David’s succinct explanation says it all:
The fundamental in these positions is to keep as many points as you can as long as you can. You win by keeping your opponent dancing, not be bearing off quickly or getting hit to try to hit again on the way around. You have five points. Can you keep five? Yes. Keep them. 6-4, 6-2. If you can't keep five, then look around for the best play which keeps four. There are exceptions to this rule, especially with doublets. But, this is the fundamental.
In order to better understand this decision, I went through all 21 subsequent rolls under the assumption that White would fan. The results are summarized in the table below. Creating the table was a very worthwhile experience.
Some points emerged during its preparation:
- If Blue rips two off on this turn, as in the right-hand diagram, the gap on his 4pt causes problems when he rolls a 4 next turn. Except for 64, all his 4s are air balls, by which I mean that he cannot bear off any checkers. One reason for this is that 4 can be utilized to remake the 2pt that Blue gratuitously abandoned on the prior turn. When he rolls a 4, he has to switch to the 2pt by moving both checkers off the 6pt.
- Holding the block as long as possible is one of the most important aspects of play. In order to win, Blue needs White to stay out not just for this turn, but for three or four turns running. Bearing off an extra checker only gets you half a turn, so it is not the top priority.
- Opening a lower point now probably won’t hurt much on this turn. Downstream, however, it can lead to a much faster board collapse, with many more blots.
- Blots matter. Not on this turn, perhaps, but later on, for sure. By the time Blue gets down to 3 or 4 rolls left, he cannot afford to be hit. At that point, even when White enters, Blue is just one or two sets from victory. Being hit then, means losing that equity. An orderly approach, which avoids opening low points early, reduces the chance that a late blot will scuttle Blue’s chances.
- The same orderly approach also means that by the time White does enter, Blue will have a speed board.
- At no time does the bot opt to leave two blots in this position.
- When there is a tradeoff between bearing off, and keeping a made point, bearing off often takes a back seat. When the block can be held, however, bearing off generally takes precedence over safety. Leaving a blot is fine in those cases. One place you can see this is in the left half of the table when Blue rolls a 2. On any roll of a 2, Blue has the choice of safe play, but only at the expense of bearing off one less checker. The strength of his block is the same either way. XG rips the maximum every time.
The averages at the bottom of the table tell a story all by themselves. Lifting the 6pt now, instead of ripping two checkers, means that after his next turn Blue will have an average of 0.6 extra made points and half as many blots.
If you have the inclination, I recommend setting up the two positions above, and clicking through the dice rolls. Run a quick eval, and see which plays were rejected. That’s every bit as informative as seeing the top plays below.
Mike |