Re: Interesting question/experiment about value of cube ownership
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. From: MK Sent: Wednesday, April 3, 2024 10:29:11 pm To: Ian Shaw ; GnuBg Bug 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..? MK
Re: Interesting question/experiment about value of cube ownership
MK: What I PROPOSE is doing the same thing done training TD-Gammon v.1, I.E. random self-play, but this time also cubeful and MATCHFUL, i.e. random cube as well as checker decisions. As I remember it (though it's many years since I read the research), the self-play wasn't accomplished by picking random moves. It was the initial network weights that were random. The move picked was the best-ranked move of all the evaluated moves. This is a calculation, not a random selection. How do you propose to rank double vs no double, and take vs pass? From: MK Sent: Wednesday, April 3, 2024 10:01:17 PM To: Ian Shaw ; GnuBg Bug Subject: Re: Interesting question/experiment about value of cube ownership On 4/2/2024 5:13 AM, Ian Shaw wrote: > What would be your proposed structure for training a > cubeful bot? What gains and obstacles do you foresee. I don't know what you mean by "structure". What I propose is doing the same thing done training TD-Gammon v.1, i.e. random self-play, but this time also cubeful and matchful, i.e. random cube as well as checker decisions. Apparently Tseauro still works at IBM with access to huge CPU powers. Perhaps he can be put to shame for the damage he caused to BG AI by what he did with TD-Gammon v.2 and be urged to redeem himself. In other forums, people talk about doing "XG rollouts on Amazon's cloud servers", etc. Doing more biased rollouts is plain stupid/illogical. Any such efforts would be put to better use in training a new bot instead. The question is who would volunteer to do it. People like the Alpha-Zero team, etc. don't seem to want to touch "gamblegammon" with a ten feet pole, possibly because of the gambling nature of the game. In the past, I have suggested in RGB that random rollout feature can be added to GnuBG and results from trustable users can be collected over time in a central database to gradually create a bot that won't rely on concocted, biased/inaccurate cube formulas and match equity tables. Unfortunately the faithfuls are happy with their dogmas and no better bots are likely in the near future... :( MK
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..? MK
Re: Interesting question/experiment about value of cube ownership
On 4/2/2024 5:13 AM, Ian Shaw wrote: What would be your proposed structure for training a cubeful bot? What gains and obstacles do you foresee. I don't know what you mean by "structure". What I propose is doing the same thing done training TD-Gammon v.1, i.e. random self-play, but this time also cubeful and matchful, i.e. random cube as well as checker decisions. Apparently Tseauro still works at IBM with access to huge CPU powers. Perhaps he can be put to shame for the damage he caused to BG AI by what he did with TD-Gammon v.2 and be urged to redeem himself. In other forums, people talk about doing "XG rollouts on Amazon's cloud servers", etc. Doing more biased rollouts is plain stupid/illogical. Any such efforts would be put to better use in training a new bot instead. The question is who would volunteer to do it. People like the Alpha-Zero team, etc. don't seem to want to touch "gamblegammon" with a ten feet pole, possibly because of the gambling nature of the game. In the past, I have suggested in RGB that random rollout feature can be added to GnuBG and results from trustable users can be collected over time in a central database to gradually create a bot that won't rely on concocted, biased/inaccurate cube formulas and match equity tables. Unfortunately the faithfuls are happy with their dogmas and no better bots are likely in the near future... :( MK
Re: Interesting question/experiment about value of cube ownership
Of course I don't assume that gnubg always wins. That would be naive. A cube strategy against a bot that never passes: only double when (a) you are 100% to win (b) it's the last roll of the game and you have an advantage. The bot can also take a double deeper than normal, since the mutant will always take the recube to 4. So the risk is 1 point and the reward is 5 points (instead of 3). So the take point is 16.7%. Gammons complicate it, but I'm sure you get the idea. From: MK Sent: Tuesday, April 2, 2024 12:08:49 pm To: Ian Shaw ; GnuBg Bug Subject: Re: Interesting question/experiment about value of cube ownership On 3/31/2024 4:18 AM, Ian Shaw wrote: > If the mutant strategy is always to take, then gnubg GAINS when > Mutant > takes a D/P because that increases the points GnuBg wins. Yes, of course, but only and only if the GnuBG wins. Obviously you faithfully assume that GnuBG will always win and keep raking in the higher cube points but experiment like the ones I did may prove it otherwise. And this is only speaking about winning more than 50% of points. To this day, I have never been able get you guys to talk about mutant strategies winning more than what would be expected from their cube error rates, which is even more important in debunking the elaborate so-called "cube skill theory" a complete mound of cow pies... > Currently, gnubg is assuming it is playing against a player using > it's own cube strategy. And this is why they are as easy to derail as toy trains on tracks around the xmas tree and to beat even by people like me, who is a nobody compared to gamblegammon giants. See my 10-years old experiments against various bots at my site: https://montanaonline.net/backgammon/ I do however believe that future bots, trained through cubeful and matchful self-play, will come very close to "perfect" play that no human may possibly beat but current bots, including GnuBG, are not even worth a mention by that measure. > It could be reprogrammed to take advantage of knowing that it's > opponent would never pass. Okay, well, I'm daring to tell me how do you propose the bot could be reprogrammed to do that? You don't need to post the programming code here. Just explain how the bot would achieve that in plain language. I bet you won't be able to do. Empty talk is cheap... Let me hold your hand to make another baby step: even if you could reprogram a bot to to that, it would become just another version of the same toy train on tracks going in circles around the xmas tree, with the same weakness of exploitability by being totally predictable. After that, you would have to reprogram you bot by revising your jackoffski cube formulae again... Do you see your problem..? MK > > *From:* MK > *Sent:* Friday, March 29, 2024 2:28:09 AM > *To:* Ian Shaw ; GnuBg Bug > *Subject:* Re: Interesting question/experiment about value of cube ownership > On 3/19/2024 3:54 AM, Ian Shaw wrote: > >> MK "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." > >> Agreed. Against a worse player, you can take with fewer winning chances. >> If your opponent will give up enough equity in errors to overcome the >> error of the bad take (and your own subsequent errors), then you should >> still come out ahead. > > I hope you are realizing that you are agreeing with the bot, not with me. > What you quoted from me above was in response to your previously saying: > > "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. > > Would you drop if you knew that the mutant would roll 77? You wouldn't. > (Just exaggerating to make a point, while reminiscing how Jellyfish was > not only rolling 77's but shamelessly playing them to escape 6-primes:) > > Once the mutant conditionally pre-doubles, (i.e. if rules allow it, in > case it wins the opening roll), you will become hostage to its strategy, > or in better sounding words, you will be dancing to its tune... ;) > > Reaching a D/P later won't help you either because the mutant will not > drop and will force you to keep playing until the last roll, perhaps > trading the cube more times back and forth. > > Letting the bot play for both side after the "opening double" actually > defeats the purpose o
Re: Interesting question/experiment about value of cube ownership
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 Sent: Tuesday, April 2, 2024 11:43:40 AM To: Ian Shaw ; GnuBg Bug 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 > *Sent:* Friday, March 29, 2024 4:34:39 AM > *To:* Ian Shaw ; GnuBg Bug > *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 th
Re: Interesting question/experiment about value of cube ownership
On 3/31/2024 4:18 AM, Ian Shaw wrote: If the mutant strategy is always to take, then gnubg GAINS when > Mutant takes a D/P because that increases the points GnuBg wins. Yes, of course, but only and only if the GnuBG wins. Obviously you faithfully assume that GnuBG will always win and keep raking in the higher cube points but experiment like the ones I did may prove it otherwise. And this is only speaking about winning more than 50% of points. To this day, I have never been able get you guys to talk about mutant strategies winning more than what would be expected from their cube error rates, which is even more important in debunking the elaborate so-called "cube skill theory" a complete mound of cow pies... Currently, gnubg is assuming it is playing against a player using it's own cube strategy. And this is why they are as easy to derail as toy trains on tracks around the xmas tree and to beat even by people like me, who is a nobody compared to gamblegammon giants. See my 10-years old experiments against various bots at my site: https://montanaonline.net/backgammon/ I do however believe that future bots, trained through cubeful and matchful self-play, will come very close to "perfect" play that no human may possibly beat but current bots, including GnuBG, are not even worth a mention by that measure. It could be reprogrammed to take advantage of knowing that it's opponent would never pass. Okay, well, I'm daring to tell me how do you propose the bot could be reprogrammed to do that? You don't need to post the programming code here. Just explain how the bot would achieve that in plain language. I bet you won't be able to do. Empty talk is cheap... Let me hold your hand to make another baby step: even if you could reprogram a bot to to that, it would become just another version of the same toy train on tracks going in circles around the xmas tree, with the same weakness of exploitability by being totally predictable. After that, you would have to reprogram you bot by revising your jackoffski cube formulae again... Do you see your problem..? MK *From:* MK *Sent:* Friday, March 29, 2024 2:28:09 AM *To:* Ian Shaw ; GnuBg Bug *Subject:* Re: Interesting question/experiment about value of cube ownership On 3/19/2024 3:54 AM, Ian Shaw