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Better examples of equity differences in 3-checker HyperGammon and GambleGammon

Posted By: MK
Date: Saturday, 31 October 2026, at 10:09 a.m.

I enjoy with a sadistical pleasure to see how dumbfounded are the so-called giants and mathematicians in this forum, (unfortunately to include Chow even if at a lesser degree since he occasionally engages), in the face of my arguments about "cubeful equities" based on "jackoffsky" formulas (oops formulae;) being mostly bogus, bullshit.

In bug-gnubg forum, at least one person (Phillippe Michel) paid attention and correctly pointed out that my HyperGammon opening position example had possible gammons and backgammons while in GambleGammon it didn't.

I replied to him in that forum with another example position that excluded possible gammons and backgammons.

Later I found some time to generate a 3-checker HyperGammon database and look for some positions to illustrate and support my argument that GnuBG's as well as other GambleGammon bots like XG's cubeful equity calculations are demonstrably inaccurate by an unknown magnitude.

Without wasting much of my time on this, below is the first telling position I encountered. If you won't mind wasting your own times on it, feel free to offer more supporting and/or contradicting position examples. (Notice that no gammons or backgammons are possible for HyperGammon or GambleGammon in that position).

If HyperGammon is indeed solved, I hope that no bot-worshipping mentally ill addicted bg gambler giants will get suicidal because of what I'm posting here...

MK

PS: Sorry for not being able post formatted text in this forum as was produced by GnuBG but I'm sure you can decypher it and get the final idea which matters.

BTW: If you paste the position in XG or other bots that can't offer HyperGammon, you will only see the GambleGammon rendering of it.

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Position ID: IAAAAYAgAAAAAA Match ID: cAkAAAAAAAAE

Evaluator: Hypergammon-3

Player Opponent Position 265 159

Owned cube : +0.3146 Centered cube : +0.2103 Centered cube (Jacoby rule) : +0.2103 Opponent owns cube : +0.0134

Win W(g) W(bg) L(g) L(bg) Equity Cubeful static: 56.6 0.0 0.0 0.0 0.0 +0.132 +0.210 1 ply: 56.6 0.0 0.0 0.0 0.0 +0.132 +0.210 2 ply: 56.6 0.0 0.0 0.0 0.0 +0.132 +0.210 3 ply: 56.6 0.0 0.0 0.0 0.0 +0.132 +0.210 4 ply: 56.6 0.0 0.0 0.0 0.0 +0.132 +0.210

Cube analysis 4-ply cubeless equity +0.132

56.6 0.0 0.0 - 43.4 0.0 0.0 Cubeful equities: 1. No double +0.210 2. Double, pass +1.000 (+0.790) 3. Double, take +0.027 (-0.183) Proper cube action: No double, take (18.9%)

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Position ID: IAAAAYAgAAAAAA Match ID: cAkAAAAAAAAE

Evaluator: Crashed

Win W(g) W(bg) L(g) L(bg) Equity Cubeful static: 55.7 0.0 0.0 0.0 0.0 +0.115 +0.173 1 ply: 56.8 0.0 0.0 0.0 0.0 +0.136 +0.205 2 ply: 53.1 0.0 0.0 0.0 0.0 +0.062 +0.099 3 ply: 52.8 0.0 0.0 0.0 0.0 +0.055 +0.069 4 ply: 54.3 0.0 0.0 0.0 0.0 +0.086 +0.138

Cube analysis 4-ply cubeless equity +0.086

54.3 0.0 0.0 - 45.7 0.0 0.0 Cubeful equities: 1. No double +0.138 2. Double, pass +1.000 (+0.862) 3. Double, take -0.101 (-0.239) Proper cube action: No double, beaver (21.7%)

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