Being puzzled by the inability of all the bozos here to
understand that the equity before the opening roll can
be non-zero, I just couldn't stop thinking about it.
I remember that equity gained by winning the opening
roll had been talked about many times in RGB, including
by me, but never regarding how the bots calculated it.
For example, I had given this link in a different context:
https://bkgm.com/openings/rollouts.html
In my this post:
https://groups.google.com/g/rec.games.backgammon/c/k61QtBwlsBk/m/SP86Am44DQAJ
In the introduction section, the undated article says:
"The rollouts on this page where performed using
"Gnu Backgammon, version 0.14, which is the latest
"and strongest version of Gnu BG as of early 2006.
"The rollouts were performed using 2-ply play.....
"Rollouts were performed using cubeless money play.
And in the summary section at the end, its says:
"Here are all the opening rolls ranked from best to
"worst. The best roll is 31 with an equity of +.1670.
"The worst roll is 41 with an equity of +.0024. Your
"average equity if you win the opening roll is +.0393.
All of you bozos here, read that last line very slowly so
that you may understand what it says!
According to Gnubg's Temperature Map, the best roll
is 31 with an equity of +0.218 and the worst roll is 41
with an equity of -0.006 (at the same 2-ply) and the
average equity if you win the opening roll is +0.0543
(excluding doubles).
According to XG's Dice Distribution, the best roll is 31
with an equity of +0.234 and the worst roll is 41 with
an equity of -0.005 (at 1-ply) and the average equity if
you win the opening roll is +0.0547 (excluding doubles).
Then I became curious about how "the fallacy of zero
equity before the opening roll" came about.
I wondered how Snowie calculated the opening roll
equities.
According to its Dice Panel, the best roll is 31 with an
equity of +0.161 and the worst roll is 41 with an equity
of -0.000, and the average equity (Snowie calls "initial
equity") if you win the opening roll is +0.073 including
doubles (but should be +0.0358 excluding doubles).
A quick search using the keywords "Snowie Dice Panel"
struck gold within minutes. Snowie was subtracting the
"initial equity" from the opening roll correctly but was
subtracting the wrong amount +0.073 including doubles.
When people discovered it, they correctly called it a bug
but suggested the wrong correction. For example, see:
https://groups.google.com/g/rec.games.backgammon/c/QwgEfduYVAs/m/dzL6A3cVKTAJ
https://groups.google.com/g/rec.games.backgammon/c/1eSH9FHvQ9Q/m/PXggrEP29D8J
There you have the venerable David Montgomery of
the gamblegammon world, saying:
"Since your equity was 0 before the game started,
"the luck calculation should be based on this .154.
"Snowie instead compares your potential equity
"with the 31 (+.154) to the equity with you on roll
"in the opening position -- including doubles --
"which Snowie estimates as +.072.
Apparently intelligent people can also be stupid! :(
"Before the game starts' is not the same as "before
the opening roll" is rolled!
The game start with determining which player will
roll first, (by whatever ways in different flavors of
backgammon). Once a player "wins the opening roll",
that player's equity is already the "initial", "average",
etc. equity that he will gain after rolling the first roll!
Because in the westernized way of deciding who wins
the opening roll is simultaneous with rolling it, it looks
like all the gamblegammon bozos are confused by that.
This is also why even the brightest of gamblegammon
giants assumed that recycling to the opening position
would take at least 5 rolls. See:
https://www.bkgm.com/rgb/rgb.cgi?view+68
My 4 rolls solution may seem illegal to those people
who can't think for themselves, but there is nothing
to prevent recycling to the opening position more
than once, or twice, or ten times... Thus, not only in
traditional backgammon that the opening position
can be recycled to in 4 rolls, but in gamblegammon
also after the first iteration.
The reason I'm dwelling on this is because a bot or
human with an assuming mind will see the "opening
position" as only just that, and not as any position
that can occur and reoccur after the first roll in a
game. This is very important!
Unless a peson is capable of unbiased/independent
thinking, no amount of reading books, paid lessons,
etc. will help; not even having a PHD in arithmetics,
mathematics, computer programming, etc... :(
I can't know if Montgomery was *the one" and/or
*the only one* who started this fallacy but it seems
like bots like Gnubg and its sibling XG that followed
Snowie, have implemented this fallacy by throwing
out the baby with the bath water... :(
This is a perfect example of how people who acquire
an undeserved credibility can lead the flock of sheep
in the wrong direction, all the way, for a long time...
Now, let's see how long it will take for those same
"mis-intelligent" shepherds to admit their mistakes,
and for the bots to start calculating opening luck
rates correctly...??
MK
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