1. Rollout¹ 13/11 13/10 eq:+0,906
Player : 79,43% (G:33,22% B:1,06%)
Opponent: 20,57% (G:2,93% B:0,25%)
Confidence: ± 0,005 (+0,901<E<+0,911)
Duration: 17 minutes 32 seconds
2. Rollout¹ 13/10 8/6 eq:+0,895 (-0,011)
Player : 79,00% (G:33,07% B:1,07%)
Opponent: 21,00% (G:2,93% B:0,21%)
Confidence: ± 0,005 (+0,890<E<+0,900)
Duration: 14 minutes 20 seconds
3. Rollout¹ 13/8 eq:+0,894 (-0,012)
Player : 79,60% (G:31,59% B:1,07%)
Opponent: 20,40% (G:2,74% B:0,22%)
Confidence: ± 0,005 (+0,889<E<+0,899)
Duration: 12 minutes 32 seconds
4. Rollout¹ 13/11 8/5 eq:+0,885 (-0,021)
Player : 78,72% (G:33,03% B:1,08%)
Opponent: 21,28% (G:2,98% B:0,23%)
Confidence: ± 0,005 (+0,880<E<+0,890)
Duration: 12 minutes 16 seconds
Under analysis - does this 'maximising equity per move' directly translate into a good luck rating in analysis...quite simply because the program is is using potential equity changes to measure how lucky a player is in a match?
Does anyone understand that - and am I completely missing the point?
I have heard tell that a good player will appear more lucky, because they are 'creating luck', a concept I am wrestling with.
I havent checked GnuBG's source code, but I am pretty sure 'luck' is calculated as follows:
For a specific roll, luck is the difference between the equity/MWC after playing the roll correctly and the weighed average of 21 equities/MWC's after playing all 21 possible rolls correctly.
Luck for a game/match for a specific player is the sum of luck for all rolls for the player during that game/match.
I have heard tell that a good player will appear more lucky, because they are 'creating luck', a concept I am wrestling with.
I think the best way to understand this is that there are two notions of the term "luck" .
For example, a beginner will think it's "unlucky" that he misses an indirect shot seven points away (1 in 6 or 17% chance), and then think it's "lucky" that his opponent hits a direct shot six points away ( 17/36 or 47% chance) But the player who understands that there's a huge difference between two seemingly very similar positions will play the percentages, and the player who doesn't understand the game will think it's luck.
In my head...if you play well and increase the number of rolls which 'work well' next go, then they will give higher equity change - and therefore rate as 'lucky'.
Does this accumulation of the positive equity equate to, say, bots appearing more lucky [on analysis] more often?
Does this accumulation of the positive equity equate to, say, bots appearing more lucky [on analysis] more often?
I agree with boomslang. The total amount of luck between two sides must tend towards zero over time, because there is an equal total of positive and negative luck on every roll. However, this doesn't mean that there are an equal number of lucky and unlucky rolls on each turn. 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. The lesser player will balance this out with a greater amount of luck in fewer matches, thus wasting a lot of it.
i think the data over time would confirm by tending toward zero sum "luck"
If I roll Zorbas 3-1 opening as described above - and play the optimum move, I have an equity change about that roll.
If I play it correctly, I influence the potential equity change on the next roll positively....
If I play it wrongly, I have the opposite effect.
Any one else have long stats about their luck?
vic shouting everytime he looses to a bot does NOT count as evidence
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.
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 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.
NO ONE has ever offered concrete evidence that fibs dice r legit. So until that happens be wary!
Any one else have long stats about their luck?
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 ..
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.
In other words, overall luck will approach zero for any player, in the long run.
BTW, XG offers some graphs on the luck distribution per game, weighted game, match or weighted match.
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
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...
I too, would be interested in this bell curve...I am a scientist - nothing appeals to me more than a good bell curve
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.
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.
XG uses (your luck minus opponent's luck) for luck, like Snowie does (and unlike GnuBG does).
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.
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%).
What does "optimizing 'luck' potential" even mean? It sounds like a confused way of simply saying "maximizing equity".
What does "optimizing 'luck' potential" even mean?
So here's a puzzle:
I let gnu play one-pointers against itself with both players set to the same level of skill. The outcome of these matches should be completely luck dependent.
