Trouble calculating fully live take points

[Lasse Hjorth Madsen]

Hi all,

The GNU Backgammon Manual V1.00.0, has a section on the calculation of live cube take points: “10.4.5.2 Live cube equities”. There’s a table with some live cube take points for a specific position and a specific match score. It mentions, “The calculation of these are left as an exercise to the reader.” I’m trying to complete that exercise, but I'm having some troubles.

For example, there’s a live take point quoted as 24.5%. This is for a player trailing 7-away, 4-away, facing an initial double, using the Woolsey MET, in a position with the following probabilities:

  Win   Win G  Win BG    Lose  Lose G Lose BG 

  0.454   0.103   0.001   0.546   0.106   0.003  

When I apply the provided formula:

TP(live, n Cube)=TP(effective, n cube) * (1 - TP(live, 2n cube))

I get a take point of only 21.7%

The dead-cube take point I get, 35.3%, agrees with GNU BG. Also, the opponent’s take point of a possible recube, 38.5%, is what GNU reports and also in the same table.

So per the above formula, the fully live cube take point would be:

35.3% * (100% - 38.5%) = 21.7%

But alas, that is far from the expected 24.5%.  

Funny enough, when I try examples with no gammons, I can reproduce GNUs fully live TPs exactly.

If anybody can explain what I’m doing wrong, I would be forever grateful.

Thanks,

Lasse