RE: No bugs, just a question
Hi Tim, What an awesome explanation. Thanks a lot. -- Ian -Original Message- From: Bug-gnubg On Behalf Of Timothy Y. Chow Sent: 06 July 2022 14:59 To: bug-gnubg@gnu.org Subject: Re: No bugs, just a question There is a subtle point about luck that is not well understood even by some professional mathematicians. In a series of games (or matches, but for simplicity let me focus on games), one must distinguish between 1. counting the number of games in which I was luckier, and 2. determining who was luckier overall on a roll-by-roll basis. The distinction is subtle, but very important, so let me belabor it a bit. For #2, what we do is to examine each roll individually, note how lucky it was, and add up the luck over all rolls in all games. For #1, what we do is to examine each game in turn and, *restricting our attention to only the rolls in that game*, determine who had more total luck. If I had more total luck in that game, then I declare that game to be a "game in which I was luckier"; otherwise, it's a game in which I was unluckier. Let me emphasize that in #1, we ignore *how much luckier* I was in that game. I could be massively luckier, or just barely luckier, but as long as I'm luckier, I declare that game to be one in which "I was luckier." Similarly, I ignore whether I was massively unluckier or just barely unluckier when declaring a game to be one in which I was unluckier. Now here is the crucial observation. It is entirely possible, and in fact common, for two players to be equally lucky in sense #2, and yet for there to be a highly lopsided count in sense #1. That is, I might be unluckier in many more games, and yet equally lucky on a roll-by-roll basis. This sounds like a contradiction, but it is not; for example, maybe I am unluckier in 90% of the games, but in each of those games, my net luck is -0.1 per game, whereas in the 10% of the games in which I am luckier, my net luck is +0.9 per game. Then I am much unluckier in sense #1 but equally lucky in sense #2. "Okay," you might grudgingly concede, "that's *possible*, but surely that's highly *unlikely*." If backgammon were purely a game of luck, then you're right; it would be highly unlikely. However, this is where skill comes in: The more skillful player will (almost always) be luckier in sense #1. This fact is highly counterintuitive to most people. After all, the more skillful player is just as likely as the less skillful player to be luckier in sense #2. There is no correlation between skill and "luck #2," so how could there be a correlation between skill and "luck #1"? A full mathematical proof is complicated, but here is the main idea: If I'm more skillful, then I need less luck to win the game. In most games, I'll get the small margin of luck that I need to win the game, and only rarely will I suffer the long string of bad luck that will cause me to lose. Here's a much simpler game to illustrate the idea: "Unfair Football." There's a ball on a field and it moves left and right randomly until it crosses one of the two goal lines. The ball's random motion is symmetric; it is just as likely to move left as it is to move right. But the game is unfair *because the ball doesn't start in the middle.* The ball starts closer to one of the goal posts. Obviously, the team with the unfair advantage will win more often, even though the motion of the ball is "fair" in some sense. Although the analogy with backgammon is not perfect, it is pretty good; having more skill is analogous to having an unfair advantage in Unfair Football. In both games, if you examine luck on a move-by-move basis, it is unbiased; nevertheless, one side consistently wins more often. In particular, in Unfair Football, the luckier player (in sense #1) *always* wins. In backgammon, the luckier player (in sense #1) does not always win, but we expect that the luckier player (in sense #1) will almost always win, for basically the same reasons. This doesn't mean that skill is irrelevant in backgammon, any more than the bias in Unfair Football is irrelevant. The skillful player will win more often, *because greater skill causes greater luck in sense #1* (even though it cannot affect luck in sense #2). The beauty of backgammon as a gambling game lies precisely in this seeming paradox. The "mark" will notice that the "shark" only wins when the shark is luckier, and reasons that luck must even out in the end. So the mark keeps playing and keeps losing, because the mark does not understand the difference between luck #1 and luck #2. Tim
Re: No bugs, just a question
