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Gerard's paradox + position variant

Posted By: Carlo Melzi
Date: Wednesday, 11 October 2017, at 8:25 p.m.

In Response To: What is Gerard's paradox? *NM* (Sean Garber)

Gerard's Paradox is mentioned in the book "How little we know about backgammon" by Danny Kleiman.

The name Gerard comes from Gerard Duguet-Grasser, a famous French player at the time I believe.

It basically states what others already wrote in this thread: in a 2aw-2aw score, you should always double as an underdog with market losers as long as you always have a take anyway on the next roll.

While originally stated at 2aw-2aw score, it happens also at other scores, as long as the cube action kills the cube.

I am coming to the conclusion that correct doubles below the minimum doubling point do always involve some form of Gerard's paradox. Do you agree?

Let's take a look at this variant:





White is Player 2

score: 9
pip: 67
11 point match
pip: 80
score: 4

Blue is Player 1
XGID=-BBBCBB-----a----B-cbcbd--:0:0:1:00:4:9:0:11:10
Blue on roll, cube action?

Analyzed in XG Roller+ No double Double/Take
Player Winning Chances: 55.90% (G:1.39% B:0.02%) 55.98% (G:1.28% B:0.01%)
Opponent Winning Chances: 44.10% (G:0.23% B:0.00%) 44.02% (G:0.20% B:0.00%)
Cubeless Equities +0.129 -0.024
Cubeful Equities
No double:-0.056 (-0.032)
Double/Take:-0.024
Double/Pass:+1.000 (+1.024)
Best Cube action: Double / Take

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

This is again a proper initial cube even though GWC are much lower than the minimum doubling point. Now the proper following after a miss is often a Double/Pass. However, some form of Gerard's Paradox is still present, and probably this is what makes the double correct in the first place.

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