Yes, I am referring to theoretical continuous model for the 20% value, and agree it would apply to any suitable game, not just backgammon.
But backgammon isn't a continuous game. It has jumps in equity betewen one opportunity to double and the next. The concept of cube efficiency is the estimate to allow for this. What other approximations are there? If course, at deeper plies than 0, bots look at the outcomes of all possible sequences so the effect of the cube efficiency approximation diminishes. What would be your proposed structure for training a cubeful bot? What gains and obstacles do you foresee. If course I think similarly about your other insulting terminology. Speaking personally, it reduces the amount of pleasure I get from the discussion and therefore the amount of time I'm prepared to put in. ________________________________ From: MK <playbg-...@yahoo.com> Sent: Tuesday, April 2, 2024 11:43:40 AM To: Ian Shaw <ian.s...@riverauto.co.uk>; GnuBg Bug <bug-gnubg@gnu.org> Subject: Re: Interesting question/experiment about value of cube ownership On 3/31/2024 3:53 AM, Ian Shaw wrote: > I'm glad we agree on the basic 25% take point. Do you also agree on > the the theoretical 20% take point for perfect cube efficiency? If by "theoretical" you mean a purely mathematical proposition, i.e. not specifically related to cubeful backgammon, cubeful hopscotch, cubeful snakes and ladders, etc., or (to repeat myself) as applied in simple games where you can calculate those 25% and 20% accurately and consistently, then I would say I agree with you. > As far as I know, the only part of cube theory not calculated > mathematically is the estimate made for cube efficiency. But it's > a long time since I read Janowski so I may be wrong on that. Since no bot was ever trained through cubeful self-play, all cubeful calculations of all kinds are "mythematically" calculated, by using repeatedly adjusted constants to produce the results desired by the humans of faith... > (I think you are using "gamble gammon" as a pejorative. I suspect > that every time you do so, you lose credibility with anyone likely > to read this. You may wish to take this into account, bearing in > mind that most backgammon with the cube isn't played for money.) I like writing poems, coining new expressions, country music lyrics, word plays, puns, etc. and ta times I use them pejoratively but not so much with "gamblegammon", for which I used worse names. There was a game called "backgammon" before the "doubling cube" was introduced to it for gambling purposes, which changed it drastically enough for it to be considered a "variant" of backgammon, just like any other such variants. I have argued for over 20 years that the "cubeful backgammon variant" needs to be given a new name and I proposed "gamblegammon", which I thought was quite appropriate. I have been calling it "gamblegammon" in other forums like RGB ever since and invited others to suggest other names for it if they didn't like my "gamblegammon". Feel free to offer your suggestion. While on the subject, I'm surprised that you didn't catch on to many other expressions that I have been using pejoratively, such as my "fartoffski cube skill formula" against the "jackoffski cube skill formula", etc. Focus on understanding and refuting my arguments. If you (all) can't, then I really don't care about my credibility with people who can't understand my arguments, let alone rise up to defeat my arguments. MK > ---------------------------------------------------------------------------------------------------- > *From:* MK <playbg-...@yahoo.com> > *Sent:* Friday, March 29, 2024 4:34:39 AM > *To:* Ian Shaw <ian.s...@riverauto.co.uk>; GnuBg Bug <bug-gnubg@gnu.org> > *Subject:* Re: Interesting question/experiment about value of cube ownership > On 3/19/2024 7:44 AM, Ian Shaw wrote: > >> I don’t "divinely believe" in the current cube theory. I understand >> the maths behind it. If you have found errors in the maths, then I >> would be glad to re-evaluate. > >> Let's find out where you disagree by starting from the beginning. >> What is your analysis of the basic 25% takepoint calculation? > > > I'm not questioning whether a simple doubling theory, (assuming it > can be called a "theory"), can be applied in simple game where you > can calculate that 25% accurately and consistently. > > I'm questioning whether some doubling strategy can be applied in > gamblegammon, based on a jumble of incomplete/inaccurate empirical > statistics and mathematical calculation formulas that were several > times retrofitted to produce some expected results, and call it a > "cube skill theory". > > In RGB, some mathematicians had argued that it could be called a > "theory" because it was mathematically proven, which can not be > because the so-called "cube skill" is not a purely mathematical > proposition. > > In a game involving luck like gamblegammon, (more luck than skill > in my personal opinion), the proposition is necessarily statistical, > empirical one and thus needs to be empirically proven. > > You say "let's start from the beginning". Yes, let's do so indeed. > > TD-Gammon v.1 was empirically trained through self-play of cubeless > "money games", including gammons but not backgammons, and perhaps > not enough trials. That's it. That's your beginning... > > To that, you use all kinds of "maths and mirrors" to add backgammon > rates, cubeful equity formulas, cubeful matchful equity tables, etc. > to "estimate" your winning chances, in order to apply to it what you > a "basic 25% take point". And I'm questioning sanity of all this, in > fact I'm arguing that it's all a pile of cow pies. > > Shortcuts was taken in the days of TD-Gammon because of not having > enough CPU power, which is no longer true. Yet, there is no signs > of any willingness out there to create cubefully, matcfully trained > better gamblegammon bots. > > It's easier to destroy a falsely claimed "theory" by poking holes in > it than to prove a proposition so that you can call it a theory, and > this is what I'm trying to accomplish with my experiments. > > Since I can't single-handedly create a better bot, I'm trying what > I can do to create a need for, thus an incentive for the creation of > such a bot, "from scratch". > > My "fartoffski mutant cube strategy", (based on arbitrary stages of > game and double/take points), in my experiments 11 and 12 came within > margin of error of beating GnuBG 2-ply. Folks, it's time for better > gamblegammon bots... > > MK
