How do 'luck' calculations work..

[socksey]

vic shouting everytime he looses to a bot does NOT count as evidence

Maybe..........maybe not!     Keep in mind vic's rating and keep in mind vic has been playing this game since he was a child.   '

socksey



"Why does your OB/Gyn leave the room when you get undressed if they are going to look there anyway?" - Anonymous

[diane]

You cannot "gain" equity with a good move; all you can do is avoid losing equity by not making any errors.

So a bad move, lowers your equity right away. It doesn't per se influence anything on the next roll. You just start out with lower equity.

A good move, i.e. the correct move, gives you the equity the bot thinks you should have (i.e. higher than after any other move). It doesn't per se influence anything on the next roll either. You just start out with the equity you should have had.

I didn't say you gain equity ...well, not intentionally    I am saying the equity is there on the move - and that is added into the overall luck factor as quoted by the bot at the end of the match. And I think how you play a move must influence what options you have on the next roll...dorbel seems to be following my warped mind...

Good play will lead to more "lucky" than "unlucky" rolls in the course of a game, hence the better player will be slightly more likely to have positive luck at the end of each game and at the end of each match.

So forget about luck and play better! You'll get luckier.

I am 'forgetting about luck'...what I am trying to build here is a persuasive argument to put to others obsessing about luck  In words that any one can understand 

The whole trend towards analysing matches and focussing in on how lucky or unlucky a player is detracts from what is really going on IMO. 

I know there *is* luck involved - and if two highly skilled bots play each other, the luck will decide it.

But since the majority of matches played by people are not in that scenario...the thought that you can make yourself more lucky by playing well is the inspiration needed to focus people in on playing well...I think

[rebcalale]

I didn't say you gain equity ...well, not intentionally    I am saying the equity is there on the move - and that is added into the overall luck factor as quoted by the bot at the end of the match. And I think how you play a move must influence what options you have on the next roll...dorbel seems to be following my warped mind...

I am 'forgetting about luck'...what I am trying to build here is a persuasive argument to put to others obsessing about luck  In words that any one can understand 

But since the majority of matches played by people are not in that scenario...the thought that you can make yourself more lucky by playing well is the inspiration needed to focus people in on playing well...I think

LUCK is easy to understand: u or anyone else should have the same chance to get the rolls u/or your opponent need to win.  Play to the odds and u should win more than u lose.  Of course it is not a straight line and there will be situations where luck seems to favor one or the other player regardless of how well u play.  However beware of game environments where the dice r not legit.  This is common on the Internet.   For example, on fibs the dice r simply not reasonable.  Why do I write this, easy just chart the rolls an u will see that what I mean.  Far too many once in a lifetime rolls and if u keep track u will see there r just too many repeated rolls.  Now does this mean fibs favors one or the other player?  Hard to prove but it does look like it is biased. Interesting that NO ONE, let me repeat that, NO ONE has ever offered concrete evidence that fibs dice r legit.  So until that happens be wary!

[diane]

LUCK is easy to understand: u or anyone else should have the same chance to get the rolls u/or your opponent need to win. 

NO ONE has ever offered concrete evidence that fibs dice r legit.  So until that happens be wary!

Point 1- this thread is proving that that is simply not the case...

Point 2 - NO ONE has ever offered concrete evidence that fibs dice arent legit

But that isn't the conversation here - please have that on the other thread.

[pck]

Any one else have long stats about their luck?

gumpi was kind enough to run 1100 of my fibs matches from the past 3 years through XG and my total luck came out almost exactly zero.

[sixty_something]

WAY

i just scrolled back and discovered quite a few interesting posts i missed over the weekend .. i have been busy getting an email based chess game going with my grandson .. luck is the great equalizer .. its complete absence in chess is one of the reasons i love backgammon so much more .. for example, i could never hope to beat Bobby Fischer at chess, but i can beat dorbel every now and then  

pck, or gumpi, does that summary of 1100 matches include a luck analysis for each game in some kind of summary form .. if so, i would love to see "luck" by match in a frequency distribution .. for a PerfectBot, i suspect that distribution would tend toward a very traditional Normal Distribution bell-shaped curve .. understaniding the standard deviation for that curve would also be most interesting .. for individual players, i suspect it may be slightly skewed toward unlucky for all the best moves we may miss .. if there is any correlation, diane, between making "our own luck" such skewing would prove it .. however, "making" is a misnomer as i doubt that ANY human player or bot would have a curve skewed toward luck over a large number of rolls, although blitzxz seems to suggest otherwise .. finally, individual "luck" distributions may even reveal variances in outliers, standard deviations, max and min values, and more for those of us who take bigger chances, for those who play a much more conservative game, and perhaps may even be correlated to individual ratings

sounds like good thesis material to me  

if necessary, i'd be glad to help extract some of those details for individual matches and stick them in Excel .. hopefully, it won't be necessary .. otherwise, i'll b simulating luck in no time  

[pck]

pck, or gumpi, does that summary of 1100 matches include a luck analysis for each game in some kind of summary form .. if so, i would love to see "luck" by match in a frequency distribution .. for a PerfectBot, i suspect that distribution would tend toward a very traditional Normal Distribution bell-shaped curve ..

