info
Google Groups no longer supports new Usenet posts or subscriptions. Historical content remains viewable.
Dismiss
"Lucky Position" vs "Lucky Roll"
67 views
Skip to first unread message
mu...@compuplus.net
Jan 21, 2015, 8:48:22 PM1/21/15
to
On Monday, January 19, 2015 at 3:55:37 PM UTC-7, Walt wrote:
> On 1/19/2015 4:45 PM, Tim Chow wrote:
>> ... I was addressing *Walt's* misconception...
> It's not a misconception so much as writing very quickly and imprecisely.
>
> Yes, good players place their checkers so that more rolls play well, so
> they have more "lucky" rolls than poor players. Poor players place
> their checkers so that only a few rolls play well, but when the good
> rolls inevitable do come up they have a high luck factor. Eventually,
> this all evens out, which is what I was trying to get across - the dice
> favor neither player in the long run, so if you throw away a bunch of
> equity by playing poorly eventually you'll get an example that disproves
> the assertion.
>
> It is not true that a poor player (or a decent player deliberately
> playing poorly) playing a series of one-pointers will have positive luck
> 50% of the time. When I said 50-50 I was speaking figuratively.
The above is a perfect example for what I have been wanting to
write about for a while now. Interestingly he states a fallacy,
debunks it and goes right back to it within the same paragraph.
Then he has to weasel out of his own confusion by claiming to
have spoken figuratively and unfortunately throwing what was a
good argument... :(
When we say "the better player is luckier because he makes
the better moves that allow him to make the most out of any
dice on his next roll", in order to measure the luck value of
any roll, it becomes necessary to look at the previous play
to see if it was in fact his better play that lead to the current
position where his particular roll ended up being rated lucky.
In my mind, this line of arguments introduces the concept of
"lucky position" vs "lucky roll".
If this doesn't grab your fancy thus far or you can't understand
it, you don't need to read the rest of this post.
In the distant past, anyone complaining against his opponent's
luck was simply countered with the "selective memory" argument
which applied equally whether the complainer was the weaker or
the stronger player.
With the emergence of extra terrestrial bots and world class
(nevertheless worldly humanling) players who aspired to imitate
the bots, first came the "selective memory" argument being used
only against the weaker players, because the bots (the strongest
players) never complained about their opponents' luck. Of course,
that made it a taboo for bot wannabes to complain about luck.
But it wasn't all so bad until the birth of the fallacy that the
stronger player somehow created his own luck. Of course, again,
this fallacy was an instant hit with the world class worldly human
players because whenever they were accused of being lucky, they
could claim credit for being the more skilled one.
This "skill creates luck" fallacy next lead to folk-scientists
to mix the oil and water to concoct some gourmet recipes, or
should I say fancy grade AAA mathematical formulaes ;)
Now, let's look at why this is a fallacy that doesn't work.
Let's start with why this line of reasoning was necessary and
intuitively almost seemed valid with the bots.
I believe all current bots are based on the strategy of picking
the moves that will yield the most immediate benefit. So, they
play "from position to position", without a "game plan". This is
true at all ply levels because regardless how far ahead they look,
they still pick the "best" move immediately then and there.
The "best" move is, of course, totally subjective and biased,
but for the sake of this discussion we don't need to get into
that because this is all the bots are capable of today. Hopefully
these kind of discussions will lead to better bots in the future.
So then, of course, since the bot always picks the "best" move
and plays without errors, his success must be due purely to
skill. Because it doesn't need any luck to win, any excess of
its luck has to go somewhere, must be accounted for somehow,
thus it's conveniently injected/absorbed back into its skill.
Let's talk a little more about picking the best move. What the
bot or human player actually picks is one of available positions
as the one where he wants to be for his next roll.
It considers the benefits of all possible positions in terms
of leading to least chances of leaving blots, getting hit,
getting stuck with a difficult or forced move, etc. and picks
the position that it deems best.
So, when we say the stronger player picks the move that will
allow him to make best use of the following dice regardless
of what he rolls, we are really saying that he pick the
"luckiest position" that he wants to be in, on his next roll.
Before I delve into this "lucky position" concept, let me
raise a question about the bots' ignoring forced moves in their
calculations of skill. Doesn't it take skill to avoid getting
stuck with forced moves? Shouldn't the player who has to make a
forced move be retroactively penalized for his lack of skill,
i.e. points subtracted from his skill, for not being able to
have avoided it in his previous decision?
