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Posted By: Taper_Mike
Date: Tuesday, 3 November 2015, at 10:21 p.m.

In Response To: Fewest-rolls Puzzle (Nack Ballard)

 White is Player 2 score: 0 pip: 160 Unlimited GameJacoby Beaver pip: 156 score: 0 Blue is Player 1
XGID=-b---BD-C---cDa--d-e--A-A-:0:0:1:00:0:0:3:0:10

Blue on roll

Eric asks, My DQ is when you approach a puzzle like this do you work from back to front or front to back?

I find these retrograde problems to be an interesting challenge. The requirement that solutions be optimal is means there is a lot of learning that goes on. As you try out possible moves, you get to look at a number of positions. You get a ton of practice making early-game checker plays.

I generally work these problems from both sides. It is almost always useful to picture the last move played. In every sequence, and especially in shorter sequences, it is also useful to imagine how the opening must have gone. I used both techniques in this position.

As I mentioned in the thread, I had discarded the obvious three-move solution because I thought that Blue had to be on-roll at the end. That led to a guess that the solution would be four or five moves. That also meant that most (or all) checkers would be moved only once. Each move had to take a checker to its final destination.

So the question arose about how the opponent got a checker on his 11pt. After some false starts, I concluded that it had probably been moved there on his first move. Right away, 62S became a prime candidate. Other 2s are too complicated.

21S would have meant moving a checker to the 23pt. Afterwards, that checker would need to be hit, and reentered on the 24pt. That is too much action for this short sequence. Blue cannot hit on the 23pt. Therefore, White would need move up from the 23pt before he was hit, either to his 20pt, or into the outer board. That's too many moves. For a similar reason, 32S and 52S became unlikely. Since 22 and 42 were not candidates, that left 62S. In the end, 62S became White's opening move in both of my solutions:

21\$-62S-22G-51Z
Turn Blue White
1 21\$ = 13/11, 6/5 62S = 24/18, 13/11
2 22G = 24/22, 11/7*/5 51Z = bar/24, 13/8
3 Blue on roll

62S-62X-F-21P-51Z
Turn White Blue
1 62S = 24/18, 13/11 62X = 24/22, 13/7*
2 F = fan 21P = 7/5, 6/5
3 51Z = bar/24, 13/8 Blue on roll

Another question I looked at was Blue's split. Besides 52S = 24/22, 13/8, there are not a lot of opening moves that leave a checker on the 22pt. Opening 32, for instance, is better played to 21pt. After a bit of fiddling, I determined that 52S was not going to work. That led to me try some hit-and-split plays. 62X = 24/22, 13/7* quickly became a prime candidate. My five-move solution uses it.

A third question I focused on was White's entering roll. It was clear that he had to split and get hit. His entering roll had to involve an ace that was played bar/24. The other number, therefore, was most likely a 2 or 5 that was played down from the midpoint. After trying out a few combinations, it became clear that 21 would never be played as 21Z = bar/24 13/11 in the short sequences I was seeking.

That meant that the entering roll was probably 51Z = bar/24 13/8. For that to be true, it also meant that Blue owned his 5pt at the time. Otherwise, the 5 of an entering 51, would be played bar/20. I concluded, therefore, that 51Z was probably White's last move in the sequence, and indeed, it was.

I have found that GnuBg works better for me than XG for these problems. I set GnuBg to human-vs-human play with manual dice. When I want to test a move, I copy the GnuBg ID and paste it into XG for an eval.

Mike

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