wrote: MK "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." Agreed. Against a worse player, you can take with fewer winning chances. If your opponent will give up enough equity in errors to overcome the error of the bad take (and your own subsequent errors), then you should still come out ahead. I hope you are realizing that you are agreeing with the bot, not with me. What you quoted from me above was in response to your previously saying: "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. Would you drop if you knew that the mutant would roll 77? You wouldn't. (Just exaggerating to make a point, while reminiscing how Jellyfish was not only rolling 77's but shamelessly playing them to escape 6-primes:) Once the mutant conditionally pre-doubles, (i.e. if rules allow it, in case it wins the opening roll), you will become hostage to its strategy, or in better sounding words, you will be dancing to its tune... ;) Reaching a D/P later won't help you either because the mutant will not drop and will force you to keep playing until the last roll, perhaps trading the cube more times back and forth. Letting the bot play for both side after the "opening double" actually defeats the purpose of the experiment but since there is no "separately existing, fully functional mutant bot (that would play like me;)" to make it play against GnuBG 2-ply, this is the only way we can do it and it's better than nothing. So, this way the really "semi-mutant" play will lose but it still will not lose more than what would be expected from the cube error rate that the mutant incurs from this "opening double". This alone is enough to prove that the currently dogmatized "cube skill theory" is a jarful of cow chip cookies... MK
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 *Sent:* Friday, March 29, 2024 4:34:39 AM *To:* Ian Shaw ; GnuBg Bug *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
Re: Interesting question/experiment about value of cube ownership
If the mutant strategy is always to take, then gnubg GAINS when Mutant takes a D/P because that increases the points GnuBg wins. Currently, gnubg is assuming it is playing against a player using it's own cube strategy. It could be reprogrammed to take advantage of knowing that it's opponent would never pass. From: MK Sent: Friday, March 29, 2024 2:28:09 AM To: Ian Shaw ; GnuBg Bug Subject: Re: Interesting question/experiment about value of cube ownership On 3/19/2024 3:54 AM, Ian Shaw wrote: > MK "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." > Agreed. Against a worse player, you can take with fewer winning chances. > If your opponent will give up enough equity in errors to overcome the > error of the bad take (and your own subsequent errors), then you should > still come out ahead. I hope you are realizing that you are agreeing with the bot, not with me. What you quoted from me above was in response to your previously saying: "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. Would you drop if you knew that the mutant would roll 77? You wouldn't. (Just exaggerating to make a point, while reminiscing how Jellyfish was not only rolling 77's but shamelessly playing them to escape 6-primes:) Once the mutant conditionally pre-doubles, (i.e. if rules allow it, in case it wins the opening roll), you will become hostage to its strategy, or in better sounding words, you will be dancing to its tune... ;) Reaching a D/P later won't help you either because the mutant will not drop and will force you to keep playing until the last roll, perhaps trading the cube more times back and forth. Letting the bot play for both side after the "opening double" actually defeats the purpose of the experiment but since there is no "separately existing, fully functional mutant bot (that would play like me;)" to make it play against GnuBG 2-ply, this is the only way we can do it and it's better than nothing. So, this way the really "semi-mutant" play will lose but it still will not lose more than what would be expected from the cube error rate that the mutant incurs from this "opening double". This alone is enough to prove that the currently dogmatized "cube skill theory" is a jarful of cow chip cookies... MK
Re: Interesting question/experiment about value of cube ownership
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? 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. (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.) Regards, Ian Shaw From: MK Sent: Friday, March 29, 2024 4:34:39 AM To: Ian Shaw ; GnuBg Bug 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
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
Re: Interesting question/experiment about value of cube ownership
On 3/19/2024 7:37 AM, Ian Shaw wrote: MK: This is why I am doing my various experiments. One of which that I had previously mentioned in this very thread involves a "mutant cubestrategy" 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. These sound similar enough that I'll combine them. Overall, the mutant strategy if doubling as soon as you had an advantage lost 0.1343 points per game. Always doubling immediately lost 0.36 ppg. So, not doubling until you are winning appears to be a better strategy than always doubling. But, as you expected, the mutant strategy isn't as good as the current cube algorithm, which loses 0 ppg. I think you misunderstood the whole thing. You need to compare the first mutant strategy to the bot playing against itself straight. The mutant is expected to lose. The fact that it didn't lose too badly is a separate point by itself. Then you need to compare mutant's variant strategy of doubling at once to bot's regular play against itself with the only difference of doubling at once. Now we are comparing mutant variant against mutant and bot variant against bot. In the case of the bot, doubling at once causes the variant bot to lose points. However, in the case of the mutant, doubling at once causes the variant mutant ti win more points, not compared to the bot but compared to the mutant itself! I can imagine how difficult it may be for some of you guys to stick your heads out of the box and try to understand what I'm trying to demonstrate. I'm not saying that the above crude mutant cube strategy is better than the 2-ply bot but that if it was the only way people played gamblegammon on a different planet, then doubling as soon as winning the opening roll would be the correct cube action that wins more points than not doubling. I hope this is clear now, because I don't know how else I can explain this. However, I don’t think 4 trials is enough. Your strategy has huge variance. Have you calculated the statistical significance as suggested by one of the earlier responders? I recall that he suggested a similar experiment with lower variance to reduce the required number of trials, but you didn't want to try it. I can't find that post at the moment, so I don’t know how many trials he calculated, but since your cube can get very high you would inevitably need more trials. You must be thinking of the first experiment that I had mention, in which the mutant would double/take/drop totally randomly. In that the cube has gone astronomically high and I abandoned it after only 30,000 games since I realized that even a million trials may not be enough, let alone a few hundred thousands that was suggested to me. In the above experiment the variance is surely big but I wouldn't say huge. I agree that 20,000 trials for each mutant variant is barely enough to give a glimpse of the possible results. With my now shared scripts, nothing prevents anyone to run as many trials as they consider enough. (I may do some more myself also if I find the time for it). My preliminary results may be considered well enough indicators to justify pursuing the experiment further with more trials. MK
Re: Interesting question/experiment about value of cube ownership
On 3/19/2024 3:54 AM, Ian Shaw wrote: MK "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." Agreed. Against a worse player, you can take with fewer winning chances. If your opponent will give up enough equity in errors to overcome the error of the bad take (and your own subsequent errors), then you should still come out ahead. I hope you are realizing that you are agreeing with the bot, not with me. What you quoted from me above was in response to your previously saying: "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. Would you drop if you knew that the mutant would roll 77? You wouldn't. (Just exaggerating to make a point, while reminiscing how Jellyfish was not only rolling 77's but shamelessly playing them to escape 6-primes:) Once the mutant conditionally pre-doubles, (i.e. if rules allow it, in case it wins the opening roll), you will become hostage to its strategy, or in better sounding words, you will be dancing to its tune... ;) Reaching a D/P later won't help you either because the mutant will not drop and will force you to keep playing until the last roll, perhaps trading the cube more times back and forth. Letting the bot play for both side after the "opening double" actually defeats the purpose of the experiment but since there is no "separately existing, fully functional mutant bot (that would play like me;)" to make it play against GnuBG 2-ply, this is the only way we can do it and it's better than nothing. So, this way the really "semi-mutant" play will lose but it still will not lose more than what would be expected from the cube error rate that the mutant incurs from this "opening double". This alone is enough to prove that the currently dogmatized "cube skill theory" is a jarful of cow chip cookies... MK
RE: Interesting question/experiment about value of cube ownership
MK: 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. 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? -- Ian
RE: Interesting question/experiment about value of cube ownership
MK: 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. These sound similar enough that I'll combine them. Overall, the mutant strategy if doubling as soon as you had an advantage lost 0.1343 points per game. Always doubling immediately lost 0.36 ppg. So, not doubling until you are winning appears to be a better strategy than always doubling. But, as you expected, the mutant strategy isn't as good as the current cube algorithm, which loses 0 ppg. However, I don’t think 4 trials is enough. Your strategy has huge variance. Have you calculated the statistical significance as suggested by one of the earlier responders? I recall that he suggested a similar experiment with lower variance to reduce the required number of trials, but you didn't want to try it. I can't find that post at the moment, so I don’t know how many trials he calculated, but since your cube can get very high you would inevitably need more trials.
