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EPC for stack+stragglers, continued

Posted By: Karol Szczerek
Date: Saturday, 1 July 2017, at 9:31 p.m.

Following the discussion here, I'm posting the original position, that I came across.





White is Player 2

score: 0
pip: 25 (EPC: 38.8)
Unlimited Game
pip: 33 (EPC: about 42.7)
score: 0

Blue is Player 1
XGID=-BA----------A--A----bccb-:0:0:-1:00:0:0:0:0:10
White on roll. Blue's GWC: 19.2%.

eXtreme Gammon Version: 2.10

Blue's EPC is about 42.7. This is deducted from moving the spares around with the support of XG's generated EPC database and agrees with Zare's formula quoted by John here (epc = 3.5 x #checkers + stragglers pips - 4).

White's EPC is 38.8.

So Blue trails by almost exactly 10% EPC with White on roll.

This should give about 16% GWC to Blue in this type of position (roll vs roll, and from my research roll vs roll w/stragglers is similar in that regard), but his GWC are actually over 19% here. Quite a difference. I can't figure out what's so special about this position.

A note about Gnu's one-sided rollout feature. It puts Blue on 43.5 EPC, but it uses suboptimal play, so its values are usually overestimated. Even if it was precise for this position though, the GWC of 19% would be even stranger, since Blue would trail by more than 10% EPC.

Some other examples from this category of positions with 1 and 2 stragglers to show that trailer has about 16% GWC when behind by 10% EPC:





White is Player 2

score: 0
pip: 26 (EPC: 50.1)
Unlimited Game
Jacoby Beaver
pip: 40 (EPC: 54.9)
score: 0

Blue is Player 1
XGID=-CCBA----A--A--------acde-:0:0:-1:00:0:0:3:0:10
White on roll. Blue's GWC: 16.4%.





White is Player 2

score: 0
pip: 14 (EPC: 36)
Unlimited Game
Jacoby Beaver
pip: 25 (EPC: 39.6)
score: 0

Blue is Player 1
XGID=-DA------AA------------ed-:0:0:-1:00:0:0:3:0:10
White on roll. Blue's GWC: 15.8%.





White is Player 2

score: 0
pip: 14 (EPC: 29.3)
Unlimited Game
Jacoby Beaver
pip: 21 (EPC: 32.3)
score: 0

Blue is Player 1
XGID=-C-----A---A----------bcb-:0:0:-1:00:0:0:3:0:10
White on roll. Blue's GWC: 14.9%.





White is Player 2

score: 0
pip: 17 (EPC: 30.5)
1 point match
pip: 22 (EPC: 33.5)
score: 0

Blue is Player 1
XGID=-BB--A-----A----------ccb-:0:0:-1:00:0:0:0:1:10
White on roll. Blue's GWC: 15.7%.





White is Player 2

score: 0
pip: 27 (EPC: 44.8)
1 point match
pip: 31 (EPC: 49.3)
score: 0

Blue is Player 1
XGID=-CDC-------A---------addc-:0:0:-1:00:0:0:0:1:10
White on roll. Blue's GWC: 15.7%.





White is Player 2

score: 0
pip: 14 (EPC: 29.6)
1 point match
pip: 19 (EPC: 32.6)
score: 0

Blue is Player 1
XGID=-CB---------A---------adc-:0:0:-1:00:0:0:0:1:10
White on roll. Blue's GWC: 15.2%.





White is Player 2

score: 0
pip: 16 (EPC: 36.1)
1 point match
pip: 24 (EPC: 39.6)
score: 0

Blue is Player 1
XGID=-CCA--------A---------bcd-:0:0:-1:00:0:0:0:1:10
White on roll. Blue's GWC: 16.1%.

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