But the stats say otherwise: The "Luck adjusted result" was never 0%, but varied between 3 and 15% in my tests.
The Luck adjusted result is calculated as 50% - the luck difference of the players, which should be their skill difference, which should be zero.
Any ideas what's wrong with this picture?
Luck adjusted results are notoriously inaccurate in single games or matches. It's actually worthless number to me. I once tried this same test playing, analyzing and analyzing luck with same ply and I think my record was over +50% luck adjusted result to other identical gnubg. I tried analyzing the same match (and luck also) with higher ply but it really didn't help, still the other bot was hugely more skillful. I can't really understand what is the cause of this. However in my long stats (fibs matches), luck adjusted results and unnormalized error rates seemed to converge.
1) The neural nets are not 'perfect'. With perfect nets you would expect that the equity of the current position (after your opponent moved and prior to your roll) would be equal to the expected equity after playing your 21 possible rolls correctly. In practice this is not the case. If the nets would be perfect there would be no need to set a bot to 2 plies.
2) If you analysed the match at a different level as the playing level of the 2 players it might be that both players did not make the same error total during that match. The difference in errors doesnt cancel out then.
pck's theoretical argument is correct and is actually pretty trivial from the definition of luck, for a statistician.
Yes, it's mathematically trivial because there is hardly any math involved! I was mainly concerned with giving an explanation of how we arrive at the confused notion that "skill begets luck".
What I had assumed was that non-perfect equity calculations should at least be internally consistent, that is, the numbers should add up. Obviously that is not the case. About the reason I still wonder.
Player "You" rolls a 45, gnu says that's an equity gain of +1.587% MWC. Player "gnubg" of course loses this amount of equity, as well as another 3.551% on its first roll, a 63. So gnubg's equity after rolling that 63 should be 50 - 1.587 - 3.551 = 44.862. But what it actually says is 45.77, a discrepancy of 0.908% after only one roll on each side. This is too large to be attributed to rounding errors. And if player gnubg's equity is calculated independently from previous equities, then why does gnu not adjust the -3.551 accordingly? Perhaps that would have other undesirable consequences I'm not seeing.
If I understand you correctly you are just adding up equity loses. It doesn't work that way. If you lose 1% first roll and 2% second it doesn't mean that now you have 47% chances to win. I haven't figured it out yet but I'm guessing some sort of multiplying is needed to add up equity loses and to come up with over all chances.
is it safe to say we can drop the word "trivial" from your and Zorba's somewhat dismissive rebuttals of my suggestions?
i think you may be observing some of the same things i did when i first looked at "luck" calculatioins in detail ... like you, i "still wonder" about the reasons why what seems conceptually obvious simply does not add up when put to the test of striking a balance sheet for "luck" calculations
when observed values don't match theory and assumed concepts, perhaps it is time to revisit both with an open mind .. i am
My "mathematically trivial" was not intended to be dismissive of your remarks.
Yes, it's mathematically trivial because there is hardly any math involved! I was mainly concerned with giving an explanation of how we arrive at the confused notion that "skill begets luck". What I wrote in #30 is not a theoretical argument (for it can neither be verified nor falsified), but an attempt at a conceptual elucidation by looking at how "luck" and "skill" are used in everyday language and how these terms are related to their mathematical counterparts.
There is no a priori concept of "the correct definition of luck" for us to discover.
Hence the "dipped bell shape" of the curve is a misleading expression. It consists rather of two bell shapes which are superimposed, with their high points at those good/bad luck values which are most common.
So here's a puzzle:
I let gnu play one-pointers against itself with both players set to the same level of skill. The outcome of these matches should be completely luck dependent.
But the stats say otherwise: The "Luck adjusted result" was never 0%, but varied between 3 and 15% in my tests.
The Luck adjusted result is calculated as 50% - the luck difference of the players, which should be their skill difference, which should be zero.
Any ideas what's wrong with this picture?
I agree. What I had assumed was that non-perfect equity calculations should at least be internally consistent, that is, the numbers should add up. Obviously that is not the case. About the reason I still wonder.
