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Retro Logic and Solution

Posted By: Taper_Mike
Date: Tuesday, 1 December 2015, at 12:16 a.m.

In Response To: 1) Blue to play 32, and 2) How did we get here (Taper_Mike)





White is Player 2

score: 0
pip: 160
Unlimited Game
Jacoby Beaver
pip: 161
score: 0

Blue is Player 1
XGID=-b----E-C-B-dC---bbe----B-:0:0:1:32:0:0:3:0:10
Blue to play 32

I’ve got a rollout cooking for this. It looks pretty close.

In the meantime, let me congratulate Roberto for a job well done! His solution of the retro puzzle is correct. This puzzle is a little tricky because so few pips have been moved. In two turns, White has moved only 7 pips, and Blue, a net of 6.

Simple arithmetic, together with the stipulation that the game has been perfectly played up to this point, make is clear that Blue has been hit. Otherwise, he can only have played back-to-back 21s. No other pair of rolls adds up to 6 pips. Since Blue moved first, he would have had to play 21D = 13/10 on the opening roll, a play that is plainly less than perfect.

So Blue got hit, and the most likely location is the 18pt. That suggests an opening roll of 63S = 24/18 13/10.

Next, we need White to hit. The trap is to assume he hits with a 6. If you try that, White will have only 1 pip left to play in two moves! So let White hit with an ace, and look around for the other number. If we give White a 21 on this turn, then he will have 4 pips leftover for the next turn. If you give him a 31 on this turn, there will be only 3 pips leftover. No other rolls allow White to remain at 7 pips for two moves.

Now, 31 cannot be right. After 63S on the opening move, 31 is best played by making the 5pt. So lets try 21H = 13/11 8/7*. This leads to the position below.





White is Player 2

score: 0
pip: 164
Unlimited Game
Jacoby Beaver
pip: 165
score: 0

Blue is Player 1
XGID=-b----E-C-A-dDa--bae----AA:0:0:1:31:0:0:3:0:10
Blue to play 31

Things are looking good. If we give Blue a 31, he will arrive at precisely the position we are looking for on his side of the board. 31Z = bar/24 13/10, which makes the 10pt, is his best play.

So the big question is whether White should use a 31 to make his bar point. If so, then we have our solution.





White is Player 2

score: 0
pip: 164
Unlimited Game
Jacoby Beaver
pip: 161
score: 0

Blue is Player 1
XGID=-b----E-C-B-dCa--bae----B-:0:0:-1:31:0:0:3:0:10
White to play 31

1.XG Roller++11/7eq: -0.058
Player:
Opponent:		48.59% (G:13.21% B:0.57%)
51.41% (G:14.89% B:0.76%)
2.XG Roller++8/5 6/5eq: -0.066 (-0.008)
Player:
Opponent:		48.44% (G:14.69% B:0.67%)
51.56% (G:16.33% B:1.24%)
3.XG Roller++13/10 8/7eq: -0.173 (-0.115)
Player:
Opponent:		46.09% (G:13.34% B:0.62%)
53.91% (G:17.47% B:1.28%)
4.XG Roller++13/10 11/10eq: -0.185 (-0.126)
Player:
Opponent:		45.52% (G:12.69% B:0.58%)
54.48% (G:16.38% B:1.05%)
5.XG Roller++8/7 8/5eq: -0.185 (-0.127)
Player:
Opponent:		45.93% (G:12.78% B:0.56%)
54.07% (G:17.09% B:1.20%)
6.XG Roller++24/21 8/7eq: -0.224 (-0.166)
Player:
Opponent:		44.84% (G:11.81% B:0.56%)
55.16% (G:17.05% B:0.95%)

eXtreme Gammon Version: 2.10

It's close, but D = 11/7 is right!

The final sequence, including the 32 Blue has to play on the fifth roll, is:

63S-21H-31Z-31D-32

The third move, 31Z, and the fourth, 31D, can both be nactated in the P (Point) family. Thus, the exact same moves can be nactated like this:

63S-21H-31P-31P-32

Mike

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