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BGonline.org Forums
Live Cube equity:A root value in BG based on a math axiom
Posted By: Michael
Date: Saturday, 2 September 2017, at 6:45 p.m.
I would like to learn your opinion on the correctness of the Live Cube in backgammon.
It's most known application in Backgammon are the gammonless Live Cube Take Points at various scores.
The axiom says:
The Live Cube TP is so much lower than the Dead Cube TP, as the Live TP of the opponent at next Cube value.
I am going to explain how it's done for those who don't know, so that as many people as possible
would follow and express their opinion. If you already know you may skip the rest.
Let's take the case of gammonless 4Away 7Away
The dead Cube TPs are easily calculated from the XG2 MET using the well known formula Risk/(Risk+Gain).
In this case the Risk= Drop-(Take and eventually Lose)
The Gain= (Take and eventually Win)-Drop.
Taking values from the MET for the case where the 7A player would Double to 2:
Drop MWC%= 64.285%
Take and eventually Lose=57.732%
Take and eventually Win=84.225%
We would eventually end up with the TP Dead for the 4A player= 24.73%
Similarly for the rest, and this would fill in the first row of the table.
The TP Live now should always be lower than the TP Dead because cube ownership has a value.
The question is how much lower? Well, this is my whole point. The axiom says:
The Live Cube TP is so much lower than the Dead Cube TP, as the Live TP of the opponent at next Cube value.
To fill in the table you have to start from the far right.
The Live TP of Player A when B redoubles to 8 is his Dead Point (42.85%) reduced by Player's B Live TP at Cube 16 which is zero.
(not shown on the Table as it actually doesn't exist).
So we get our first Live TP for filling up the Table.
From that we can now calculate Player's B TP Live when the Cube goes from 2 to 4.
That equals to 27.6% reduced by 42.85%
--> 27.6*(1-0.4285)= 15.78%
And so on until we get the Live TPs for both Players when either one Doubles to 2.
The final values are shown on the table.
PlayerA PlayerB PlayerA PlayerB PlayerA PlayerB PlayerA PlayerB Away Away Cube 1 to 2 Cube 2 to 4 Cube 4 to 8 TP Dead TP Live TP Dead TP Live TP Dead TP Live TP Dead TP Live TP Dead TP Live TP Dead TP Live
4 7 24.73% 30.26% 26.04% 27.60% 42.85% 0% 0%
4 7 24.73% 30.26% 26.04% 27.60% 42.85% 42.85% 0% 0%
4 7 24.73% 30.26% 26.04% 27.60% 15.78% 42.85% 42.85% 0% 0%
4 7 24.73% 20.83% 30.26% 22.38% 26.04% 26.04% 27.60% 15.78% 42.85% 42.85% 0% 0%
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