There is a subtle point about luck that is not well understood even by some professional mathematicians. In a series of games (or matches, but for simplicity let me focus on games), one must distinguish between 1. counting the number of games in which I was luckier, and 2. determining who was luckier overall on a roll-by-roll basis. The distinction is subtle, but very important, so let me belabor it a bit. For #2, what we do is to examine each roll individually, note how lucky it was, and add up the luck over all rolls in all games. For #1, what we do is to examine each game in turn and, *restricting our attention to only the rolls in that game*, determine who had more total luck. If I had more total luck in that game, then I declare that game to be a "game in which I was luckier"; otherwise, it's a game in which I was unluckier. Let me emphasize that in #1, we ignore *how much luckier* I was in that game. I could be massively luckier, or just barely luckier, but as long as I'm luckier, I declare that game to be one in which "I was luckier." Similarly, I ignore whether I was massively unluckier or just barely unluckier when declaring a game to be one in which I was unluckier. Now here is the crucial observation. It is entirely possible, and in fact common, for two players to be equally lucky in sense #2, and yet for there to be a highly lopsided count in sense #1. That is, I might be unluckier in many more games, and yet equally lucky on a roll-by-roll basis. This sounds like a contradiction, but it is not; for example, maybe I am unluckier in 90% of the games, but in each of those games, my net luck is -0.1 per game, whereas in the 10% of the games in which I am luckier, my net luck is +0.9 per game. Then I am much unluckier in sense #1 but equally lucky in sense #2. "Okay," you might grudgingly concede, "that's *possible*, but surely that's highly *unlikely*." If backgammon were purely a game of luck, then you're right; it would be highly unlikely. However, this is where skill comes in: The more skillful player will (almost always) be luckier in sense #1. This fact is highly counterintuitive to most people. After all, the more skillful player is just as likely as the less skillful player to be luckier in sense #2. There is no correlation between skill and "luck #2," so how could there be a correlation between skill and "luck #1"? A full mathematical proof is complicated, but here is the main idea: If I'm more skillful, then I need less luck to win the game. In most games, I'll get the small margin of luck that I need to win the game, and only rarely will I suffer the long string of bad luck that will cause me to lose. Here's a much simpler game to illustrate the idea: "Unfair Football." There's a ball on a field and it moves left and right randomly until it crosses one of the two goal lines. The ball's random motion is symmetric; it is just as likely to move left as it is to move right. But the game is unfair *because the ball doesn't start in the middle.* The ball starts closer to one of the goal posts. Obviously, the team with the unfair advantage will win more often, even though the motion of the ball is "fair" in some sense. Although the analogy with backgammon is not perfect, it is pretty good; having more skill is analogous to having an unfair advantage in Unfair Football. In both games, if you examine luck on a move-by-move basis, it is unbiased; nevertheless, one side consistently wins more often. In particular, in Unfair Football, the luckier player (in sense #1) *always* wins. In backgammon, the luckier player (in sense #1) does not always win, but we expect that the luckier player (in sense #1) will almost always win, for basically the same reasons. This doesn't mean that skill is irrelevant in backgammon, any more than the bias in Unfair Football is irrelevant. The skillful player will win more often, *because greater skill causes greater luck in sense #1* (even though it cannot affect luck in sense #2). The beauty of backgammon as a gambling game lies precisely in this seeming paradox. The "mark" will notice that the "shark" only wins when the shark is luckier, and reasons that luck must even out in the end. So the mark keeps playing and keeps losing, because the mark does not understand the difference between luck #1 and luck #2. Tim
Re: No bugs, just a question
Maybe you should ask yourself this: what makes a position strong? You can argue that in such positions most rolls are "lucky", as in giving you another strong position, or most opponent rolls are "unlucky". This might go some way to explain this perceived impression. You make a bad move, your position is much the worst for it, so you allowed your opponent to "get lucky" -Joseph On Sat, 2 Jul 2022 at 15:35, Tom Moulton wrote: > There is no such logic in the code that I have ever seen > > The human mind has a great ability to find patterns in chaos. > > This topic comes up a lot with the playing bots on fibs.com > > Tom > > > On July 1, 2022 10:47:11 PM EDT, Paul Thornett > wrote: >> >> I play backgammon to a reasonable standard and have