Nevertheless this is very important for the consideration of what we call "skill". If we can attribute the term "skill" only to the whole of a bot's algorithm, that is, to its behaviour in all possible match situations, and if it could further happen that algorithm A1 beats A2 (in the long run), A2 beats A3, and A3 beats A1, then that would eliminate the possibility of attribution of skill for these three bots. Skill would only be a partial order on the set of all possible bot-algorithms. To prove that this is or isn't possible should be difficult.
is it safe to say we can drop the word "trivial" from your and Zorba's somewhat dismissive rebuttals of my suggestions?
i think you may be observing some of the same things i did when i first looked at "luck" calculatioins in detail ... like you, i "still wonder" about the reasons why what seems conceptually obvious simply does not add up when put to the test of striking a balance sheet for "luck" calculations
when observed values don't match theory and assumed concepts, perhaps it is time to revisit both with an open mind .. i am
Just because GnuBG 0-ply plays both sides, does not mean it plays both sides equally well in individual games. Only in the long run will they show equal skill levels. So the outcome of a particular match is not completely luck dependent: one side may have given up much more equity in errors than the other side.There is one case where gnu (or any bot) should play both sides equally well: If analysis and player plys are set to equal levels, gnu should not find that any player has made any mistake. And indeed it doesn't. Both ERs are always 0. Hence all equity change in the match should be attributed to luck and the luck adjusted result should always be zero.
Furthermore, GnuBG's luck evaluations, just like its error evaluations, are not perfect, so this is another factor contributing to inaccuracies, especially noticeable in the short run.I assume ply_analysis = ply_players. Analyses may not be perfect, but the hard question is, why can gnu not make the numbers consistent (as opposed to correct) within any of its n-ply worlds, however flawed they may be in an absolute sense. Why is it not possible, with both ERs = 0 and skill out of the picture, to add up all equity changes produced by the dice rolls and get a total change of +50% for the winner and -50% for the loser?
BTW, for practical purposes: GnuBG defaults to using 0-ply for its luck calculations. Luck calculations can be considered more difficult than normal evaluations, as 21 different dice rolls and their best plays have to be considered, so it's no surprise that 0-ply luck analysis can give rather inaccurate results generally. Use GnuBG's command line and the command boomslang mentioned to increase the ply level of GnuBG's luck analysis.With different methods/ply-levels for luck and move evaluations, it is clear that discrepancies can occur (see below).
Another interesting thing to consider here is that a n-ply luck analysis is closer to a (n+1)-ply error analysis than to a n-ply error analysis, due to the 21 different rolls that have to be analyzed. This is also true for the time it takes to do such an analysis: using 2-ply for luck analysis is about as slow as doing a 3-ply error analysis.I ran a few tests. First I set luckanalysis and everything else to 2-ply (which took much longer than 3-ply analysis). The discrepancies still showed up but seemed to be lower than before (around 3-6% as opposed to 7-15%). But I could run only very few test matches because evaluation took so long (Intel Core 2 Duo 7300, 2.6 GHz, gnu set to use both cores). Next I tried luckanalysis at 1-ply and everything else at 2-ply (your n -> n+1 suggestion). In my first trial match, the LAR discrepancy was almost zero. But my celebratory mood subsided when in further trials it went back to 5-7%, and in one particular 1-point match I got an LAR as big as 23%.
I don't know if it that's true, it seems very hard to find out what kind of distribution of net luck per move really underlies the graph.
What we're aiming for with skill assessments is a measure of error against a perfect bot. That's why apart from 0-ply or 2-ply evaluations, many players use 3- or 4-ply for evaluations and better yet, rollouts, to try and remove as much bias as possible from the bots numbers.
What's so interesting about luck evaluations (compared to error evaluations) is that they are, by definition, unbiased, so they can't favour certain game type or strategies more than any other, in the long run. This is not true for error evaluations, which can be (and actually are) biased, as the bots play certain game types much better than others.
No, but this is not about philosophy. Once you've settled for a definition, like the bots have and which has been explained here and elsewhere, there are correct and false conclusions you can draw from it.And how do we settle on a definition? Surely not any definition will do. We need conceptual analysis before we can put our thoughts into a formula.
I simply mean the theoretical (mathematical) argument that luck will tend towards zero in the long run, regardless of a player's skill. That can be verified quite easily using mathematics.Your statement above is correct, but it cannot contribute to the understanding of the phenomena of luck and skill.