Yes, of course, but the problem is that we can't know if that
player was weak and made an error on his previous move or was
strong/skilled and made the best possible move but got unlucky
on his following roll anyway... :)
To keep the fallacy alive, we conveniently ignore forced moves. ;)
Okay, so, with the "luckier/unluckier positions" concept, we
should be able to look at millions of positions, (for the north
and south player), and rate/rank them based on the average luck
of all rolls at each given position.
Looking at a game as a sequence of horizontal groups of tiles
(possible positions at each turn), if a player can hopscotch
from one lucky tile to another and reach the finish line before
his opponent, we perhaps could then call that skill.
I find and propose that the concept of "lucky position" is more
intuitive than "lucky roll", but it's still as fallacious to mix
and equate skill with luck.
This is so, simply because given a random position, of any luck
ranking, we can't tell how the players arrived at that position
and thus can't tell which side is the stronger player.
Especially so with early and late game positions. Middle game
positions with one side clearly ahead or behind may be more
telling but still not nearly reliably enough to bet money on.
If we add more data like the match length, number of games
already played, current score, etc. then we may become able
to guess with increasing accuracy which side is the stronger
player. (And that's exactly what the bots should do evaluating
each position but I don't know if they do or not).
This post is getting too long already, let me try to wrap it up
bu saying that without looking at all the possible moves at the
previous position and verifying whether the assumed stronger
player had indeed picked the best move, there is no continuity
in the game and it's not possible to make the statement that
"current skill can result in future luck".
Even if we look at the previous move, it still would be a one
sided fallacy because we never say that a player "got unlucky
because he made the best move in the previous position".
And then there is the case of people like me who argue that a
player may chose to make an inferior move as part of a "game
plan"... What if such a player gets lucky as a result of his
blunder?
In fact, look for that in my match against a bot on FIBS that
was discussed just recently in a different thread. As Michael
has pointed out, both sides were about equally unlucky (or lucky)
despite the apparently huge skill difference between me and the
bot (as *inaccurately* indicated by our error rates).
So, my two conclusions are:
1- Arguments like "skill creates luck" may occasionally and
situationally appear to be a valid observation but they are
mere fallacies within the entirety of the subject.
2- You can't measure luck by mixing and matching it with skill
or derive anything meaningful from the results of doing such.
MK
> On 1/19/2015 4:45 PM, Tim Chow wrote:
>> ... I was addressing *Walt's* misconception...
> It's not a misconception so much as writing very quickly and imprecisely.
>
> Yes, good players place their checkers so that more rolls play well, so
> they have more "lucky" rolls than poor players. Poor players place
> their checkers so that only a few rolls play well, but when the good
> rolls inevitable do come up they have a high luck factor. Eventually,
> this all evens out, which is what I was trying to get across - the dice
> favor neither player in the long run, so if you throw away a bunch of
> equity by playing poorly eventually you'll get an example that disproves
> the assertion.
>
> It is not true that a poor player (or a decent player deliberately
> playing poorly) playing a series of one-pointers will have positive luck
> 50% of the time. When I said 50-50 I was speaking figuratively.
The above is a perfect example for what I have been wanting to
write about for a while now. Interestingly he states a fallacy,
debunks it and goes right back to it within the same paragraph.
Then he has to weasel out of his own confusion by claiming to
have spoken figuratively and unfortunately throwing what was a
good argument... :(
When we say "the better player is luckier because he makes
the better moves that allow him to make the most out of any
dice on his next roll", in order to measure the luck value of
any roll, it becomes necessary to look at the previous play
to see if it was in fact his better play that lead to the current
position where his particular roll ended up being rated lucky.
In my mind, this line of arguments introduces the concept of
"lucky position" vs "lucky roll".
If this doesn't grab your fancy thus far or you can't understand
it, you don't need to read the rest of this post.
In the distant past, anyone complaining against his opponent's
luck was simply countered with the "selective memory" argument
which applied equally whether the complainer was the weaker or
the stronger player.
With the emergence of extra terrestrial bots and world class
(nevertheless worldly humanling) players who aspired to imitate
the bots, first came the "selective memory" argument being used
only against the weaker players, because the bots (the strongest
players) never complained about their opponents' luck. Of course,
that made it a taboo for bot wannabes to complain about luck.