RE: Interesting question/experiment about value of cube ownership
MK "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." Agreed. Against a worse player, you can take with fewer winning chances. If your opponent will give up enough equity in errors to overcome the error of the bad take (and your own subsequent errors), then you should still come out ahead.
Re: Interesting question/experiment about value of cube ownership
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
Fwd: Interesting question/experiment about value of cube ownership
MK, You wrote "Not the "equity" but the "equity difference" between the "from" position and the "to" position." I can't see any difference in outcome between selecting the play that maximises the equity of the move made, and maximising the equity gain between the current position and the new position. The latter option just adds an unnecessary subtraction step, so I doubt that's how it's programmed. I agree that the Temp Map you posted is showing the equity with doubles allowed. I've put then into a spreadsheet so you can see the calculations. https://docs.google.com/spreadsheets/d/17XFvQPvWNqGMRgZScl2qcTW2ovNeCISq/edit?usp=sharing=117015456330598325471=true=true The equity of 31 after returning to the opening position is +0.219. The equity after an opening 31 is also +0.219. I conclude that there is no problem with the equity calculation that would affect how gnubg plays. The temp map was a later addition to gnubg, so I don't think it's used in the luck calculation. Even if the luck calculation is down as per the temperature map, and there is an error in the luck calculation of the opening roll, it won't permeate through to other rolls. The luck calculation is based on the actual roll compared to the other 21 (14 in the opening) possible rolls. The luck of 31 after returning to the opening position is +0.112. It's a good roll but not as good as any double. It's just above the average of +0.107. The worst roll is 14 at -0.113. The luck of an opening 31 is +0.219. It's a great roll, compared to the average of 0.000. The worst roll is 14 at -0.219. You want to make a distinction between the game not started being on roll before the move. For example, if you tossed a coin to see who started and then the winner rolls any non-double and plays it. Then winning the opening roll would show a luck of +0.052. The luck of an opening 31 is +0.167. This adds to +0.219, the same as above. This all seems consistent to me. Your argument about a fallacy appears to be a semantic one. When I say, "the equity before the opening roll is zero", I'm aware that the opening roll also defines who rolls first, and I'm using it in that context. If the opening roll were a coin toss, I wouldn’t speak in the same terms. I would say, "the equity before the toss is zero" because that's the average equity of all 30 possible outcomes (player 1 wind the toss & rolls, player 2 wins the toss and rolls). I would also say, "the equity having won the toss is +0.052 before rolling" because that's the average equity of the remaining 15 possible outcomes. Do you agree with the preceding paragraph? 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. "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. A couple of final points. I'm sure the match equity tables are calculated correctly. The starting player of any subsequent game is equally likely, so the equity of each game starts at zero. I did read some of the old rgb threads. They descended into rudeness and I lost interest. For some reason, your last 2 messages got caught in my spam filter, hence the late reply. Regards, Ian -Original Message- From: MK Sent: Wednesday, March 6, 2024 9:35 PM To: Ian Shaw ; bug-gnubg@gnu.org Cc: Philippe Michel Subject: Re: Interesting question/experiment about value of cube ownership On 3/4/2024 5:26 AM, Ian Shaw wrote: Since at least you care to continue this discussion, I will invest more of my time and effort mainly for the sake of improving GnuBG. > Sorry, MK, I didn't read back over the old threads, It was in my a previous post in this current thread here but it's no big deal. However, if you are serious about discussing this issue, which one of many related ones, you really need to read at least this thread in RGB (which I had mentioned in my last post): https://groups.google.com/g/rec.games.backgammon/c/QU1jM9aatO0/m/peIBhLJNAgAJ There is a lot in there, including a bug that I had pointed out in "analysis.c" that had been there since 2014, which is still there. See lines 243-246 in 2022 and 272-275 in current version: https://cvs.savannah.gnu.org/viewvc/gnubg/gnubg/analysis.c?revision=1.241=markup https://cvs.savannah.gnu.org/viewvc/gnubg/gnubg/analysis.c?revision=1.263=markup Too bad that the development/maintenance team isn't hearing me. > Yo
Re: Interesting question/experiment about value of cube ownership
Cat got your tongues? Meow... ;) MK
Re: Interesting question/experiment about value of cube ownership
On 3/4/2024 5:26 AM, Ian Shaw wrote: Since at least you care to continue this discussion, I will invest more of my time and effort mainly for the sake of improving GnuBG. Sorry, MK, I didn't read back over the old threads, It was in my a previous post in this current thread here but it's no big deal. However, if you are serious about discussing this issue, which one of many related ones, you really need to read at least this thread in RGB (which I had mentioned in my last post): https://groups.google.com/g/rec.games.backgammon/c/QU1jM9aatO0/m/peIBhLJNAgAJ There is a lot in there, including a bug that I had pointed out in "analysis.c" that had been there since 2014, which is still there. See lines 243-246 in 2022 and 272-275 in current version: https://cvs.savannah.gnu.org/viewvc/gnubg/gnubg/analysis.c?revision=1.241=markup https://cvs.savannah.gnu.org/viewvc/gnubg/gnubg/analysis.c?revision=1.263=markup Too bad that the development/maintenance team isn't hearing me. You asked earlier about the GNUBG ID I used. It was: 4HPwATDgc/ABMA:cAkA This is the ID obtained after the sequence I suggested: 4HPwATDgc/ABMA:cAkA They are identical, so there is no indication in the ID to indicate whether it is the opening roll. Let's clarify things. The starting position when you open GnuBG is 4HPwATDgc/ABMA:cAgAAAE at which analyze functions aren't yet available. 4HPwATDgc/ABMA:cAkAAAE (g changed to k) sets the game started flag (with nothing happened yet) and analyze functions become available. 