On 3/16/2024 6:15 PM, Ian Shaw via wrote: As this thread became more about the starting position than the original subject, I will branch out a separate thread for that and only reply to the cube issue in this one.
Knowing the absolute equity is only useful for cube actions, and since the rules prohibit doubling on the opening roll, it's not very useful to me to make a distinction.
It's just another arbitrary rule. All rules can be changed. Since I am trying to engage you all in theorizing for new ideas and better understanding concepts, it is very useful.
"In fact, I'd argue that with the cube centered, you should be allowed to double if you want before you open your eyes > but this is a whole different subject and for one of the experiments that I have done and will share soon."
I wouldn’t double. As shown by the rollouts, I'd be giving up 0.36 points per game, on average. Even if I knew you would roll 66, I would still take, because the equity of -0.276 * 2 is still better than giving up a whole 1.000 point.
Those numbers are based on how the bot would play against itself. If you accept the bot's decisions as best/perfect and if you try to play just like bot, assuming that your opponent will also try to play just like the bot, of course you wouldn't/shouldn't double. However, there has never been any empirical evidence, based on "double-blind experiments", offered to support that. This is why I am doing my various experiments. One of which that I had previously mentioned in this very thread involves a "mutant cube strategy" of doubling at GWC > 50% and taking at GWC > 0%. In that experiment of 20,000 money games, the mutant won 40.80% of total points against GnuBG 2-ply. Since winning the opening roll gives the player GWC > 50%, I ran a variant of the above experiment making the mutant also double if it wins the opening roll. This time, after 20,000 money games the mutant won 45.77% of total points. In a control experiment of bot 2-ply vs bot 2-ply, with the only mutation being that the winner of the opening roll did double immediately, after 20,000 money games the mutant won 51.45% of total points. I have completed my 13 experiments and trying to make them available as a neat web page but I just can't seem to spare enough time to finalize it, which I keep saying soon. When I finish, you can download all data and scripts to run your own experiment to whatever number of trial you will consider statistically significant. Based on my own experiments, which I consider well enough, I predict that you won't like what you will discover... Even though I think most of you won't absorb what I wrote above, because you all "divinely believe" in the current "cube skill theory", I won't consider it a total waste of my time even if it sows a seed of doubt in just one mind. MK
