Re: Interesting question/experiment about value of cube ownership

[EDWARD GOLDBERG]

Can I be removed from this email list please?

> On Feb 10, 2024, at 9:59 PM, MK <playbg-rgb@yahoo.com> wrote:
> 
> 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
>