The only surprise for me in this set of rollouts is that here the small split is (nearly) as good as the big split.
Here are a couple of tidbits that might help with reconciliation. First is that Z (reverse split) is often as good or better than S (Split) in early game positions. For example, consider these bot aggregate results of second roll positions, just isolating the "little" (Z) and "big" (S) split plays:
31P-32 [Z S5]
61P-32 [Z S2]
41S-32 [Z=S]
63S-32 [Z S1]
53P-43 [Z S14]
21S-43 [Z S22]
41S-43 [Z S11]
64P-43 [Z S6]
65R-43 [Z S18]
The above are all split choices when the numbers on the dice differ by 1. We have less experience when the dice numbers differ by 2, because with 42 we're usually making our 4pt (the point that in this case is already made). Granted a difference of 2 should make us lean towards the large split, but it shouldn't be a big adjustment.
That's one way to reconcile that playing Z and S with 42 should at least be close. Another (though minor) way to reconcile is that after 42P-42P-42Z (diagrammed below), Blue's 9pt blot cannot be hit with 53 (as it can when his 4pt is not blocking that indirect shot). It happens that White can point on the 3pt instead, but that still costs her an average equity of .060 / 18, which is between .003 and .004.
| |
|---|---|
| Position after 42P-42P-42Z, an error of only .003 | |
Nack