Most everything that's being discussed here is described very well in these articles by Douglas Zare:These are good articles, but the reason they make sense is not that they define something, but that what they define is in harmony with our common understanding of luck and skill. If their definitions weren't, we would have no use for them, or at least wouldn't call them definitions of "luck" and/or "skill".
http://www.bkgm.com/articles/Zare/AMeasureOfLuck.html (http://www.bkgm.com/articles/Zare/AMeasureOfLuck.html)
http://www.bkgm.com/articles/Zare/HedgingTowardSkill.html (http://www.bkgm.com/articles/Zare/HedgingTowardSkill.html)
What you can argue about, is how it comes that some people feel "something's wrong" with this approach. Maybe you don't agree with the above definition of luck. But in that case, perhaps you should try to come up with an alternative definition of luck. In the process, you might start to appreciate the current definition of luck ;)Zorba recommending conceptual investigation. I never thought I'd see the day. :: D--(
I'm all for an open mind, but I feel pretty strongly that it's no use to draw the conclusion from a very small sample (such as my earlier posted luck curve) that "observed values don't match theory". Actually, pck earlier claimed that in his larger sample, luck got very close to zero. If you do very long sessions with bots playing each other, as many people have done, luck will also tend towards zero.I already remarked in a previous posting that luck/skill discrepancies may well cancel each other out over a lot of matches if their noise goes both ways (for which I see no reason why it shouldn't). It is quite possible to arrive at a result which matches the theory by means not justified by the theory.
Another interesting thing to consider here is that a n-ply luck analysis is closer to a (n+1)-ply error analysis than to a n-ply error analysis, due to the 21 different rolls that have to be analyzed.I experimented a little more and found a counterexample. The attached match was played and analysed at 2-ply. Its luck analysis ply-level is 1. The luck adjusted result is -23%. If you set luck analysis to 2-ply and re-analyse, the LAR becomes -13%. So there are matches where it gets better instead of worse when you switch from n,n+1 to n,n.
Maybe it's an English thing! :lol:
I got a wee bit lost amongst those calculations but this clip reminds me there's always someone even unluckier than me:
I think if you look at the luck of bots (and good players) have during a match or game, then you will see that they are more often 'lucky' (meaning having a positive sum of MWC/equity) than 'unlucky' (meaning having a negative sum of MWC/equity).
[...]
I dont know if anyone can back this up with empirical data though. I might give it a go if I can find some spare time.
The better player (blue) had a positive luck 57% of the games.
Many congratulations to boomslang for his elegant experiment, even though much of his mathematical language is incomprehensible to this reader! I have believed what he now shows to be true for a long time.What exactly have you believed? That skill creates better luck, or that the definition of luck as used by the bots is flawed?
In the second graph are two kernel density plots of the two players' total EMG luck in each game. Both distributions look bell shaped but are also not normally distributed (Lilliefors test p < 0.0002).Thanks as well for being careful enough to include the crucial "if" here. As I argued in previous postings, we cannot possibly accept the definition of luck as it shows itself through these numbers (barring statistical flukes which I rule out because of the large number of rolls in the experiment). The densities in the second graph should be symmetrical around zero instead of showing the biases they do. As you say, these biases are responsible for the asymmetry in the 3rd graph, since in generating graph 3 from graph 2 the relation
The better player (blue) had a positive luck 57% of the games. This differs significantly from 50% (p = 0.0001). This means that if you consider a bot 'lucky' when it has a positive luck, it not just appears lucky more often, it actually is. However, it was really unlucky quite a few times: the distribution is skewed to the left.
net luck diff = endresult(X) - 50% + error(X) - error(O).is enforced.
A net luck of zero will require that the total error of the loser equals the total error of the winner plus 50% (I am talking GWC here). When a good player plays against a weaker player (150pts weaker on average as in Zorba's example, or maybe 500 pts lower as in my simulated example) then apparently the nature of backgammon makes this very unlikely.So what do you think? Have you shown with this that total luck does not tend to zero in the long run if the skill difference between the players is large? Or have you shown that gnu's calculation of luck is defective? You're obviously aware of the problem or you wouldn't have included that "if" above.
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
This figure coincides with my own shorter studies of matches played between me and gbots on fibs. I have broken the study down into games rather than matches.
However the better player, which in my study is at least occasionally me, gets the positive luck more often.
The densities in the second graph should be symmetrical around zero instead of showing the biases they do.