always regarded >> myself as an unlucky player, both as a real-life player and when >> playing the gnubg version. >> >> But, over several years, I have become convinced of a strong tendency >> in gnubg to punish what it may regard as a bad move with remarkable, >> even outrageous, luck. This has become so apparent to me that I can >> usually predict extraordinarily lucky throws by the computer >> immediately before they are made. This also, on occasion, works in >> reverse. Occasionally the computer makes what I would regard as a bad >> move. This has then resulted in a series of ridiculously lucky throws >> by myself. >> >> I can offer no evidence for this wild assertion, it's purely anecdotal. >> -- >> Regards, >> Paul Thornett >> >> >> Regards, >> >> Paul Thornett >> >> >> On Tue, 28 Jun 2022 at 03:32, Ian Shaw wrote: >> >>> >>> Hi Teddy, >>> >>> >>> >>> The luckier player wins a lot of the time. However, I’ve definitely seen >>> many games where the luckier player had played badly enough to still lose. >>> It’s often me! >>> >>> >>> >>> Perhaps you’re sample size is not large enough. That’s all I can suggest. >>> >>> >>> >>> (I’m not sure what happens if you play on any setting lower than ‘expert’). >>> >>> >>> >>> Best regards, >>> >>> Ian Shaw >>> >>> >>> >>> From: Bug-gnubg On >>> Behalf Of hereodt Z >>> Sent: 25 June 2022 20:04 >>> To: bug-gnubg@gnu.org >>> Subject: No bugs, just a question >>> >>> >>> >>> Dear all who created GNUBg, >>> >>> >>> >>> >>> >>> Thank you for your wonderful, GREAT software. >>> >>> >>> >>> It provided me with countless hours of fun and relaxation.Maybe a little >>> TOO much, but that's my problem ;). >>> >>> >>> >>> >>> >>> >>> >>> How come the winner, be it me or the computer, is always the luckiest >>> player? >>> >>> >>> >>> I thought backgammon was a game of skill. 'Course, luck plays a role, but >>> the outcome of the game to be SOLELY based on LUCK?! C'mon! How is it >>> possible? >>> >>> >>> >>> Let's say I am not skilled and indeed, I can win only if I get lucky . >>> >>> >>> >>> But the computer is World Class, after all. How come IT never wins when it >>> is less lucky than me? >>> >>> >>> >>> >>> >>> Thank you and Best regards, >>> >>> Teddy >>> >>> >>> >>> >>> >>> >>> >> -- > Sent from my Android device with K-9 Mail. Please excuse my brevity. >
Re: No bugs, just a question
There is no such logic in the code that I have ever seen The human mind has a great ability to find patterns in chaos. This topic comes up a lot with the playing bots on fibs.com Tom On July 1, 2022 10:47:11 PM EDT, Paul Thornett wrote: >I play backgammon to a reasonable standard and have always regarded >myself as an unlucky player, both as a real-life player and when >playing the gnubg version. > >But, over several years, I have become convinced of a strong tendency >in gnubg to punish what it may regard as a bad move with remarkable, >even outrageous, luck. This has become so apparent to me that I can >usually predict extraordinarily lucky throws by the computer >immediately before they are made. This also, on occasion, works in >reverse. Occasionally the computer makes what I would regard as a bad >move. This has then resulted in a series of ridiculously lucky throws >by myself. > >I can offer no evidence for this wild assertion, it's purely anecdotal. > >- >Regards, > Paul Thornett > > >Regards, > >Paul Thornett > > >On Tue, 28 Jun 2022 at 03:32, Ian Shaw wrote: >> >> Hi Teddy, >> >> >> >> The luckier player wins a lot of the time. However, I’ve definitely seen >> many games where the luckier player had played badly enough to still lose. >> It’s often me! >> >> >> >> Perhaps you’re sample size is not large enough. That’s all I can suggest. >> >> >> >> (I’m not sure what happens if you play on any setting lower than ‘expert’). >> >> >> >> Best regards, >> >> Ian Shaw >> >> >> >> From: Bug-gnubg On >> Behalf Of hereodt Z >> Sent: 25 June 2022 20:04 >> To: bug-gnubg@gnu.org >> Subject: No bugs, just a question >> >> >> >> Dear all who created GNUBg, >> >> >> >> >> >> Thank you for your wonderful, GREAT software. >> >> >> >> It provided me with countless hours of fun and relaxation.Maybe a little TOO >> much, but that's my problem ;). >> >> >> >> >> >> >> >> How come the winner, be it me or the computer, is always the luckiest player? >> >> >> >> I thought backgammon was a game of skill. 'Course, luck plays a role, but >> the outcome of the game to be SOLELY based on LUCK?! C'mon! How is it >> possible? >> >> >> >> Let's say I am not skilled and indeed, I can win only if I get lucky . >> >> >> >> But the computer is World Class, after all. How come IT never wins when it >> is less lucky than me? >> >> >> >> >> >> Thank you and Best regards, >> >> Teddy >> >> >> >> >> >> > -- Sent from my Android device with K-9 Mail. Please excuse my brevity.
