MK, I'm absolutely not a spokesperson for the group. I'm merely an enthusiastic user who tries to take some the load off the devs by answering those questions that I'm able to. If they are not commenting, it's for their own reasons and that shouldn't be interpreted as a tacit endorsement of my opinions.
MK: 1) You acknowledged that the bot becomes inadequate against even a most primitive mutant cube strategy, (hopefully we will discuss my more elaborate ones later also), and is obligated to adjust its "cube skill theory", The gnubg cube strategy assumes that the other player plays like gnubg. I suggested a strategy that I thought could better if it was known that the opponent was always taking. Ways to improve results when playing against humans as opposed bot v. bot move arises frequently in bg discussions. MK: 2) You switched to a strategy of minimizing your losings instead of maximizing your winnings, which is the exact opposite of what the "cube skill theory" is supposed to promote I don't know how you conclude that. I consider improving net points difference, be that + or -. Nor have I considered whether my strategy would be optimal. My answer to why I "wouldn't double at 99%" is indeed about minimizing losses, but it's in the context of maximising net points won. The only reasons to double "now" rather than wait a turn is that (a) your position might improve to a point where they will drop the cube and you only win one point - you "lose your market" (b) the game might end before your next turn, so you only win one point (c) the game might go badly, and you regret doubling. My strategy was to maximise the points won through a & b, and to minimise the points lost at c. Crudely speaking: a) doesn’t apply if your opponent will never drop the cube b) if you are >50% and <= 4 crossovers left so doubles could end the game, cube (This is an oversimplification to illustrate the concept) c) minimise the losses on the 1% of games that go badly. Given condition a, it is always correct to wait a turn because your opponent will still take. You can never lose your market. MK: After 1,000 games mutant won 1,411 points (56.66%) vs bot's 1,079... there was almost no fluctuation with the cube never going past 2, with the mutant almost always reaching GWC > 50% and doubling early in the game and your bot never doubling at GWC < 100%, at which the mutant dropped. There were also a few 1-point wins. My strategy was not to double until 100%, on the understanding that your strategy would always take (which also means that it would never be Too Good to Double). But since your bot WAS dropping when win chances were 100%, then mine was always losing its market. Your experiment demonstrates the importance of doubling before you lose your market. -----Original Message----- From: Murat K <playbg-...@yahoo.com> Sent: Wednesday, April 10, 2024 7:51 AM To: bug-gnubg@gnu.org; Ian Shaw <ian.s...@riverauto.co.uk> Subject: Mutant cube skills; Two birds in the bush better than one in the hand? Hi Ian, On the one hand, since nobody else in this forum negates, nor even adds anything to support your arguments, I feel that I'm debating with a spokesperson for the group, but on the other hand I feel that our ideas don't attain their full potential. With this thread having become too long and more about mutant cube strategies than value of cube ownership, I will take the opportunity to start a new thread responding to your last post, not only here in bug-gnubg but also in rec.games.backgammon and bgonline.org forums where you had posted in the past, for the sake of creating more interest on the subject and hoping that you will participate in those forums also. > ------------------------------------------------------------- > *From:* MK <playbg-...@yahoo.com> > *Sent:* Wednesday, April 3, 2024 10:29:11 pm > *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 > 4/2/2024 7:08 AM, Ian Shaw wrote: > >> A cube strategy against a bot that never passes: > > Not never but we loosely say that since it takes at GWC > 0, > i.e. even at > 0.0001% > >> only double when (a) you are 100% to win > > I don't > understand why you wouldn't double at 99%? Can you > explain this? > >> (b) it's the last roll of the game and you have an advantage. > > Yes, this is very bad for the mutant and already happens now. > >> So the take point is 16.7%. Gammons complicate it, but I'm >> sure you get >> the idea. > > If you can clearly define your strategy, I would be glad to > create a > script to run the experiment to see what will happen. > > BTW: you are still avoiding the issue of how much the mutant > will win > compared to what it would be expected to win based on > its total "cube > error rate". > > What win rate would