Interplay between the Three and the Deuce

We have clarified the reasons that explain how 3-up and 3-down are equal, but 2-down is clearly superior to 2-up. Does that mean we can eliminate the two opening 32 plays that include playing 2-up?

We cannot remove them automatically without taking into account the dynamic interplay between the choice of the 3 and playing 2-up. However, we have also done that. (the details of which are beyond the scope of this article).

Our conclusion is that interplay narrows the gap, the inferiority of playing the 2-up remains the deciding factor. In the case of combining 3-up with 2-up, it is clearly insufficient to overcome 2-up's inferiority. However, in the case of 3-down with 2-up, we discovered enough positive interplay to cause 32-reverse-split to be a very close third choice. We have simplified the contest to the two finalists that play the proper deuce (2-down) from the cross-table of diagrams presented earlier (i.e., 1A and 1B, but not 1C and 1D):

And now let us analyze the interplay between our two finalists: The negative aspect of combining 3-down with 2-down (as shown in 1I) is that it reduces the flexible midpoint to three checkers. If a third midpoint checker is afterwards used to make a point or hit, then the midpoint would be stripped to two checkers; to use it yet again would either leave a blot, relinquish outfield control, or both. The positive aspect of combining 3-down with 2-down is the synergy between the 11pt and 10pt checkers. If White hits with a 9, Red has added 51 41 21 11 to his arsenal of numbers that hit back. If Red is not hit, 30 numbers will make a key point (7pt, 5pt or 4pt) on his next roll. The negative aspect outweighs the positive aspect by a tiny margin. However, for practical purposes, 32-down (1I) can be measured as tied with 32-split (1J). They are close enough that stylistic preference will often be the deciding issue.