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| 65R-55A-42Z: Blue to play 41, 51 or 61 | |
I looked into this trio (and related ones) several years ago; it's right to hit with 61 but not 51 or 41. As I recall, 41 evaluated as the closest decision and in a truncated rollout P (Point, 13/8) was better than X (hit-and-split, 6/2* 24/23) by around .04.
With 61 it is possible to hit and split, whereas with 51 you can only do one or the other. Whether hitting or not (though especially when hitting), the usual value of splitting is further enhanced because of the opponent's 9pt blot/builder. 61X (hit-and-split) is right by a mile, and 51S (Split, 24/23 13/8) is right by a mile; it's a big hit vs no-hit contrast.
One might expect 41 to be in the same camp as 61, but it actually falls on the other side of the fence. After 41X (as opposed to 61X), the 8pt blot is now hit with 53 and 44, a second checker is hit with 62, and there are other variations in which this blot needs looking after (unlike the safe 6pt spare, which is a much better checker on average). As a bonus, 41P's resulting 8pt+1pt combination work together better than 61P's resulting 7pt+1pt (which are six apart). These differences add up to a clear overturn; hence the quiet 41P is the prudent move.
When blitzing or otherwise putting two checkers in the air, one can afford to play much more loosely, because there is more time to consolidate when the blitz fails, and there is a higher probability of being missed wherever and outfield blots will be used to build inside points or be themselves covered.
By contrast, when putting only one checker in the air, it is more important to be aware of the existence and exact location of outfield blots/builders, not only one's own but also those of the opponent. For example, if you move White's 9pt blot to her 10pt (both less potent for building and less exposed), Blue's 61X is only a close winner, and (as I recall) if you safety White's blot altogether to her 8pt (or midpoint), Blue's 61P (making the 7pt) becomes the better play.
In other words, in the three positions diagrammed below (a tangential but equally fine trio), while Blue shouldn't hit with 41 or 51, his decision to hit with 61 is governed by the placement of White's blot/builder. The caption below each diagram clarifies.
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| 65R-55A-42Z-61: X is a standout | |
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| 65R-55A-32Z-61: X is a close winner | |
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| 65R-55A-52Z-61: P is best | |
Summary of captions:
65R-55A-42Z-61: X is a standout
65R-55A-32Z-61: X is a close winner
65R-55A-52Z-61: P is best
Nack