4HPwATDgc/ABMA:cAg is the same position with the stupid JacKoby on :( Sorry for not being more careful. It makes a slight -0.0075 difference in the average equity of the position (+0.0989 vs +0.1064). The Contact Net does not have an input for Opening Roll, which makes sense. The bot plays by maximizing the equity of the next position. The opening layout – with doubles prohibited - is never the next position. Not the "equity" but the "equity difference" between the "from" position and the "to" position. The starting position has an average equity just like any other position except that it has two different equities depending on its initial and subsequent (recycled) occurrences. This is the issue here. Comparing evaluation, Rollout as Normal Position, Rollout as Initial Position, we can see that the evaluation is close to the value of the rollout. "Close" but not the "same" because the evaluation is based on erroneously including doubles in the average position equity even in the initial occurrence of the starting position! See the bug in the code above, which is only part of the reason. (Also see the attached temp map and eval images). The rollout as the initial position is lower since it doesn’t include those useful doubles. That's why I had asked if bot's auto-playing was the same as roll-outs... If you paste the 4HPwATDgc/ABMA:cAkAAAE and look at the temperature map, you can see that the average position equity of +0.1064 includes doubles and is almost twice what it should be +0.0521 (a difference of +0.0543). This makes all subsequent equity and luck calculations wrong! since they are all based on the equity difference between two positions, before and after what is rolled (and how it's played). If a bot is claimed to be superior to humans, it can't contain such inaccuracies... I don’t think the value of 0.36 ppg for cube ownership that we both obtained is a "coincidence". I think it's evidence that your script is a good emulation of a rollout. It wouldn't be a coincidence for it to be "close enough", based the above facts, but it being exactly the same must have been a coincidence. If you think 0.36 is inaccurate, I’m open to persuasion. Do you have a theory as to why it’s wrong, or what you think the correct value is? I believe I have provided enough factual evidence above... Regarding the equity at the beginning of the game, I’m not aware of any “age-old fallacy”. It's well established that winning the opening roll confers an advantage. I don’t think there's any theory that says the equity (between equal opponents) is non-zero before the opening roll. There wasn't/isn't. That's what I'm calling "a fallacy" because the equity between equal players before the "opening roll" isn't zero. You all confuse "before the game starts" and "before the opening roll" because in GambleGammon (what I call the BG variant played with the cube), deciding who goes first and the opening roll happen simultaneously. Imagine we are equal players wanting to play just one game. You roll your die with your eyes closed and ask who won the opening roll. I say you did. At that point you are on roll but haven't rolled the opening roll yet, (your eyes are still closed and you don't yet know the numbers lying on the board). For having won the opening roll, you already accrued an average +0.0521 equity. In fact, I'd argue that with the cube centered, you should be
RE: Interesting question/experiment about value of cube ownership
Sorry, MK, I didn't read back over the old threads, to see what links you had referenced, before I replied. It was late at night, and I was using my phone rather than a PC. In that case, I must have misunderstood what you meant by, "Is making the bot auto-play the same as doing rollouts?" It seemed to me that, since only you know what’s in your scripts, it was most likely that you were asking about rollouts are, although that also seemed unlikely. You asked earlier about the GNUBG ID I used. It was: 4HPwATDgc/ABMA:cAkA This is the ID obtained after the sequence I suggested: 4HPwATDgc/ABMA:cAkA (Thanks for the link to the BKGM post. I’d forgotten about it, but fortunately it had recently been discussed on Daily Gammon, where someone else also found your 4-roll solution!) They are identical, so there is no indication in the ID to indicate whether it is the opening roll. Therefore, the evaluation is the same. The Contact Net does not have an input for Opening Roll, which makes sense. The bot plays by maximizing the equity of the next position. The opening layout – with doubles prohibited - is never the next position. Comparing evaluation, Rollout as Normal Position, Rollout as Initial Position, we can see that the evaluation is close to the value of the rollout. The rollout as the initial position is lower since it doesn’t include those useful doubles. Ply Cube Pwin Pwin2 Pwin3 Plose Plose2 Plose3 E cubeless E No Double E Double/Take Action 2 eval n/a 0.5248 0.1495 0.0069 0.4752 0.1248 0.0053 +0.0759 +0.0982 ‑0.1712 NB (23.0%) 2 1Cen 0.5256 0.1532 0.0082 0.4744 0.1287 0.0053 +0.0785 +0.1187 Normal 2Opp 0.5274 0.1521 0.0074 0.4726 0.1295 0.0056 +0.1586 -0.2127 NB (27.3%) 2 1Cen 0.5130 0.1461 0.0069 0.4870 0.1336 0.0058 +0.0395 +0.0580 Initial 2Opp 0.5147 0.1468 0.0068 0.4853 0.1332 0.0059 +0.0881 -0.3002 NB (27.6%) I don’t think the value of 0.36 ppg for cube ownership that we both obtained is a "coincidence". I think it's evidence that your script is a good emulation of a rollout. If you think 0.36 is inaccurate, I’m open to persuasion. Do you have a theory as to why it’s wrong, or what you think the correct value is? Regarding the equity at the beginning of the game, I’m not aware of any “age-old fallacy”. It's well established that winning the opening roll confers an advantage. I don’t think there's any theory that says the equity (between equal opponents) is non-zero before the opening roll. Indeed, the construction of most match equity tables is based on the equity at the start of the game being zero (unless they are assuming unequal players). Finally, please lay off the disparagement. “What will it take for you guys to give some credit/benefit of the doubt to others than just yourselves?” is unnecessary. I’m not sure which group of ‘guys’ you lump me into; I’m just a gnubg user and a moderate player. I give lots of credit to loads of people who have contributed far more to backgammon than I ever will. Ian --Original Message- From: MK mailto:playbg-...@yahoo.com>> Sent: Monday, March 4, 2024 3:17 AM To: Ian Shaw mailto:ian.s...@riverauto.co.uk>>; bug-gnubg@gnu.org<mailto:bug-gnubg@gnu.org> Cc: Philippe Michel mailto:philippe.mich...@free.fr>> Subject: Re: Interesting question/experiment about value of cube ownership On 3/1/2024 6:02 PM, Ian Shaw wrote: > "Is making the bot auto-play the > same as doing rollouts?" > > It sounds like you are asking what a rollout is? I wasn't. > https://www.gnu.org/software/gnubg/manual/html_node/Introduction-to-ro > llouts.html I had read it many a times before. > https://www.bkgm.com/openings/rollouts.html This is funny. You are referring me back to the same link that I had given in my reply to you on February 10, here in this very same thread... :) What will it take for you guys to give some credit/benefit of the doubt to others than just yourselves? > Your auto-play script sounds very similar but I don't know exactly > what it does. Fair enough. My explaining in my previous post about what it does in this specific experiment was probably too brief and not very clear. > The main difference would be that you can make your scripts double > using your own algorithm. Yes, in some experiment I did that but not in this one. > Or indeed, veer from the bot's best chequer play. I haven't done any checker experiments yet but I may. > Minor differences might be the play settings for search depth and > pruning. Okay. You now made me realize that even unchecking all of the optional settings in roll-outs, it will not be the same as bot auto-playing. We both must have come up with the same 0.36 ppg by coincidence. Regardless, I believe that it's inaccurate in eith
Re: Interesting question/experiment about value of cube ownership
On 3/3/2024 8:16 PM, MK wrote: The next day after that, I checked it in Snowie and I posted a comprehensive recap about the subject. See: Sorry I forgot to give the link. Here it is: https://groups.google.com/g/rec.games.backgammon/c/rFZyUcg8IPQ/m/gxuWiERmCAAJ MK
Re: Interesting question/experiment about value of cube ownership
