The availability of the cube has the potential to shift optimal checker play away from the raw cubeless optimal play in certain positions where competing strategies involve varying levels of potential cube efficiency. The modern bots are able to naturally exploit these factors in evaluating optimal checker play for both money and matches. ExtremeGammon is exceptional in this regard. The following example attempts to illustrate the issues. Consider position 5-15 from Robertie’s excellent work “Modern Backgammon”, with White to play 11, where Black owns the cube:
XG gives the following results which are consistent with Robertie’s analysis:
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| XGID=-EBc-BB-BB---a----abbbbb--:1:-1:1:11:0:0:0:0:10 | ||||||||||||||||
 to play 11 | ||||||||||||||||
| 1. | Rollout1 | 9/8(2) 6/5(2) | eq: +0.264 | |||
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| 2. | Rollout1 | 9/7(2) | eq: +0.212 (-0.052) | |||
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| 3. | Rollout1 | 9/8 9/6 | eq: +0.202 (-0.062) | |||
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| 1 10368 Games rolled with Variance Reduction. Moves and cube decisions: 2 ply | ||||||
eXtreme Gammon Version: 1.14
Out of curiosity, I also had XG roll out the identical position but with White owning the cube and the cube in the middle with somewhat surprising results (see below). Where White has access to the cube the smoother 9/7(2) is now slightly preferable (by about 0.010 ppg) to the stackier 9/8(2), 6/5(2) despite the fact that the latter play is clearly superior in terms of its raw cubeless equity (about 0.045 ppg better)
Cube owned by White:
 is Player 2score: 0 pip: 125 | ||||||||||||||||
 | Money session | |||||||||||||||
 | pip: 65 score: 0 is Player 1 | |||||||||||||||
| XGID=-EBc-BB-BB---a----abbbbb--:1:1:1:11:0:0:0:0:10 | ||||||||||||||||
| to play 11 | ||||||||||||||||
| 1. | Rollout1 | 9/7(2) | eq: +0.540 | |||
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| 2. | Rollout1 | 9/8 9/6 | eq: +0.530 (-0.010) | |||
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| 3. | Rollout1 | 9/8(2) 6/5(2) | eq: +0.528 (-0.012) | |||
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| 1 10368 Games rolled with Variance Reduction. Moves and cube decisions: 2 ply | ||||||
eXtreme Gammon Version: 1.14
Cube in the middle:
| is Player 2 score: 0 pip: 125 | ||||||||||||||||
| |  | Money session | ||||||||||||||
| pip: 65 score: 0 is Player 1 | ||||||||||||||||
| XGID=-EBc-BB-BB---a----abbbbb--:0:0:1:11:0:0:0:0:10 | ||||||||||||||||
| to play 11 | ||||||||||||||||
| 1. | Rollout1 | 9/7(2) | eq: +0.501 | |||
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| 2. | Rollout1 | 9/8(2) 6/5(2) | eq: +0.490 (-0.010) | |||
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| 3. | Rollout1 | 9/8 9/6 | eq: +0.485 (-0.015) | |||
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| 1 10368 Games rolled with Variance Reduction. Moves and cube decisions: 2 ply | ||||||
eXtreme Gammon Version: 1.14
The only logical reason for this shift in order of preference that I can see is related to the potential efficiency of future doubles by White. In the original position, where Black owns the cube, White’s potential cube efficiency is not significantly influential, so optimal play would normally be identical to cubeless optimal play unless Black is close to doubling and there is some opportunity for White to productively limit Black’s cube efficiency. Analysis of cube-efficiency for the three plays supports this rationale. White’s cube efficiency is about 80% with the smoother plays 9/7(2) and 9/8, 9/6, but only about 60% with the stacky 9/8(2), 6/5(2). For all three plays, Black’s cube efficiency is broadly consistent at about 40% (probably fairly typical of anchor games where a hit normally results in significant market loss). I wondered why the stacky play is less efficient. I believe the main reason is that in this position White cannot normally double until he has cleared the first stack leaving a single point and perhaps an additional blot in front of Black’s back men. As a double at this point would normally miss its market by a mile, the cube utility is significantly reduced. Conversely, with the smoother plays, White is often able to reach efficient doubling positions where there remain two points close to Black's back men with or without an additional blot.
There appear to be several other positions in “Modern Backgammon” and “New Ideas in Backgammon” which demonstrate this phenomenon. It should be noted that when these texts were written the available bots generally evaluated optimal checker play from cubeless rather than transformed cubeful equities. However, where errors occur, with very few exceptions, they are not likely to exceed 0.025 ppg from my estimation.