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
