Re: Interesting question/experiment about value of cube ownership

[MK]

Hi Ian,

Thanks for the additional info. Unfortunately it didn't help
me understand anything better or answer my own question. I'm
still trying and hope that you or others will continue this
subject to help me with it, which will benefit all in the end.

For the cubeless equity of the opening position, I'm going by
the rollout results, (which had taken 7 months to do), from:

https://bkgm.com/openings/rollouts.html

In the summary section towards the end, it says:

"Your average equity if you win the opening roll is +.0393."

So, if I run 10,000 cubeless games with "X" always winning the
opening roll, "X" will win 393 points, i.e. 3.93%, more than "O"?

=================================================================
When the mutant ("X") is on roll (i.e. won the opening roll),

GNUbg ID: 4HPwATDgc/ABMA:cAkAAAAAAAAA evaluate says:

        Win     W(g)    W(bg)   L(g)    L(bg)   Equity    Cubeful
 2 ply:  52.5    14.9     0.7    12.5     0.5   +0.076    +0.099

2-ply cubeless equity +0.076
   52.5  14.9   0.7 -  47.5  12.5   0.5
Cubeful equities:
1. No double           +0.099
2. Double, pass        +1.000  (+0.901)
3. Double, take        -0.171  (-0.270)

How do I relate any of these numbers to the +0.0393 above? Why is
the cubeless equity +0.076?

I suppose the cubeful equity +0.099 is somehow extrapolated using
some formulas and I should accept it as just that?

=================================================================

When I set cube to 2 owned by the bot ("O"), with "X" on roll,

GNUbg ID: 4HPwATDgc/ABMA:QQkAAAAAAAAA evaluate says:

        Win     W(g)    W(bg)   L(g)    L(bg)   Equity    Cubeful
 2 ply:  52.5    14.9     0.7    12.5     0.5   +0.076    -0.086

Cubeless equity is the same. Shouldn't the cubeful equity be
+0.076 - 0.171 = -0.095? Why is it -0.086? Which one is correct?

=================================================================

If I set the cube to 2 owned by mutant ("X") who is also on roll,

GNUbg ID: 4HPwATDgc/ABMA:UQkAAAAAAAAA evaluate says:

        Win     W(g)    W(bg)   L(g)    L(bg)   Equity    Cubeful
 2 ply:  52.5    14.9     0.7    12.5     0.5   +0.076    +0.255

2-ply cubeless equity +0.076
   52.5  14.9   0.7 -  47.5  12.5   0.5
Cubeful equities:
1. No double           +0.255
2. Double, pass        +1.000  (+0.745)
3. Double, take        -0.171  (-0.426)

Cubeless equity is still the same. Should I try to understand why
the D/T is the same as centered cube but now the cubeful equity is
+0.255? Is it +0.076 + 0.171 = +0.247 close enough or what is it??

=================================================================

So, again, what I would like to know is if I run 10,000 games from
each of the above three positions, what results should I expect?

In other words, which one of these many different equity numbers
(with no obvious correspondences for me) do I use to multiply by
10,000 to predict by how much the mutant will win or lose?

MK