On 3/1/2024 6:02 PM, Ian Shaw wrote: "Is making the bot auto-play the same as doing rollouts?" It sounds like you are asking what a rollout is? I wasn't. https://www.gnu.org/software/gnubg/manual/html_node/Introduction-to-rollouts.html I had read it many a times before. https://www.bkgm.com/openings/rollouts.html This is funny. You are referring me back to the same link that I had given in my reply to you on February 10, here in this very same thread... :) What will it take for you guys to give some credit/benefit of the doubt to others than just yourselves? Your auto-play script sounds very similar but I don't know exactly what it does. Fair enough. My explaining in my previous post about what it does in this specific experiment was probably too brief and not very clear. The main difference would be that you can make your scripts double using your own algorithm. Yes, in some experiment I did that but not in this one. Or indeed, veer from the bot's best chequer play. I haven't done any checker experiments yet but I may. Minor differences might be the play settings for search depth and pruning. Okay. You now made me realize that even unchecking all of the optional settings in roll-outs, it will not be the same as bot auto-playing. We both must have come up with the same 0.36 ppg by coincidence. Regardless, I believe that it's inaccurate in either case anyway. Try this manual sequence, and evaluate the next move. This gets you back to the start position. But doubles would be allowed, so the bot evaluation should not be the same as that of the opening roll. 64: 13/7 24/20 33: 24/18* 13/7 21: bar/24 20/18* 51: bar/24 18/13 32: 18/13 Ah, it's getting interesting. GnuBG doesn't know the difference between the initial and recycled "starting position". XG does but wrongly, backwards. Snowie did but adjusted it by the wrong amount. I first wrote about this problem with XG in response to a related discussion in RGB, on Dec 26, 2022. See: https://groups.google.com/g/rec.games.backgammon/c/RgcdohfwyYs/m/NtnrIaUTCAAJ Then I checked the same problem in Gnubg and I posted about it on the same day. See: https://groups.google.com/g/rec.games.backgammon/c/QU1jM9aatO0/m/EBkivQ3vBQAJ The next day after that, I checked it in Snowie and I posted a comprehensive recap about the subject. See: This is a very important issue regarding the ages-old fallacy that the equity at the start of the game, i.e. the equity of the starting position, is zero. It's not! Anyone who really cares about the accuracy of bots' equity calculations should make time to read the above three threads or at least the first article in each, because miscalculating the equity of the opening moves ripple through the following moves, causing them all to be wrong even if slightly but also compoundingly depending on which bot does what how... Incidentally, in the third thread above, you'll find a link to one of my only two posts that ever appeared on BKGM, this one being about the shortest possible moves to recycle to the starting position. See: https://www.bkgm.com/rgb/rgb.cgi?view+68 My 4-rolls solution allowed doubles and I had explained later in RBG that it would be legal not only if initial doubles are allowed in some variants but also when we recycled to the starting position more than once. See: https://groups.google.com/g/rec.games.backgammon/c/8vUhA8fpEN0/m/nXMtpFOrmFoJ So, yes, I was the one who not only didn't assume you could recycle only once but also tested the three bots to see if/how they would treat the starting position if it occurred multiple times. I guess I just like to not stop until I get to the bottom of things... MK
Re: Interesting question/experiment about value of cube ownership
"Is making the bot auto-play the
same as doing rollouts?"
It sounds like you are asking what a rollout is? There are plenty of resources
on the net.
https://www.gnu.org/software/gnubg/manual/html_node/Introduction-to-rollouts.html
https://www.bkgm.com/openings/rollouts.html
Your auto-play script sounds very similar but I don't know exactly what it does.
The main difference would be that you can make your scripts double using your
own algorithm. Or indeed, veer from the bot's best chequer play.
Minor differences might be the play settings for search depth and pruning.
Try this manual sequence, and evaluate the next move. This gets you back to the
start position. But doubles would be allowed, so the bot evaluation should not
be the same as that of the opening roll.
64: 13/7 24/20
33: 24/18* 13/7
21: bar/24 20/18*
51: bar/24 18/13
32: 18/13
From: MK
Sent: Friday, March 1, 2024 10:46:29 PM
To: Ian Shaw ; bug-gnubg@gnu.org
Cc: Philippe Michel
Subject: Re: Interesting question/experiment about value of cube ownership
On 3/1/2024 6:22 AM, Ian Shaw wrote:
> 27000 trials at 0-ply and 1-ply. 135000 trials at 2-ply.
> There’s almost no difference in value between the rollout
> that took 8 minutes and the one that tool 23 hours, which
> speaks to the strength of the initial evaluation.
This is good to know. Can you post the position ID so that
there is no misassumptions.
> The rollout suggests that the value of cube ownership in
> the initial position is worth about 0.36 points.
This is very interesting. Is making the bot auto-play the
same as doing rollouts? During the past weeks, I have done
12 different experiments with 20,000 games in each. I'm now
putting it all on a neatly organized web page which I will
share here soon.
Six of my experiments were about the value of winning the
opening roll and/or owning the cube from the start (i.e.
before the first move for the mutant but before the second
move for the bot since it always auto-plays and there is no
way to intercept before its first move).
Very interestingly I also came up with 0.36 ppg and 0.28 ppc
("points per cube" decision).
I collected and tabulated quite a lot of various stats which
will be on my web page, along with the actual scripts I ran,
saved games, log files, etc. so that you all can derive your
own conclusions with or without replicating my experiments,
with the important ones being about "mutant cube strategies".
> One thing to notice is that the rollout has the on-roll
> player winning about 1% less than the evaluations posted
> by MK. I think this is due to the evaluation assuming that
> initial doubles may be played, whereas I set the rollout
> to play as the initial position.
I'm not sure what you are referring to here. What I had posted
was the GnuBG's 2-ply evaluation of the opening position (i.e.
without initial doubles). So, that 1% must be the difference
between that and your rollouts?? (as well as my experiments?)
> I haven’t found a way toa ask gnubg for an evaluation for the
> initial roll. Is there one?
> You could get a 1-ply evaluation by combining all 15 0-ply
> evaluations of the first roll, and so forth.
I don't understand these. Hopefully others will pitch in their
comments in response...
MK
> *From:*bug-gnubg-bounces+ian.shaw=riverauto.co...@gnu.org
> *On Behalf Of *Ian Shaw
> via Bug reports for and
> general discussion about GNU Backgammon.
> *Sent:* Thursday, February 8, 2024 11:39 AM
> *To:* playbg-...@yahoo.com; bug-gnubg@gnu.org
> *Cc:* Philippe Michel
> *Subject:* RE: Interesting question/experiment about value of cube ownership
>
> It just so happens that I rolled out the opening position a few days ago for
> another reason. This
> was at 7-away 7-away rather than $ play, because I was interested in match
> play. I doubt that makes
> a huge difference.
>
> This was using gnubg-1_08_dev-20240103-setup.exe not the newest
> gnubg-1_08_001-20240204-setup.exe
> that Philippe released recently.
>
> Philippe, am I correct in thinking that the cube handling on these two
> versions is the same? Your
> announcement emails both include the same comment.
