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Very nice analysis!

Posted By: Nack Ballard
Date: Friday, 15 July 2011, at 12:28 a.m.

In Response To: Very nice analysis! (Casper van der Tak)

How important is the 3 duplication in Timothy's position?

I intentionally didn't mention the 3 duplication because it applies to all of the positions I diagrammed. But I'll still answer your question. :)

To determine how important 3 duplication is specifically in Tim's position, compare the eval or rollout result if you have the time) of 61P-61P-63S-63R to that of the average of 61P-61P-63S-62R and 61P-61P-63S-64R (not just to one of them; you want to factor out the additional value of 1 race pip). This methodology is never 100% accurate because the playability of every roll has an influence, but it is sound enough to give you a very good idea. Here are Snowie evals:

    61P-61P-63S-62R –.174
    61P-61P-63S-63R –.130
    61P-61P-63S-64R –.157

    61P-61P-63S-63H –.182 (for reference)

As you can see, 63R shows a noticeable hiccup. If the 3 duplication didn't exist, the 63R equity would be about –.165, halfway between the two equities flanking it. That suggests that the 3 duplication is worth about .035.

[On the side, I just did similar flank-comparisons for the sparser 21U-6xR, 53S-6xR, 61P-21U-6xR and 61P-53S-6xR (three evals for each of four positions). The 3 duplications are worth .019, .023, .023, and .016, respectively. Evidently, the 3 duplication is worth about .015 more in Tim's position (I have a hunch why, but it's beyond the scope of this post), but that's not much; in a comparison to other positions in which 3 duplication is also a factor, other effects are much more important.]

IMO, too many analysts latch on to one factor and conclude, for example, "Blue should run because of 3 duplication." This aspect is valid, but profoundly incomplete. It seems to imply that if the 3 duplication didn't exist, hitting would be best, which isn't true. Worse, without an appropriate frame of reference, readers might then blunder by running in the second roll position 32S-63 (or 54) or 43Z-63 (or 54), for example. That is why I chose a set of basic 3-duplication positions from which to draw a basis of comparison.

Nack

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