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Interpreting the rollouts

Posted By: Rick Janowski
Date: Wednesday, 24 July 2013, at 7:20 p.m.

In Response To: Interpreting the rollouts (Matt Cohn-Geier)

I concur with Matt’s derivation of the cube efficiency coefficients. To understand the relative weighting of cube efficiency in comparison to the gammon value effects, I considered the hypothetical case where each of the two play has the same x1 and x2 values; these being the average values of x1 = .674 and x2 = 0.841. Plugging these values, together with key data from Matt’s cubeless rollout into equations (8), (9) and (10) from Appendix B of my paper “Take-Points in Money Games” gives the following estimates of the margins in favour of 23/15 where relative cube-efficiency is effectively neutral:

Cube-Owned: margin = 0.029 (cf. 0.035 from rollout)

Cube-Unavailable: margin = 0.028 (cf. 0.045 from rollout)

Cube-Centred: margin = 0.033 (cf. 0.056 from rollout)

It is interesting to note that all these values are close to each other and also close to Matt’s cubeless rollout out margin of 0.034; though this is not a general tendency (usually cubeful margins are larger than cubeless margins).

Let’s consider the journey from DMP where both gammon and cube effects are zero to the actual position with both gammons and cube effects operative.

At DMP the margin for the running play 23/15 is about -0.027 (taking the win percentages from Matt’s cubeless rollout as a reasonable estimate). At the hypothetical intermediate point where both gammons and the cube are active but cube-efficiency effects are neutral the margin is about +0.033, a swing of about 0.060. At the final position, the margin is +0.056, an overall swing of about 0.083. Consequently, the ratio of gammon related effects to cube-efficiency related effects appears to be about 2.6 to 1.

I know many players find this approach tough to understand and perhaps over-elaborate and maybe boring too, but as far as I know there is no simple solution involving minimal effort, equivalent to just removing the outer packaging and microwaving for 30 seconds, unless the developers of the bots see some market in adding such a speciality to their menus.

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