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Retrograde Backgammon – Puzzle #2 Solution

Posted By: Taper_Mike
Date: Wednesday, 11 November 2015, at 6:49 p.m.

In Response To: Retrograde Backgammon – Puzzle #2 Solution (Taper_Mike)

Puzzle 2.

Find a perfectly played, 5-move sequence leading to this position. Blue is on roll. The cube is centered.

 White is Player 2 score: 0 pip: 159 Unlimited Game pip: 142 score: 0 Blue is Player 1
XGID=aB-B-aC-B---dD---d-e----B-:0:0:1:00:0:0:0:0:10
Blue on roll, cube action?

Nack alerted me that my fourth solution, 52S-32N-F-55A-5-C, is not perfectly played! It is based on an opening 52S = 24/22 13/8, followed by 32N = 13/11 6/3*. So far, so good.

 White is Player 2 score: 0 pip: 160 Unlimited GameJacoby Beaver pip: 167 score: 0 Blue is Player 1
XGID=-a-a--E-C---dE---d-e----B-:0:0:1:32:0:0:3:0:10
Blue to play 32

1.Book113/11 6/3* eq: -0.1258
 Player:Opponent: 47.46% (G:13.07% B:0.56%)52.54% (G:16.49% B:1.09%) Conf.: ±0.0050 (-0.1308...-0.1209) - [98.9%]
2.Book124/21 13/11eq: -0.1338 (-0.0079)
 Player:Opponent: 46.99% (G:12.24% B:0.50%)53.01% (G:15.37% B:0.73%) Conf.: ±0.0047 (-0.1385...-0.1290) - [1.1%]
3.Book26/3* 3/1* eq: -0.1448 (-0.0190)
 Player:Opponent: 46.58% (G:13.01% B:0.40%)53.42% (G:15.59% B:0.80%) Conf.: ±0.0027 (-0.1475...-0.1421) - [0.0%]

1 Generated by Steven Carey on 4/7/2013 using eXtreme Gammon 2.10
15552 Games rolled with Variance Reduction.
Dice Seed: 32325706
Moves: 3-ply, cube decisions: XG Roller

2 Generated by Steven Carey on 3/31/2013 using eXtreme Gammon 2.10
46656 Games rolled with Variance Reduction.
Dice Seed: 90680458
Moves: 3-ply, cube decisions: XG Roller

eXtreme Gammon Version: 2.10

As is shown in the rollout above, 32N = 13/11 6/3* is the best play. This move can also be nactated as 32H, so 52S-32H-F-55A-5-C is another way to nactate the sequence.

After a fan, 55 is a problem. The move in my solution, 55A = 11/1, 8/3, 6/1, is not perfect. As Nack reported, it trails by around 0.01. Here is my rollout.

 White is Player 2 score: 0 pip: 163 Unlimited Game pip: 162 score: 0 Blue is Player 1
Blue to play 55

1.Rollout113/3 6/1*(2) eq: +0.7409
 Player:Opponent: 63.68% (G:34.70% B:0.53%)36.32% (G:9.07% B:0.45%) Conf.: ±0.0030 (+0.7379...+0.7439) - [100.0%]Duration: 1 hour 49 minutes
2.Rollout111/1* 8/3 6/1eq: +0.7296 (-0.0113)
 Player:Opponent: 63.57% (G:34.42% B:0.52%)36.43% (G:8.97% B:0.43%) Conf.: ±0.0030 (+0.7266...+0.7327) - [0.0%]Duration: 1 hour 42 minutes

1 31104 Games rolled with Variance Reduction.
Dice Seed: 59637544
Moves: 3-ply, cube decisions: XG Roller

 Rollout by Taper_Mike 2015-Nov-11 eXtreme Gammon Version: 2.10.199.2658 52S-32H-F-55-n-tm.xgp n[I A11] "<=31 n[I A2.5] "&e

eXtreme Gammon Version: 2.10

In addition to identifying this imperfect 55 above, Nack also discovered another solution that was perfect. It is very similar to the ones detailed in the preceding post. Instead of entering only one checker on the third roll, it enters two:

51S-41K-53-55J-F

Mike

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