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Even better

Posted By: Bob Koca
Date: Friday, 6 June 2014, at 1:13 p.m.

In Response To: Even better (phil simborg)

"Or you can put in a position with gammons at 3away 3away and look at the number of net gammons, multiply by .5, and add that to 25 percent to get a GAT and see if that works."

Similarly for money play you would do the same thing but add to 21.5% Let's test that a bit. Note that this a good test of the basic idea since the problems of changing gammon prices and near autocubes that may occur in a match are completely eliminated.

A long race.





White is Player 2

score: 0
pip: 110
Unlimited Game
pip: 98
score: 0

Blue is Player 1
XGID=---ABCCBB---Baaaacbbbb----:1:1:1:00:0:0:0:0:10
Blue on roll, cube action?

Analyzed in XG Roller++ No redouble Redouble/Take
Player Winning Chances: 78.38% (G:0.00% B:0.00%) 78.42% (G:0.00% B:0.00%)
Opponent Winning Chances: 21.62% (G:0.00% B:0.00%) 21.58% (G:0.00% B:0.00%)
Cubeless Equities +0.568 +1.137
Cubeful Equities
No redouble:+0.889 (-0.110)
Redouble/Take:+0.998
Redouble/Pass:+1.000 (+0.002)
Best Cube action: Redouble / Take

eXtreme Gammon Version: 2.10

Works great.

What about a position with the taking side losing a lot of gammons:





White is Player 2

score: 0
pip: 176
Unlimited Game
pip: 81
score: 0

Blue is Player 1
XGID=-bcBCCCBB--------acbbb----:1:1:1:00:0:0:0:0:10
Blue on roll, cube action?

Analyzed in XG Roller++ No redouble Redouble/Take
Player Winning Chances: 62.76% (G:33.88% B:6.89%) 62.84% (G:33.90% B:6.92%)
Opponent Winning Chances: 37.24% (G:1.20% B:0.04%) 37.16% (G:1.22% B:0.04%)
Cubeless Equities +0.650 +1.305
Cubeful Equities
No redouble:+0.927 (-0.073)
Redouble/Take:+0.999
Redouble/Pass:+1.000 (+0.001)
Best Cube action: Redouble / Take

eXtreme Gammon Version: 2.10

Net gammon difference of 32.68 * 0.5 = 16.34% Net backgammon difference of 6.88% * 0.5 = 3.44%

21.5% + 16.34% + 3.44% = 41.28% needed to take by your technique. (Unless I have totally misunderstood it).

But in actuality it is a bare take at only 37.16%. Not really that good at all. This is due to a theoretical flaw in the model you are using. Essentially you are saying that cubeless equity of .570 is the breakeven point. This works fine for gammonless positions usually. A .570 position though in which the taker is losing a lot of gammons (along with more wins of course so cubeless equity is still .570) is better than a .570 position in which one is losing no gammons. One has a shorter path to get to the recube level. Janowski's paper discusses this well. Also Douglas Zare suggested that using a gammon value that is lowered to compensate for this effect can be done. I think for money it is .42

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