XG doesn't provide, as far as I know, stats on luck variance. I agree that would be indeed be an interesting thing to have.

understanding the standard deviation for that curve would also be most interesting .. for individual players, i suspect it may be slightly skewed toward unlucky for all the best moves we may miss .. if there is any correlation, diane, between making "our own luck" such skewing would prove it .. however, "making" is a misnomer as i doubt that ANY human player or bot would have a curve skewed toward luck over a large number of rolls, ...

If any correlation between luck and skill were found, that would point either to dice manipulation or to a conceptually defective definition of "luck", since if you were able to influence your luck, the results of that ability couldn't properly be called "luck" anymore, but would instead be the outcome of a part of your skill. Conceptually, luck is what we are given without deserving it, while skill is what we make of what we have so received. All formal definitions of either luck or skill must maintain conceptual coherence with this basic idea, otherwise we will create statistical mirages prone to misinterpretation.

[Zorba]

In other words, overall luck will approach zero for any player, in the long run.

You can't create luck. You can "create" equity though, by not making (as many and as big) errors as your opponent... Strictly speaking, it's more like you can destroy equity with bad moves, and the idea of backgammon is to let your opponent do that, and not do it yourself!

BTW, XG offers some graphs on the luck distribution per game, weighted game, match or weighted match.

Mine doesn't have quite enough data to be smooth yet, but does show a kind of bell-shaped curve, however, there's a big dip slightly left of the middle: games (and even matches) with close to zero luck or very little luck for my opponent are relatively rare! That's probably because when both sides had roughly equal amounts of luck, the game will get to the end with both players still around the 50% winning chances mark, but volatility will increase as the end of the game comes in sight, and at some point either you get very lucky winning, or very unlucky losing, simply because the game has to end somewhere.

Another thing XG shows in the graphs is how many of the games you won with a certain amount of luck. I won all games in which I got lucky. I also won all games with zero luck, and I won about half the games where my opponent had a very small amount of luck. I lost all the games where my opponent had a more sizeable amount of luck.

This is all very much in line with what you'd expect, as on average I guess most of my opponents are at least 150 rating points weaker.

[sixty_something]

If any correlation between luck and skill were found, that would point either to dice manipulation or to a conceptually defective definition of "luck", since if you were able to influence your luck, the results of that ability couldn't properly be called "luck" anymore, but would instead be the outcome of a part of your skill. Conceptually, luck is what we are given without deserving it, while skill is what we make of what we have so received. All formal definitions of either luck or skill must maintain conceptual coherence with this basic idea, otherwise we will create statistical mirages prone to misinterpretation.

pck, i am NOT suggesting that we can "make" ourselves more lucky .. remember, i said "making our own luck" is probably a misnomer .. however, i am not convinced that we error prone humans might demonstrate in a frequency distribution of "luck" some statistically significant variance with a theoretically PerfectBot .. that variance, if it exists, might be deemed a result of less skillful play suggesting that 'luck" and "skill" are not independent variables .. since both are dependent on "equity", itself a construct, i would suggest that this is not a "defective definition", but rather simply the nature of the way in which we have come to think about and define both "luck" and "skill"

all that notwithstanding, that last sentence of yours is an awesome one, pck, statistically poetic even .. in the best of all possible worlds, it should be true without doubt .. but as much as i have come to appreciate "equity" as a construct, i am doubtful we will ever eliminate "statistical mirages prone to misinterpretation" .. on the other hand, we certainly don't need to be creating mirages unnecessarily

finally, if "making our own luck" is a mirage better suited for motivating us to play more skillfully and psychologically accepting bots' seemingly endless supply of good luck, then perhaps "wasting our potential" is a way to describe how less skillful play may be reflected in "luck" calculations and therefore "luck" distributions .. of course, whether it is or is just another mirage has yet to be determined, for me anyway

Zorba's post came in while i was writing this which suggests to me an encouraging possibility of "seeing" the "luck" curve for Zorba and comparing it with that of his opponents, whom he identifies as being about 150 points on average below his rating .. so, let Zorba be my theoretical PerfectBot and his opponents mere mortals with less skill (my words not his)

is there any difference between Zorba's "luck" curve and that of his opponents? whether there is or not, we haven't proved much, but it might make an interesting side bet

[pck]

In other words, overall luck will approach zero for any player, in the long run.

