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41S-63R-63 and 51S-63R-53

Posted By: Nack Ballard
Date: Thursday, 19 November 2015, at 3:07 p.m.

In Response To: Two Puzzles -- SOLUTIONS (Nack Ballard)





White is Player 2

score: 0
pip: 158
Unlimited Game
Jacoby Beaver
pip: 162
score: 0

Blue is Player 1
XGID=-a----E-CAa-eD---c-e---AA-:0:0:1:63:0:0:3:0:10

41S-63R-63


1.Rollout19/3 6/3eq: +0.068
Player:
Opponent:
50.77% (G:15.08% B:0.49%)
49.23% (G:10.55% B:0.46%)
Conf.: กำ 0.004 (+0.064...+0.071) - [56.9%]
Duration: 9 hours 41 minutes
2.Rollout124/18 13/10* eq: +0.067 (0.000)
Player:
Opponent:
51.66% (G:14.47% B:0.68%)
48.34% (G:13.41% B:0.68%)
Conf.: กำ 0.004 (+0.063...+0.071) - [43.1%]
Duration: 11 hours 48 minutes
 
1 20736 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller




White is Player 2

score: 0
pip: 158
Unlimited Game
Jacoby Beaver
pip: 161
score: 0

Blue is Player 1
XGID=-a----E-D-a-eD---c-e---AA-:0:0:1:53:0:0:3:0:10

51S-63R-53


1.Rollout123/18 13/10* eq: +0.120
Player:
Opponent:
52.93% (G:13.94% B:0.67%)
47.07% (G:12.12% B:0.51%)
Conf.: กำ 0.005 (+0.114...+0.125) - [66.2%]
Duration: 10 hours 27 minutes
2.Rollout113/10* 6/1* eq: +0.118 (-0.002)
Player:
Opponent:
52.23% (G:17.40% B:0.52%)
47.77% (G:12.62% B:0.64%)
Conf.: กำ 0.006 (+0.112...+0.124) - [33.8%]
Duration: 9 hours 48 minutes
3.Rollout213/8 13/10* eq: +0.100 (-0.020)
Player:
Opponent:
51.90% (G:15.52% B:0.68%)
48.10% (G:11.50% B:0.53%)
Conf.: กำ 0.007 (+0.092...+0.107) - [0.0%]
Duration: 4 hours 14 minutes
4.Rollout28/3 6/3eq: +0.067 (-0.053)
Player:
Opponent:
50.77% (G:15.11% B:0.49%)
49.23% (G:10.57% B:0.45%)
Conf.: กำ 0.007 (+0.060...+0.074) - [0.0%]
Duration: 3 hours 54 minutes
 
1 10368 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller

2 5184 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
 

There are two rollouts above (which will appear side by side, if you widen your window enough). If Blue makes his 3pt with 63 in the first position (left-hand), he reaches the identical position that he reaches if he makes his 3pt with 53 in the second (right-hand) position.

If Blue hits, the positions diverge. It is for this reason that on the one hand P (making the 3pt) is tied with or slightly better than X (hit and split) in the first position, while on the other hand X is much better than P in the second position.

I've isolated the key difference in the third position below. Blue has a lone ace to play, and is only permitted to choose between 24/23 and 9/8.

If you can grasp why 9/8 is .053 better than 24/23, your intuition will be in line with Blue being willing to make the 3pt in the first position but being very unwilling to make the 3pt in the second position.

Nack





White is Player 2

score: 0
pip: 168
Unlimited Game
Jacoby Beaver
pip: 154
score: 0

Blue is Player 1
XGID=aa----E-CAA-eC---cAe----A-:0:0:1:00:0:0:3:0:10

Blue to play a lone ace


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