Re: No bugs, just a question
I play backgammon to a reasonable standard and have always regarded myself as an unlucky player, both as a real-life player and when playing the gnubg version. But, over several years, I have become convinced of a strong tendency in gnubg to punish what it may regard as a bad move with remarkable, even outrageous, luck. This has become so apparent to me that I can usually predict extraordinarily lucky throws by the computer immediately before they are made. This also, on occasion, works in reverse. Occasionally the computer makes what I would regard as a bad move. This has then resulted in a series of ridiculously lucky throws by myself. I can offer no evidence for this wild assertion, it's purely anecdotal. - Regards, Paul Thornett Regards, Paul Thornett On Tue, 28 Jun 2022 at 03:32, Ian Shaw wrote: > > Hi Teddy, > > > > The luckier player wins a lot of the time. However, I’ve definitely seen many > games where the luckier player had played badly enough to still lose. It’s > often me! > > > > Perhaps you’re sample size is not large enough. That’s all I can suggest. > > > > (I’m not sure what happens if you play on any setting lower than ‘expert’). > > > > Best regards, > > Ian Shaw > > > > From: Bug-gnubg On > Behalf Of hereodt Z > Sent: 25 June 2022 20:04 > To: bug-gnubg@gnu.org > Subject: No bugs, just a question > > > > Dear all who created GNUBg, > > > > > > Thank you for your wonderful, GREAT software. > > > > It provided me with countless hours of fun and relaxation.Maybe a little TOO > much, but that's my problem ;). > > > > > > > > How come the winner, be it me or the computer, is always the luckiest player? > > > > I thought backgammon was a game of skill. 'Course, luck plays a role, but the > outcome of the game to be SOLELY based on LUCK?! C'mon! How is it possible? > > > > Let's say I am not skilled and indeed, I can win only if I get lucky . > > > > But the computer is World Class, after all. How come IT never wins when it is > less lucky than me? > > > > > > Thank you and Best regards, > > Teddy > > > > > >
Fwd: No bugs, just a question
Hi Ian, The luckier player wins a lot of the time. However, I’ve definitely seen many games where the luckier player had played badly enough to still lose. It’s often me! Lol. With GNUBg or human partner? And at what rate? That's what's bugging me. It happens way too rarely in my games, I think Perhaps you’re sample size is not large enough. That’s all I can suggest. No worries about that, I studied engineering too, IT even ;). Sample size is at least a few hundred matches, I might have reached the thousand mark even. An in this sample I have just one vague memory of one match where the luckier player (deemed so by GNUBg, 'course) lost. (I’m not sure what happens if you play on any setting lower than ‘expert’). I set the computer to "World Class". My computer is too slow for higher levels. But I played a couple of times at the next one to see what happens and the computer smashed me to pieces ha ha! Ian, thank you for trying to answer my question I just noticed that on a pretty large batch of matches, the winner is the less lucky player in, let's say, 2 out of 1000, tops. And that seems not normal. I realize that I asked this question without providing the actual data - I didn't save the games after I looked at the analysis. So you cannot possibly give me a clear answer. Let's try a different way According to your experience as both programmer and player, what is a usual percentage of the less lucky winning? If I were to save every game from now on, how many matches (minimum) would you need for it to be statistically sound? Dear Jon, Your first two remarks are too technical for me :) "I’m not sure if a more skilled player is likely to get more lucky rolls because of being in better positions - or if that gets averaged in the statistics of