you say a mutant that takes at GWC > 0.0001 > even on > the last roll, (which must be the biggest possible cube > error), will > achieve? Any guesses by anyone..? > ------------------------------------------------------------- On 4/4/2024 12:01 AM, Ian Shaw wrote: > MK: I don't understand why YOU wouldn't double at 99%? Can you > explain > this? > > If the oppenent will still take at 100% then why risk losing 2 > points 1% > of the time? > > I thought I answered your question about win rates previously. > > A bot that always doubles, I'd expect to lose 0.3 ppg. It's > hard to > search back on my phone app, so maybe that's incorrect.) > > A bot that > doubles immediately it's ahead, I'd expect to lose > about half that. > > Those values assume the bot plays as well as gnubg for the > remainder of > the game. If the opponent will make further cube > errors, then it should > be a little bit more. > ------------------------------------------------------------- To clarify again, the mutant drops at GWC = 0% but takes at > 0%, i.e. at 0.0001%. And you are right to assume that aside from the above mentioned exceptions, both sides play normally at 2-ply. I think we are miscommunicating about the mutant's "expected, i.e. relative, win rate based on its total cube error performance rate" but we can skip that for now and come back to it later since the results of the experiments won't be going anywhere. With that said, I'm elated to hear that: 1) You acknowledged that the bot becomes inadequate against even a most primitive mutant cube strategy, (hopefully we will discuss my more elaborate ones later also), and is obligated to adjust its "cube skill theory", 2) You switched to a strategy of minimizing your losings instead of maximizing your winnings, which is the exact opposite of what the "cube skill theory" is supposed to promote You haven't formulated a simple strategy that I could use in a script but I decided to go ahead and run an experiment excluding your doubling at < 100% in "last roll positions". I searched the internet about ways to discern last roll positions but couldn't find anything. If you can offer any suggestions, I'll be happy to run experiments including those also. While editing my script, I realized that I should not make your strategy double when too good and added that in. But, since I was using common cube routines for both players, my mutant also started to not double when too good, which wasn't in its initial strategy. After 1,000 games mutant won 1,411 points (56.66%) vs bot's 1,079. You may say 1,000 games are hardly enough but I consider it enough to get an initial impression, since there was almost no fluctuation with the cube never going past 2, with the mutant almost always reaching GWC > 50% and doubling early in the game and your bot never doubling at GWC < 100%, at which the mutant dropped. There were also a few 1-point wins. I had read that "last roll positions" are rare but I don't have any idea about actually how rare they are. Even so, it's possible that they could significantly change the outcome because the mutant would take even at 0.0001%. After the first run, I wondered what would happen if both players doubled even when too good and I ran that experiment also. After 1,000 games mutant won 1,321 points (59.83%) vs bot's 887. This is what triggered this thread's title. Could it be that, as BG may be played on a different planet, doubling too good may be better? Then I wondered what if your bot didn't but my mutant did double even when too good and ran that experiment too. After 1,000 games mutant won 1,323 points (53.28%) vs bot's 1,160. Hmmm. Maybe two birds in the bush are indeed better than one in the hand? Lastly, I had to run one more experiment: the reverse of the last one. After 1,000 games mutant won 1,359 points (61.58%) vs bot's 848. Yup. Two birds in the bush indeed seem to be better than one in the hand. With this finding, I think I will run a variant of my "experiment 9", with the mutant not doubling when too good and see if and/or by how much better it will do against GnuBG's unmodified 2-ply cube skill. What is more important for me here though is that my primitive mutant strategy consistently won considerably more than your bot's modified cube strategy, with so little fluctuations that I consider 4 x 1,000 trials persuasive enough that by my mutant cube strategies I destroyed the so-called and so much hyped/dogmatized "cube skill theory". If you think that including "last roll positions" would reverse these results and if you can suggest a way to code it into the script, I'll be glad to run those experiments also. But keep in mind that I can also tweak my mutant to not take at MWC = 0.0001% in those positions. MK