>
> “Improvement to cube decisions at 0- and 1-ply and weaker levels. Cube error
> rates are approximately
> halved and the repartition of errors (premature doubles vs. missed doubles
> vs. take or pass errors)
> is now similar to higher plies instead of being mostly premature doubles.”
>
> The rollout results indicate about 1% fewer wins for the roller than the
> evaluations.
>
> 4HPwATDgc/ABMA:cAngAAAE
>
> Cube analysis
>
> Rollout cubeless equity +0.0408 (Money: +0.0396)
>
> Cubeful equities:
>
> 1. No double +0.0655
>
> 2. Double, pass+1. (+0.9345)
>
> 3. Dou
Re: Interesting question/experiment about value of cube ownership
On 3/1/2024 6:22 AM, Ian Shaw wrote:
27000 trials at 0-ply and 1-ply. 135000 trials at 2-ply.
There’s almost no difference in value between the rollout
that took 8 minutes and the one that tool 23 hours, which
speaks to the strength of the initial evaluation.
This is good to know. Can you post the position ID so that
there is no misassumptions.
The rollout suggests that the value of cube ownership in
the initial position is worth about 0.36 points.
This is very interesting. Is making the bot auto-play the
same as doing rollouts? During the past weeks, I have done
12 different experiments with 20,000 games in each. I'm now
putting it all on a neatly organized web page which I will
share here soon.
Six of my experiments were about the value of winning the
opening roll and/or owning the cube from the start (i.e.
before the first move for the mutant but before the second
move for the bot since it always auto-plays and there is no
way to intercept before its first move).
Very interestingly I also came up with 0.36 ppg and 0.28 ppc
("points per cube" decision).
I collected and tabulated quite a lot of various stats which
will be on my web page, along with the actual scripts I ran,
saved games, log files, etc. so that you all can derive your
own conclusions with or without replicating my experiments,
with the important ones being about "mutant cube strategies".
One thing to notice is that the rollout has the on-roll
player winning about 1% less than the evaluations posted
by MK. I think this is due to the evaluation assuming that
initial doubles may be played, whereas I set the rollout
to play as the initial position.
I'm not sure what you are referring to here. What I had posted
was the GnuBG's 2-ply evaluation of the opening position (i.e.
without initial doubles). So, that 1% must be the difference
between that and your rollouts?? (as well as my experiments?)
I haven’t found a way toa ask gnubg for an evaluation for the
initial roll. Is there one?
You could get a 1-ply evaluation by combining all 15 0-ply
evaluations of the first roll, and so forth.
I don't understand these. Hopefully others will pitch in their
comments in response...
MK
*From:*bug-gnubg-bounces+ian.shaw=riverauto.co...@gnu.org
*On Behalf Of *Ian Shaw via Bug reports for and
general discussion about GNU Backgammon.
*Sent:* Thursday, February 8, 2024 11:39 AM
*To:* playbg-...@yahoo.com; bug-gnubg@gnu.org
*Cc:* Philippe Michel
*Subject:* RE: Interesting question/experiment about value of cube ownership
It just so happens that I rolled out the opening position a few days ago for another reason. This
was at 7-away 7-away rather than $ play, because I was interested in match play. I doubt that makes
a huge difference.
This was using gnubg-1_08_dev-20240103-setup.exe not the newest gnubg-1_08_001-20240204-setup.exe
that Philippe released recently.
Philippe, am I correct in thinking that the cube handling on these two versions is the same? Your
announcement emails both include the same comment.
“Improvement to cube decisions at 0- and 1-ply and weaker levels. Cube error rates are approximately
halved and the repartition of errors (premature doubles vs. missed doubles vs. take or pass errors)
is now similar to higher plies instead of being mostly premature doubles.”
The rollout results indicate about 1% fewer wins for the roller than the
evaluations.
4HPwATDgc/ABMA:cAngAAAE
Cube analysis
Rollout cubeless equity +0.0408 (Money: +0.0396)
Cubeful equities:
1. No double +0.0655
2. Double, pass +1. (+0.9345)
3. Double, take -0.2999 (-0.3654)
Proper cube action: No double, take (28.1%)
Rollout details:
Centered 1-cube:
0.5129 0.1480 0.0083 - 0.4871 0.1351 0.0073 CL +0.0408 CF +0.0655
[0.0001 0.0002 0.0001 - 0.0001 0.0001 0.0001 CL 0.0003 CF 0.0008]
gnubg owns 2-cube:
0.5156 0.1522 0.0091 - 0.4844 0.1375 0.0150 CL +0.1216 CF -0.2999
[0.0001 0.0002 0.0001 - 0.0001 0.0002 0.0002 CL 0.0007 CF 0.0012]
Full cubeful rollout with variance reduction
186624 games, rollout as initial position, Mersenne Twister dice generator with
seed 823069761
Play: world class 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]
Cheers,
Ian
-Original Message-
From: bug-gnubg-bounces+ian.shaw=riverauto.co...@gnu.org
<mailto:bug-gnubg-bounces+ian.shaw=riverauto.co...@gnu.org>mailto:bug-gnubg-bounces+ian.shaw=riverauto.co...@gnu.org>> On Behalf Of MK
Sent: Thursday, February 8, 2024 2:23 AM
To: bug-gnubg@gnu.org <mailto:bug-gnubg@gnu.org>
Subject: Interesting question/experiment about value of cube ownership
I'm chugging along with my mutant cube skill experiments as I can spare time, saving all games,
which I will share on my web site, when I'm done, along with my scripts.
