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Variant (1 pip different)

Posted By: Nack Ballard
Date: Monday, 31 August 2015, at 4:40 a.m.

In Response To: Variant (1 pip different) (neilkaz)

Does the weakening of the joker 22 mean this much? Or is there more to it than that?

Using XGR++ eval (close enough), double 2s gives White an equity of .908 in the original position, vs .282 in the variant position, thereby yielding an approximation of .656 / 36 = .018 for the value of double 2s when comparing the placement of the spare (6pt vs 7pt).

Subtracting that .018 from the (variant) rollout margin of .017 suggests that the plays are roughly equal if double 2s is removed the equation.

That still leaves the .037 margin that favors the anchoring play in the original rollout. Note, though, the rollout is only 1k. That is one reason I like to roll out all candidates to at least 5k -- to know more reliably what difference(s) is/are to be reconciled.

On average, White's entering numbers (even excluding double 2s) play slightly better in the original position. (That's based on a quick appraisal -- I'm too lazy to calculate.) However, that is mostly symptomatic of my observation in the next paragraph.

I believe the lion's share of the reconciliation is the value of White's spare/builder being inside, which gives her greater threats next turn (after she enters, either not hitting or hitting with the outside builder).

Note, too, that in concert, in the variant position White is able to play neither a 5 nor a 6 (instead of just not a 5) smoothly from the midpoint to a stripped point. This materially matters only if White POH, not if she anchors.

One way to test my hypothesis is to place White's spares on her 7pt and 5pt (or 8pt and 5pt) and roll out that position. In this way, White has an inside spare but no double 2s joker. If anchoring can hold its own (despite the lack of a 22 retaliation when making the 5pt), I consider that evidence that the hypothesis is correct -- because a 5pt spare is weaker than a 6pt spare (the degradation is often as much as .02 to .03).


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