On May 21, 2020 at 10:57:25 AM UTC-6, Tim Chow wrote:
> On January 25, 2020 at 3:35:04 AM UTC-5, mu...@compuplus.net
>> On January 23, 2020 at 5:10:23 PM UTC-7, Tim Chow wrote:
>>> In any case, it shouldn't be that hard to write
>>> a program from scratch to compute exact cubeful
>>> equities in Hypergammon. I might do that sometime.
>> So, in order to help you get started with an easier
>> task, I invented an even simpler BG variant than
>> HyperGammon: HypestGammon..!! :)
>> Let's see if you can write a program from scratch to
>> compute exact cubeful equities in "HypestGammon".!? :)
> One of my colleagues expressed interest in HypestGammon,
> so I did finally go ahead and write a program to compute
> the equities.
This renews my hope and interest to continue debating in RGB.
I never thought you would try even being dared. And, as you
confess, you wouldn't have if your colleague hadn't expressed
interest in it. So, if any credit may arise from your effort,
he/she should get it. Unless he requires to remain anonymous,
may we know who this "colleague" is?
More importantly than his name, I would like to know what was
the nature of his interest? Was it plain/scientific curiosity
to know/learn whithout any presuppositions? Or did he already
have an idea what the result would be and just wanted to find
out if he was right/wrong?
I'm sure we will later question and interpret your methods and
results after the fact. With that, what lead to the experiment
may be as worthy and meaningful as what came out of it.
> In fact, I did so in two different ways. The first way was
> to write down a mixed integer program and then solve it with
> CPLEX. The second way was to write an iterative program along
> the lines of what Tom Keith sketched.
Since you have already put in an effort into this, would you go
the extra step to explain and document what you have done? Even
if it may be too complex for non mathematicians at first, thru
future discussions, others may also understand eventually.
> Both methods gave the same numerical answers.
Was there ever the possibility in your mind that they woudn't?
If yes, by chance, have you even began to ask the question what
> It seems intuitively clear that the equities should exist and
> be unique, but I don't actually have a rigorous proof of that
Well, at least you started on it. Hopefully more will follow.
> Note also that since there is only one checker, it doesn't
> really make sense to talk about a gammon; a gammon is the
> same as a single win. But it does make sense to talk about
> a backgammon; if I bear off my checker when my opponent is
> on the bar or in my home board, then I win a backgammon. It
> is easy to rerun my code with whatever backgammon value you
If it's going to make cube decisions more like regular gammon,
(and it it would be meaningful doing it), a new rule can be
injected to differentiate between single games and gammons. If
the checker has at least made into the loser's home board, then
it would be a single game vs. gammon lost otherwise, etc.
> I can make the equities I computed available on my website if
> anyone is interested.
Yes, plase. I would be very interested in not only the computed
equities but any and all other info you can make available, such
as program codes, etc.
> As a spot check, I find that if you win the initial rock-paper-
> scissors game and get to go first, your cubeful equity is about
Can we also speak in MWC also, if not instead.
> If you are allowed to double after winning rock-paper-scissors
> but before rolling the die, then you should not double. Doubling
> decreases your equity to about 0.03044.
Since it's not allowed, why would you even want to know that?
Are you trying to create strawmen already..??
> In the meantime, I discovered that GNU Backgammon comes bundled
> with a program called "makehyper" that computes cubeful equities
> for HyperGammon.
I saw that too. In fact, it refers to 1, 2 or 3 checker HyperGammon.
> That has reduced my incentive for beefing up my program(s) to
> handle HyperGammon.
Nonsense. How do you know Gnubg does it right? There is no way to
compare my HypestGammon to Gnubg's 1-checker HyperGammon, (since,
I assume it uses two dice), but you can improve your programs to
handle 1, 2 and 3 checker HyperGammon, and compare the results.