While doing the double at
RE: Interesting question/experiment about value of cube ownership
I've rolled at the opening position again, at money play. 27000 trials at 0-ply and 1-ply. 135000 trials at 2-ply. There's almost no difference in value between the rollout that took 8 minutes and the one that tool 23 hours, which speaks to the strength of the initial evaluation. The rollout suggests that the value of cube ownership in the initial position is worth about 0.36 points. One thing to notice is that the rollout has the on-roll player winning about 1% less than the evaluations posted by MK. I think this is due to the evaluation assuming that initial doubles may be played, whereas I set the rollout to play as the initial position. Ply Cube Pwin Pwin2 Pwin3 Plose Plose2 Plose3 Ecl End Edt Action 0 1Cen 0.5135 0.1425 0.0065 0.4865 0.1310 0.0055 +0.0395 +0.0599 8 m 2Opp 0.5141 0.1428 0.0064 0.4859 0.1317 0.0056 +0.0804 -0.2941 NB (27.4%) 1 1Cen 0.5136 0.1472 0.0071 0.4864 0.1352 0.0059 +0.0405 +0.0594 38 m 2Opp 0.5136 0.1495 0.0074 0.4864 0.1350 0.0060 +0.0867 -0.2977 NB (27.5%) 2 1Cen 0.5130 0.1461 0.0069 0.4870 0.1336 0.0058 +0.0395 +0.0580 23 h 2Opp 0.5147 0.1468 0.0068 0.4853 0.1332 0.0059 +0.0881 -0.3002 NB (27.6%) I haven't found a way toa ask gnubg for an evaluation for the initial roll. Is there one? You could get a 1-ply evaluation by combining all 15 0-ply evaluations of the first roll, and so forth. Cheers, Ian From: bug-gnubg-bounces+ian.shaw=riverauto.co...@gnu.org On Behalf Of Ian Shaw via Bug reports for and general discussion about GNU Backgammon. Sent: Thursday, February 8, 2024 11:39 AM To: playbg-...@yahoo.com; bug-gnubg@gnu.org Cc: Philippe Michel Subject: RE: Interesting question/experiment about value of cube ownership It just so happens that I rolled out the opening position a few days ago for another reason. This was at 7-away 7-away rather than $ play, because I was interested in match play. I doubt that makes a huge difference. This was using gnubg-1_08_dev-20240103-setup.exe not the newest gnubg-1_08_001-20240204-setup.exe that Philippe released recently. Philippe, am I correct in thinking that the cube handling on these two versions is the same? Your announcement emails both include the same comment. "Improvement to cube decisions at 0- and 1-ply and weaker levels. Cube error rates are approximately halved and the repartition of errors (premature doubles vs. missed doubles vs. take or pass errors) is now similar to higher plies instead of being mostly premature doubles." The rollout results indicate about 1% fewer wins for the roller than the evaluations. 4HPwATDgc/ABMA:cAngAAAE Cube analysis Rollout cubeless equity +0.0408 (Money: +0.0396) Cubeful equities: 1. No double +0.0655 2. Double, pass+1. (+0.9345) 3. Double, take-0.2999 (-0.3654) Proper cube action: No double, take (28.1%) Rollout details: Centered 1-cube: 0.5129 0.1480 0.0083 - 0.4871 0.1351 0.0073 CL +0.0408 CF +0.0655 [0.0001 0.0002 0.0001 - 0.0001 0.0001 0.0001 CL 0.0003 CF 0.0008] gnubg owns 2-cube: 0.5156 0.1522 0.0091 - 0.4844 0.1375 0.0150 CL +0.1216 CF -0.2999 [0.0001 0.0002 0.0001 - 0.0001 0.0002 0.0002 CL 0.0007 CF 0.0012] Full cubeful rollout with variance reduction 186624 games, rollout as initial position, Mersenne Twister dice generator with seed 823069761 Play: world class 2-ply cubeful prune [world class] keep the first 0 0-ply moves and up to 8 more moves within equity 0.16 Skip pruning for 1-ply moves. Cube: 2-ply cubeful prune [world class] Cheers, Ian -Original Message- From: bug-gnubg-bounces+ian.shaw=riverauto.co...@gnu.org<mailto:bug-gnubg-bounces+ian.shaw=riverauto.co...@gnu.org> mailto:bug-gnubg-bounces+ian.shaw=riverauto.co...@gnu.org>> On Behalf Of MK Sent: Thursday, February 8, 2024 2:23 AM To: bug-gnubg@gnu.org<mailto:bug-gnubg@gnu.org> Subject: Interesting question/experiment about value of cube ownership I'm chugging along with my mutant cube skill experiments as I can spare time, saving all games, which I will share on my web site, when I'm done, along with my scripts. While doing the double at > 50% experiment, I remembered an old question I had asked in RGB about a year ago: What if the winner of the opening roll is allowed pre-double? See thread: https://groups.google.com/g/rec.games.backgammon/c/BVEnaqGM6dg/m/2c685q4DAAAJ When you evaluate the opening position in GnuBG, this is what you get: = Position ID: 4HPwATDgc/ABMA Match ID:cAkA Evaluator:Contact Win W(g)W(bg) L(g)L(bg) EquityCubeful static: 52.115.4 0.813.0 0.8 +0.067+0.084 1 ply: 52.714.8 0.912.9 0.5 +0.076+0.098 2 ply: 52.514.9 0.712.5
Re: Interesting question/experiment about value of cube ownership
On 2/11/2024 6:01 AM, EDWARD GOLDBERG wrote: Can I be removed from this email list please? https://lists.gnu.org/mailman/options/bug-gnubg/
Re: Interesting question/experiment about value of cube ownership
Can I be removed from this email list please?
> On Feb 10, 2024, at 9:59 PM, MK wrote:
>
> Hi Ian,
>
> Thanks for the additional info. Unfortunately it didn't help
> me understand anything better or answer my own question. I'm
> still trying and hope that you or others will continue this
> subject to help me with it, which will benefit all in the end.
>
> For the cubeless equity of the opening position, I'm going by
> the rollout results, (which had taken 7 months to do), from:
>
> https://bkgm.com/openings/rollouts.html
>
> In the summary section towards the end, it says:
>
> "Your average equity if you win the opening roll is +.0393."
>
> So, if I run 10,000 cubeless games with "X" always winning the
> opening roll, "X" will win 393 points, i.e. 3.93%, more than "O"?
>
> =
> When the mutant ("X") is on roll (i.e. won the opening roll),
>
> GNUbg ID: 4HPwATDgc/ABMA:cAkA evaluate says:
>
>Win W(g)W(bg) L(g)L(bg) EquityCubeful
> 2 ply: 52.514.9 0.712.5 0.5 +0.076+0.099
>
> 2-ply cubeless equity +0.076
> 52.5 14.9 0.7 - 47.5 12.5 0.5
> Cubeful equities:
> 1. No double +0.099
> 2. Double, pass+1.000 (+0.901)
> 3. Double, take-0.171 (-0.270)
>
> How do I relate any of these numbers to the +0.0393 above? Why is
> the cubeless equity +0.076?
>
> I suppose the cubeful equity +0.099 is somehow extrapolated using
> some formulas and I should accept it as just that?
>
> =
>
> When I set cube to 2 owned by the bot ("O"), with "X" on roll,
>
> GNUbg ID: 4HPwATDgc/ABMA:QQkA evaluate says:
>
>Win W(g)W(bg) L(g)L(bg) EquityCubeful
> 2 ply: 52.514.9 0.712.5 0.5 +0.076-0.086
>
> Cubeless equity is the same. Shouldn't the cubeful equity be
> +0.076 - 0.171 = -0.095? Why is it -0.086? Which one is correct?
>
> =
>
> If I set the cube to 2 owned by mutant ("X") who is also on roll,
>
> GNUbg ID: 4HPwATDgc/ABMA:UQkA evaluate says:
>
>Win W(g)W(bg) L(g)L(bg) EquityCubeful
> 2 ply: 52.514.9 0.712.5 0.5 +0.076+0.255
>
> 2-ply cubeless equity +0.076
> 52.5 14.9 0.7 - 47.5 12.5 0.5
> Cubeful equities:
> 1. No double +0.255
> 2. Double, pass+1.000 (+0.745)
> 3. Double, take-0.171 (-0.426)
>
> Cubeless equity is still the same. Should I try to understand why
> the D/T is the same as centered cube but now the cubeful equity is
> +0.255? Is it +0.076 + 0.171 = +0.247 close enough or what is it??
>
> =
>
> So, again, what I would like to know is if I run 10,000 games from
> each of the above three positions, what results should I expect?
>
> In other words, which one of these many different equity numbers
> (with no obvious correspondences for me) do I use to multiply by
> 10,000 to predict by how much the mutant will win or lose?
>
> MK
>
Re: Interesting question/experiment about value of cube ownership
Hi Ian,
Thanks for the additional info. Unfortunately it didn't help
me understand anything better or answer my own question. I'm
still trying and hope that you or others will continue this
subject to help me with it, which will benefit all in the end.
For the cubeless equity of the opening position, I'm going by
the rollout results, (which had taken 7 months to do), from:
https://bkgm.com/openings/rollouts.html
In the summary section towards the end, it says:
"Your average equity if you win the opening roll is +.0393."
So, if I run 10,000 cubeless games with "X" always winning the
opening roll, "X" will win 393 points, i.e. 3.93%, more than "O"?