To be more precise, that is the most probable outcome. All statistical convergence is probability-governed itself and hence does not occur with strict necessity.

BTW, XG offers some graphs on the luck distribution per game, weighted game, match or weighted match.

Very nice. I don't have XG, will have to ask gumpi if he can screenshot me those pages.

Incidentally, the Chi-squared distribution of my fibsdice in those 1100 matches sucked eggs. My 60.000 rolls deviated from what can be expected from fair dice so much that there is only a 3% chance of doing even worse. The same was not true for my opponents' dice. So I guess I'm vic with a license now.

[pck]

pck, i am NOT suggesting that we can "make" ourselves more lucky .. remember, i said "making our own luck" is probably a misnomer .. however, i am not convinced that we error prone humans might demonstrate in a frequency distribution of "luck" some statistically significant variance with a theoretically PerfectBot .. that variance, if it exists, might be deemed a result of less skillful play suggesting that 'luck" and "skill" are not independent variables

But that is exactly the conceptual error I was trying to point out. If luck and skill are mathematically defined in a way such that they turn out to be correlated, then these definitions have lost touch with our common understanding of the concepts. In our common understanding, luck is undeserved, and skill is not. We say that you earn victories by skillful play and that you luck out when it is felt that the dice won it for you. That is the conceptual basis, the given, which the math must reflect. Formalisms not sharing logical form with their underlying concepts will likely create the above mentioned mirages by producing numbers which do not really say what they seem to be saying.

.. since both are dependent on "equity", itself a construct, i would suggest that this is not a "defective definition", but rather simply the nature of the way in which we have come to think about and define both "luck" and "skill"

They are indeed both equity-related. And that is precisely the origin of the illusion that skill may "create" luck: Luck is equity bestowed on you by pure chance - the dice rolls. There is no "deserve" there. Skill on the other hand is equity not wasted by making the best possible moves with the rolls you get. You screw that up, it's your own fault. Good luck creates equity for you, good skill retains it. Related concepts, but yet distinct.

all that notwithstanding, that last sentence of yours is an awesome one, pck, statistically poetic even ..
in the best of all possible worlds, it should be true without doubt .. but as much as i have come to appreciate "equity" as a construct, i am doubtful we will ever eliminate "statistical mirages prone to misinterpretation" .. on the other hand, we certainly don't need to be creating mirages unnecessarily

Yes, the mirages are the pitfalls of statistics, often much more so than the complications of the underlying math (which can be considerable too of course). I do think that concerning luck and skill we can have our cake and eat it too though. We are less fortunate with other concepts, such as that of probability itself, which remains conceptually elusive due to its recursive nature.

finally, if "making our own luck" is a mirage better suited for motivating us to play more skillfully and psychologically accepting bots' seemingly endless supply of good luck, then perhaps "wasting our potential" is a way to describe how less skillful play may be reflected in "luck" calculations and therefore "luck" distributions .. of course, whether it is or is just another mirage has yet to be determined, for me anyway

See above. I hope to have made it clearer than in the first posting.

[diane]

I will read all this later when I am not having a quick lunch break    but some words to be put in are..

Refer to the title of this...I have never suggested we can have any influence over Lady Luck by anything other than human sacrifice or dice manipulation 

BUT what I am asking about is the 'luck as caluclated by a bot' - which so much store is put by...waaaaah I lose this because my 'luck score' is -208, or similar....

Since that calculation is based on numbers...the numbers regarding equity calculations must factor in...and if you can influence the equity of each move by how you move, then you can influence how lucky...or unlucky you appear to be...

I too win the games where I am lucky, and lose the ones where I am not - hence this interest...surely there has to be a way for a generally unlucky person like myself to get around this unmovable object   

I too, would be interested in this bell curve...I am a scientist - nothing appeals to me more than a good bell curve 

[pck]

I will read all this later when I am not having a quick lunch break    but some words to be put in are..
[...]
Since that calculation is based on numbers...the numbers regarding equity calculations must factor in...and if you can influence the equity of each move by how you move, then you can influence how lucky...or unlucky you appear to be...

See my reply to sixty in #30, paragraphs one and two. This is the same confusion: What you can influence by making the best move is the retention of equity post-roll. This we call the excercise of skill. The equity change from pre-roll to post-roll (but pre-move) is called luck, over which we have no control. We tend to confound and/or identify skill and luck because they are both about equity changes. The problem is conceptual, it is not "in the numbers".

I too, would be interested in this bell curve...I am a scientist - nothing appeals to me more than a good bell curve

Math is a fine subject but it needs conceptual elucidation to go along with it. Hence, yay philosophy.

[Zorba]

Here's my bell curve. Should be noted though, that I don't really have enough games played yet, and that XG considers me a bit lucky so far, which you can see in this graph.