So what do you think? Have you shown with this that total luck does not tend to zero in the long run if the skill difference between the players is large? Or have you shown that gnu's calculation of luck is defective? You're obviously aware of the problem or you wouldn't have included that "if" above.
now, boomslang, would you consider conducting another experiment to test another aspect of of this theory?
i believe that the more moves (or games) analyzed the more the calculated "luck" differential will diverge between a better player and a less skilled player probably up to some limit .. while 42,000 moves may be a large enough sample to have reached such a limit, it may not be .. so, if it isn't too time consuming, how would that last graph look after say 100,000 moves or more? any idea where that limit may be or if there is a limit at all?
finally, has anyone yet directly addressed diane's original question and really defined how the "luck" calculation really works?
I included the 'if' because of Diane's remark about bots appearing lucky.
Why do you think that? I think they should have an average of zero (because luck tends to zero in the long run), but they cannot be symmetrical because the better player will be more likely to be really unlucky than to be really lucky. (In other words, it has virtually no chance to be really lucky because its opponent gives away too many equity and it had won the game/match already. Remember, these graphs are from the situation expert vs newbie.)You're right. I was confused when I wrote that, mixing in my thoughts about my own experiments where both players had equal skill. Average of zero it is indeed.
Not sure what you mean... What I meant to explain with this quote is the source of the 'dip' in the graphs of Zorba and me.I misunderstood your remark. You said "This means that if you consider a bot 'lucky' when it has a positive luck, it not just appears lucky more often, it actually is." I didn't give due notice to the crucial "often", effectively reading "luckier" instead. ("More often" here meaning "in more games", "positive luck" meaning "more luck than opp in a particular game" (= "positive luck difference for the bot" when we talk gnu).)
I included the 'if' because of Diane's remark about bots appearing lucky. When a bg player simply looks at whether or not a bot had a positive total luck and draws his conclusion on that -- and I think a lot of players do that -- he will indeed see a lucky bot more often than an unlucky bot. It is however unfair to conclude that bots are lucky in the long run, because of the negative skewness of the distribution of luck during a game or match for the bot.
And yes, that means that I think the asymmetry of the distributions are not artefacts caused by GNUbg's inconsistency in evaluating luck and skill.I can safely return to that assumption now too, with the above confusion cleared up for me. It makes a lot more sense this way. Thanks again for the clarifications.
all i am saying is "the nature of backgammon", as boomslang says, and the nature of the "luck" calculation yield "the impression the better player is luckier" .. boomslang's graph number 4 seems to directly support this .. indeed it appears to may be more than an impression, but it is a slippery slope as we have seen to attempt to equate pure theoretical luck with "luck" calculations .. i think all of us who play bots significantly more powerful than we are have repeated first hand experience that bots just seem too damn lucky - don't we? i would contend that this perception is merely a reflection f what boomslang's experiment has shownI agree. As boomslang points out, the difference between "being luckier" and "being lucky more often" is very important and a potential source of confusion:
that quote made me think of this thread :kaffeepc:Writing is thinking. To write well is to think clearly. That's why it's so hard.
However, I don't recall ever seeing this research anywhere else and kudos to these guys for adding something new to the game right here on fibs. Applause, applause.
It is important to understand that what we mean by"luck"LUCK, usually winning a game with a joker, is something different [than calculated "luck"] and something that on average will be equal in the long run. Other than that, I am not sure how understanding what is going on will help us to play better! A good play is still a good play, same as it ever was.
The contributions of boomslang in particular, as well as pck and Zorba, have contributed to our understanding of what bots mean by "luck" and why superior players get the "luck" more often than not.
...
However, I don't recall ever seeing this research anywhere else and kudos to these guys for adding something new to the game right here on fibs. Applause, applause.
something i'd especially like to see are definitions of key terms and phrases .. for example,
- LUCK - pure luck such as that we see when rolling fair dice which we all agree is theoretically equal regardless of skill
- "luck" - the calculated expression of equity gain or loss for an individual player resulting directly from the roll of the dice in a given situation
are those definitions complete and acceptable?
can we concurr LUCK and "luck" are two independent entities with different properties?
can we further state that boomslang's work provides convincing evidence that in the long run a significantly better player tends to accumulate more "luck" than the less skilled player?