=
When the mutant ("X") is on roll (i.e. won the opening roll),
GNUbg ID: 4HPwATDgc/ABMA:cAkA evaluate says:
Win W(g)W(bg) L(g)L(bg) EquityCubeful
2 ply: 52.514.9 0.712.5 0.5 +0.076+0.099
2-ply cubeless equity +0.076
52.5 14.9 0.7 - 47.5 12.5 0.5
Cubeful equities:
1. No double +0.099
2. Double, pass+1.000 (+0.901)
3. Double, take-0.171 (-0.270)
How do I relate any of these numbers to the +0.0393 above? Why is
the cubeless equity +0.076?
I suppose the cubeful equity +0.099 is somehow extrapolated using
some formulas and I should accept it as just that?
=
When I set cube to 2 owned by the bot ("O"), with "X" on roll,
GNUbg ID: 4HPwATDgc/ABMA:QQkA evaluate says:
Win W(g)W(bg) L(g)L(bg) EquityCubeful
2 ply: 52.514.9 0.712.5 0.5 +0.076-0.086
Cubeless equity is the same. Shouldn't the cubeful equity be
+0.076 - 0.171 = -0.095? Why is it -0.086? Which one is correct?
=
If I set the cube to 2 owned by mutant ("X") who is also on roll,
GNUbg ID: 4HPwATDgc/ABMA:UQkA evaluate says:
Win W(g)W(bg) L(g)L(bg) EquityCubeful
2 ply: 52.514.9 0.712.5 0.5 +0.076+0.255
2-ply cubeless equity +0.076
52.5 14.9 0.7 - 47.5 12.5 0.5
Cubeful equities:
1. No double +0.255
2. Double, pass+1.000 (+0.745)
3. Double, take-0.171 (-0.426)
Cubeless equity is still the same. Should I try to understand why
the D/T is the same as centered cube but now the cubeful equity is
+0.255? Is it +0.076 + 0.171 = +0.247 close enough or what is it??
=
So, again, what I would like to know is if I run 10,000 games from
each of the above three positions, what results should I expect?
In other words, which one of these many different equity numbers
(with no obvious correspondences for me) do I use to multiply by
10,000 to predict by how much the mutant will win or lose?
MK
RE: Interesting question/experiment about value of cube ownership
It just so happens that I rolled out the opening position a few days ago for another reason. This was at 7-away 7-away rather than $ play, because I was interested in match play. I doubt that makes a huge difference. This was using gnubg-1_08_dev-20240103-setup.exe not the newest gnubg-1_08_001-20240204-setup.exe that Philippe released recently. Philippe, am I correct in thinking that the cube handling on these two versions is the same? Your announcement emails both include the same comment. “Improvement to cube decisions at 0- and 1-ply and weaker levels. Cube error rates are approximately halved and the repartition of errors (premature doubles vs. missed doubles vs. take or pass errors) is now similar to higher plies instead of being mostly premature doubles.” The rollout results indicate about 1% fewer wins for the roller than the evaluations. 4HPwATDgc/ABMA:cAngAAAE Cube analysis Rollout cubeless equity +0.0408 (Money: +0.0396) Cubeful equities: 1. No double +0.0655 2. Double, pass+1. (+0.9345) 3. Double, take-0.2999 (-0.3654) Proper cube action: No double, take (28.1%) Rollout details: Centered 1-cube: 0.5129 0.1480 0.0083 - 0.4871 0.1351 0.0073 CL +0.0408 CF +0.0655 [0.0001 0.0002 0.0001 - 0.0001 0.0001 0.0001 CL 0.0003 CF 0.0008] gnubg owns 2-cube: 0.5156 0.1522 0.0091 - 0.4844 0.1375 0.0150 CL +0.1216 CF -0.2999 [0.0001 0.0002 0.0001 - 0.0001 0.0002 0.0002 CL 0.0007 CF 0.0012] Full cubeful rollout with variance reduction 186624 games, rollout as initial position, Mersenne Twister dice generator with seed 823069761 Play: world class 2-ply cubeful prune [world class] keep the first 0 0-ply moves and up to 8 more moves within equity 0.16 Skip pruning for 1-ply moves. Cube: 2-ply cubeful prune [world class] Cheers, Ian -Original Message- From: bug-gnubg-bounces+ian.shaw=riverauto.co...@gnu.org On Behalf Of MK Sent: Thursday, February 8, 2024 2:23 AM To: bug-gnubg@gnu.org Subject: Interesting question/experiment about value of cube ownership I'm chugging along with my mutant cube skill experiments as I can spare time, saving all games, which I will share on my web site, when I'm done, along with my scripts. While doing the double at > 50% experiment, I remembered an old question I had asked in RGB about a year ago: What if the winner of the opening roll is allowed pre-double? See thread: https://groups.google.com/g/rec.games.backgammon/c/BVEnaqGM6dg/m/2c685q4DAAAJ When you evaluate the opening position in GnuBG, this is what you get: = Position ID: 4HPwATDgc/ABMA Match ID:cAkA Evaluator:Contact Win W(g)W(bg) L(g)L(bg) EquityCubeful static: 52.115.4 0.813.0 0.8 +0.067+0.084 1 ply: 52.714.8 0.912.9 0.5 +0.076+0.098 2 ply: 52.514.9 0.712.5 0.5 +0.076+0.099 Cube analysis 2-ply cubeless equity +0.076 52.5 14.9 0.7 - 47.5 12.5 0.5 Cubeful equities: 1. No double +0.099 2. Double, pass+1.000 (+0.901) 3. Double, take-0.171 (-0.270) Proper cube action: No double, take (23.0%) = I have created a Python script to intervene if the human player wins the opening roll, to set the cube at 2 owned by the bot, and then to execute "end game" command, for the bot to play for both sides at the same checker and cube skill settings. So, you know the equity gained by winning the opening roll and the equity lost by making the cube error at the same time, before the first move. Can anyone tell me what I will be expecting to see after, let's say, 10,000 games, in terms of which side will win/lose by what percentage? BTW: I already know. ;) I'm asking to see how confident are you in GnuBG's equity and/or error calculations and how competent are you to make mathematical predictions? MK
Interesting question/experiment about value of cube ownership
I'm chugging along with my mutant cube skill experiments as I can spare time, saving all games, which I will share on my web site, when I'm done, along with my scripts. While doing the double at > 50% experiment, I remembered an old question I had asked in RGB about a year ago: What if the winner of the opening roll is allowed pre-double? See thread: https://groups.google.com/g/rec.games.backgammon/c/BVEnaqGM6dg/m/2c685q4DAAAJ When you evaluate the opening position in GnuBG, this is what you get: = Position ID:4HPwATDgc/ABMA Match ID: cAkA Evaluator: Contact Win W(g)W(bg) L(g)L(bg) EquityCubeful static: 52.115.4 0.813.0 0.8 +0.067+0.084 1 ply: 52.714.8 0.912.9 0.5 +0.076+0.098 2 ply: 52.514.9 0.712.5 0.5 +0.076+0.099 Cube analysis 2-ply cubeless equity +0.076 52.5 14.9 0.7 - 47.5 12.5 0.5 Cubeful equities: 1. No double +0.099 2. Double, pass+1.000 (+0.901) 3. Double, take-0.171 (-0.270) Proper cube action: No double, take (23.0%) = I have created a Python script to intervene if the human player wins the opening roll, to set the cube at 2 owned by the bot, and then to execute "end game" command, for the bot to play for both sides at the same checker and cube skill settings. So, you know the equity gained by winning the opening roll and the equity lost by making the cube error at the same time, before the first move. Can anyone tell me what I will be expecting to see after, let's say, 10,000 games, in terms of which side will win/lose by what percentage? BTW: I already know. ;) I'm asking to see how confident are you in GnuBG's equity and/or error calculations and how competent are you to make mathematical predictions? MK