Also, I think XG uses "luck per move" for this graph, whereas for the puposes of this discussion you'd probably rather want the "total luck" over all moves.

If someone played opponents that are rated significantly higher on average, then the dip in the bell curve will be slightly to the right of the middle, instead of on the left. Also, you can expect to lose most games with close to zero luck or only very slight luck for you, instead of winning most of them as in my graph.

[diane]

How do I get that program?

[pck]

Here's my bell curve. Should be noted though, that I don't really have enough games played yet, and that XG considers me a bit lucky so far, which you can see in this graph.

Also, I think XG uses "luck per move" for this graph, whereas for the puposes of this discussion you'd probably rather want the "total luck" over all moves.

Interesting graph. Is the luck on the x-axis your absolute luck (per move), or is it the difference in luck between you and your opponent? The latter would make a lot more sense to me.

[pck]

Mine doesn't have quite enough data to be smooth yet, but does show a kind of bell-shaped curve, however, there's a big dip slightly left of the middle: games (and even matches) with close to zero luck or very little luck for my opponent are relatively rare! That's probably because when both sides had roughly equal amounts of luck, the game will get to the end with both players still around the 50% winning chances mark, but volatility will increase as the end of the game comes in sight, and at some point either you get very lucky winning, or very unlucky losing, simply because the game has to end somewhere.

If I understand this correctly, you're describing matches which "move away from the centre of the bell curve" at the last moment. Hence the dip.
But why isn't this counterbalanced by matches in which one player is ahead in luck until close to the end and then loses due to a big equity swing, thus moving the match *to* the centre of the bell curve?

Are matches like that rarer than the type you describe above? Are last minute swings less likely after one player has luck-wise dominated the match, compared to matches with more balanced luck for both?

[Zorba]

XG uses (your luck minus opponent's luck) for luck, like Snowie does (and unlike GnuBG does).

As to your other question, most matches "need" a lot of luck to be decided, since the skill difference alone won't be enough. Using GWC, say 20% can be gained in one game by the skill difference between a good player and a beginner. Then the best player still needs 30% luck to win, or the worst player 70%.

If that amount of luck hasn't been reached and the game is nearing the end (no contact), then barring any super blunders in the endgame, a lot of luck has to happen for either player.

The opposite is not true, if one player already has been very lucky, he's likely to have really high winning chances, like 80% or more. Then either he also gets the remaining amount of luck to win the game, or the other player gets extreme luck in the end. An amount of luck that brings the total luck back to around zero like you describe, could not finish the match (unless there was an extreme skill difference), as it would bring both players back to some wide margin around 50% GWC (say, 30-70%).

[sixty_something]

XG uses (your luck minus opponent's luck) for luck, like Snowie does (and unlike GnuBG does).

so, the graph of your "luck" in a previous post which is skewed toward the right, indicates your "lucK" exceeds that of your opponent.. is that correct, Zorba?

while you suggest your sample size is not large enough, such a skewing for a large enough sample size would support the observation that the better player minimizes his error rate, and in so doing optimizes his "luck" potential, i.e. creating the statistical allusion that the better player has better luck or makes his own luck .. if over time, Zorba's skew remains postitiive or even increases, as i expect it might, this may provide at least one counter example to pck's theoretical arguement that over time the "luck" differential will tend toward zero reflecting equal luck in the long run regarless of skill level -- is that a fair synopsis of your thesis, pck

an interesting question is how big would the sample have to be to be statistically significant?

finally, it is important to note that as previously suggested "makes his own luck" is at best a misnor and at worst misleading .. my phrasing above is the best i can come up with that i believe accurately states my thesis and that suggested by others .. in summary it is:

the better player minimizes his error rate
in so doing he optimizes his 'luck' potential
yielding the impression the better player is luckier
than less skilled opponents

although, vic vs. the bots is proof enough in shouts

[Zorba]

No, no and NO!

Minimizing your error rate does not "optimize luck potential". It maximizes equity, with the luck given, as explained in many ways in several articles in this thread earlier.

And as far as there might be illusions of better luck, then XG won't show them, as it uses mathematics like it should, not subjective perceptions or inconsistent, confused mathematical models.

pck's theoretical argument is correct and is actually pretty trivial from the definition of luck, for a statistician.

I'd suggest just accepting that most people's "intuitive" or "perceptive" concept of probabilities or statistics as in "observing luck" are notoriously bad, skewed, inconsistent, etc. and therefore, you need to use mathematics to get correct answers to your questions.

As far as your last statements:

the better player minimizes his error rate
in so doing he optimizes his 'luck' potential
yielding the impression the better player is luckier
than less skilled opponents

are concerned, this is correct apart from the second sentence, which is unclear anyhow. What does "optimizing 'luck' potential" even mean? It sounds like a confused way of simply saying "maximizing equity".