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