[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums

Rollout Results Posted

Posted By: Paul Weaver
Date: Tuesday, 6 January 2015, at 12:37 a.m.

In Response To: Generalizing John's 31 Position (Paul Weaver)

The two positions below differ by only one pip. Blue should hit in one but not the other. Not all pips are created equally. The one-pip gain from White's 13pt to White's 12pt is bigger deal than 14pt to 13pt or 12pt to 11pt because the crossover is a big deal. I hope this is not confusing, but the point numbers in the diagrams are given from Blue's perspective. I have given the point numbers in this paragraph from White's perspective.

I worked all afternoon to derive a formula that shows the relationship between White's point number and Blue's point number. Let W = White's point number and let B = Blue's point number. My brand-new formula is both simple and elegant: W = 25 - B. I have never seen this formula published anywhere else, so I am taking full credit for discovering it, although I admit I do not really understand the reason it works. I am asking Dr. Bob Koca and/or Dr. Jason Lee or anyone else to confirm the accuracy of my formula. Thanks in advance.

Speaking of crossovers, does anyone remember the definition of "Crossover Count" given on this site four years ago?

If the mood strikes me, I may work on figuring out the break-even positions at DMP, GG, GS and 4a4a.





White is Player 2

score: 0
pip: 70
Unlimited Game
Jacoby Beaver
pip: 70
score: 0

Blue is Player 1
XGID=--aDDBCB----a-------bbbcd-:1:-1:1:31:0:0:3:0:10
Blue to play 31

1.Rollout16/5 4/1eq: +0.466
Player:
Opponent:		76.34% (G:1.69% B:0.03%)
23.66% (G:0.49% B:0.00%)		Conf.: ± 0.004 (+0.463...+0.470) - [100.0%]
Duration: 30.3 seconds
2.Rollout14/1 3/2* eq: +0.452 (-0.015)
Player:
Opponent:		73.74% (G:7.16% B:0.13%)
26.26% (G:2.50% B:0.02%)		Conf.: ± 0.004 (+0.447...+0.456) - [0.0%]
Duration: 1 minute 36 seconds
3.Rollout16/2* eq: +0.396 (-0.070)
Player:
Opponent:		72.34% (G:4.19% B:0.07%)
27.66% (G:0.92% B:0.01%)		Conf.: ± 0.004 (+0.392...+0.401) - [0.0%]
Duration: 1 minute 02 seconds
4.Rollout17/6 7/4eq: +0.385 (-0.081)
Player:
Opponent:		73.33% (G:0.52% B:0.01%)
26.67% (G:0.00% B:0.00%)		Conf.: ± 0.004 (+0.381...+0.390) - [0.0%]
Duration: 7.9 seconds
1 1296 Games rolled with Variance Reduction.
First 1 moves: 3-ply, cube decisions: XG Roller+
Remaining moves: 3-ply, cube decisions: XG Roller+

eXtreme Gammon Version: 2.10





White is Player 2

score: 0
pip: 69
Unlimited Game
Jacoby Beaver
pip: 70
score: 0

Blue is Player 1
XGID=--aDDBCB-----a------bbbcd-:1:-1:1:31:0:0:3:0:10
Blue to play 31

1.Rollout14/1 3/2* eq: +0.460
Player:
Opponent:		74.14% (G:7.35% B:0.16%)
25.86% (G:2.41% B:0.02%)		Conf.: ± 0.004 (+0.455...+0.464) - [100.0%]
Duration: 1 minute 20 seconds
2.Rollout16/5 4/1eq: +0.434 (-0.025)
Player:
Opponent:		75.07% (G:1.50% B:0.03%)
24.93% (G:0.42% B:0.00%)		Conf.: ± 0.004 (+0.430...+0.439) - [0.0%]
Duration: 32.0 seconds
3.Rollout16/2* eq: +0.396 (-0.064)
Player:
Opponent:		72.30% (G:4.07% B:0.08%)
27.70% (G:0.93% B:0.01%)		Conf.: ± 0.005 (+0.391...+0.400) - [0.0%]
Duration: 1 minute 05 seconds
4.Rollout17/6 7/4eq: +0.334 (-0.126)
Player:
Opponent:		71.37% (G:0.50% B:0.01%)
28.63% (G:0.00% B:0.00%)		Conf.: ± 0.005 (+0.329...+0.338) - [0.0%]
Duration: 8.1 seconds
1 1296 Games rolled with Variance Reduction.
First 1 moves: 3-ply, cube decisions: XG Roller+
Remaining moves: 3-ply, cube decisions: XG Roller+

eXtreme Gammon Version: 2.10

Messages In This Thread

 

Post Response
Your Name:
Your E-Mail Address:
Subject:
Message:

If necessary, enter your password below:

Password:
 

 

[ View Thread ] [ Post Response ] [ Return to Index ] [ Read Prev Msg ] [ Read Next Msg ]

BGonline.org Forums is maintained by Stick with WebBBS 5.12.