the luck calculation?" This last one, I believe the first part is true from simple game observation, with GNUBg or real partners - to what degree I cannot know. The second part - not sure how GNUBg evaluates luck, but I would think so. So Hey! We could say that the better player will not only win, but also be more lucky because of their skill; and on the other hand, the less skilled can win ONLY if they get lucky (dumb luck)? Interesting thought hmm? Is it true? And to what degree? We've all studied Math, we need a quantitative answer. But I think that on big enough batch the winner should be the less lucky player more often than it happens in my games. Especially when the winner is GNUBg @ World Class. Best, Teddy On Tue, Jun 28, 2022 at 2:52 PM Jon Kinsey wrote: > If 2 players are similar in skill then luck is the determining factor. > Even if the skill difference is quite big, jokers are going to give bigger > equity swings than blunders in general. > > Cube decisions in larger matches give more opportunities for (big) > mistakes and a beginner will lose almost all the time in say a match to 11 > against gnubg. > > I’m not sure if a more skilled player is likely to get more lucky rolls > because of being in better positions - or if that gets averaged in the > statistics of the luck calculation? > > Jon > > > On 26 Jun 2022, at 01:24, hereodt Z <777theod...@gmail.com> wrote: > > > > > > Dear all who created GNUBg, > > > > > > Thank you for your wonderful, GREAT software. > > > > It provided me with countless hours of fun and relaxation.Maybe a little > TOO much, but that's my problem ;). > > > > > > > > How come the winner, be it me or the computer, is always the luckiest > player? > > > > I thought backgammon was a game of skill. 'Course, luck plays a role, > but the outcome of the game to be SOLELY based on LUCK?! C'mon! How is it > possible? > > > > Let's say I am not skilled and indeed, I can win only if I get lucky . > > > > But the computer is World Class, after all. How come IT never wins when > it is less lucky than me? > > > > > > Thank you and Best regards, > > Teddy > > > > > > >
RE: No bugs, just a question
Hi Teddy, The luckier player wins a lot of the time. However, I’ve definitely seen many games where the luckier player had played badly enough to still lose. It’s often me! Perhaps you’re sample size is not large enough. That’s all I can suggest. (I’m not sure what happens if you play on any setting lower than ‘expert’). Best regards, Ian Shaw From: Bug-gnubg On Behalf Of hereodt Z Sent: 25 June 2022 20:04 To: bug-gnubg@gnu.org Subject: No bugs, just a question Dear all who created GNUBg, Thank you for your wonderful, GREAT software. It provided me with countless hours of fun and relaxation.Maybe a little TOO much, but that's my problem ;). How come the winner, be it me or the computer, is always the luckiest player? I thought backgammon was a game of skill. 'Course, luck plays a role, but the outcome of the game to be SOLELY based on LUCK?! C'mon! How is it possible? Let's say I am not skilled and indeed, I can win only if I get lucky . But the computer is World Class, after all. How come IT never wins when it is less lucky than me? Thank you and Best regards, Teddy
No bugs, just a question
Dear all who created GNUBg, Thank you for your wonderful, GREAT software. It provided me with countless hours of fun and relaxation.Maybe a little TOO much, but that's my problem ;). How come the winner, be it me or the computer, is always the luckiest player? I thought backgammon was a game of skill. 'Course, luck plays a role, but the outcome of the game to be SOLELY based on LUCK?! C'mon! How is it possible? Let's say I am not skilled and indeed, I can win only if I get lucky . But the computer is World Class, after all. How come IT never wins when it is less lucky than me? Thank you and Best regards, Teddy
