd roll positions in money games and at DMP seems to be roughly in agreement with the answer found with other approaches to the question: what's the average money game worth? About 2.2 points. Or 2.3. Or so.

That occurred to me as well, though I wasn't sure of the soundness of the correlation. There's a couple of issues.

First, my comparison was done for second and third roll positions, most of which aren't very close to pending cubes. I'm not sure how much that matters.

What I did find is that the ratio of cubeful equities to cubeless equities averaged 1.4 (a touch higher with live cube, a little lower with Janowski), and straying surprisingly little from it. It can be seen, too, in the larger margins (say .03+) between plays and even in many smaller margins (I think you can see why it would vary more in close).

I spoke to Doug Zare a few years ago and he said that the above 1.4 ratio was news to him but it made sense it would be that way in the very early game and it would increase towards 2 in positions that are seeing cubes more regularly.

That brings us to the second issue. If (relatively) DMP is 9 and money is 20, why are GS and GG as high as 14? The only difference between DMP and GS/GG is one-sided gammons. Or looked at another way, if the cubeful:cubeless ratio is 1.4, then 20 / 1.4 is about 14, but that doesn't account for money having two-sided gammons. So, from those perspectives, shouldn't GS/GG be 11- or 12-ish?

Anyway, something to ponder.

Nack

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