But it wasn't all so bad until the birth of the fallacy that the
stronger player somehow created his own luck. Of course, again,
this fallacy was an instant hit with the world class worldly human
players because whenever they were accused of being lucky, they
could claim credit for being the more skilled one.
This "skill creates luck" fallacy next lead to folk-scientists
to mix the oil and water to concoct some gourmet recipes, or
should I say fancy grade AAA mathematical formulaes ;)
Now, let's look at why this is a fallacy that doesn't work.
Let's start with why this line of reasoning was necessary and
intuitively almost seemed valid with the bots.
I believe all current bots are based on the strategy of picking
the moves that will yield the most immediate benefit. So, they
play "from position to position", without a "game plan". This is
true at all ply levels because regardless how far ahead they look,
they still pick the "best" move immediately then and there.
The "best" move is, of course, totally subjective and biased,
but for the sake of this discussion we don't need to get into
that because this is all the bots are capable of today. Hopefully
these kind of discussions will lead to better bots in the future.
So then, of course, since the bot always picks the "best" move
and plays without errors, his success must be due purely to
skill. Because it doesn't need any luck to win, any excess of
its luck has to go somewhere, must be accounted for somehow,
thus it's conveniently injected/absorbed back into its skill.
Let's talk a little more about picking the best move. What the
bot or human player actually picks is one of available positions
as the one where he wants to be for his next roll.
It considers the benefits of all possible positions in terms
of leading to least chances of leaving blots, getting hit,
getting stuck with a difficult or forced move, etc. and picks
the position that it deems best.
So, when we say the stronger player picks the move that will
allow him to make best use of the following dice regardless
of what he rolls, we are really saying that he pick the
"luckiest position" that he wants to be in, on his next roll.
Before I delve into this "lucky position" concept, let me
raise a question about the bots' ignoring forced moves in their
calculations of skill. Doesn't it take skill to avoid getting
stuck with forced moves? Shouldn't the player who has to make a
forced move be retroactively penalized for his lack of skill,
i.e. points subtracted from his skill, for not being able to
have avoided it in his previous decision?
Yes, of course, but the problem is that we can't know if that
player was weak and made an error on his previous move or was
strong/skilled and made the best possible move but got unlucky
on his following roll anyway... :)
To keep the fallacy alive, we conveniently ignore forced moves. ;)
Okay, so, with the "luckier/unluckier positions" concept, we
should be able to look at millions of positions, (for the north
and south player), and rate/rank them based on the average luck
of all rolls at each given position.
Looking at a game as a sequence of horizontal groups of tiles
(possible positions at each turn), if a player can hopscotch
from one lucky tile to another and reach the finish line before
his opponent, we perhaps could then call that skill.
I find and propose that the concept of "lucky position" is more
intuitive than "lucky roll", but it's still as fallacious to mix
and equate skill with luck.
This is so, simply because given a random position, of any luck
ranking, we can't tell how the players arrived at that position
and thus can't tell which side is the stronger player.
Especially so with early and late game positions. Middle game
positions with one side clearly ahead or behind may be more
telling but still not nearly reliably enough to bet money on.
If we add more data like the match length, number of games
already played, current score, etc. then we may become able
to guess with increasing accuracy which side is the stronger
player. (And that's exactly what the bots should do evaluating
each position but I don't know if they do or not).
This post is getting too long already, let me try to wrap it up
bu saying that without looking at all the possible moves at the
previous position and verifying whether the assumed stronger
player had indeed picked the best move, there is no continuity
in the game and it's not possible to make the statement that
"current skill can result in future luck".
Even if we look at the previous move, it still would be a one
sided fallacy because we never say that a player "got unlucky
because he made the best move in the previous position".
And then there is the case of people like me who argue that a
player may chose to make an inferior move as part of a "game
plan"... What if such a player gets lucky as a result of his
blunder?
In fact, look for that in my match against a bot on FIBS that
was discussed just recently in a different thread. As Michael
has pointed out, both sides were about equally unlucky (or lucky)
despite the apparently huge skill difference between me and the
bot (as *inaccurately* indicated by our error rates).
So, my two conclusions are:
1- Arguments like "skill creates luck" may occasionally and
situationally appear to be a valid observation but they are
mere fallacies within the entirety of the subject.
2- You can't measure luck by mixing and matching it with skill
or derive anything meaningful from the results of doing such.
MK
Bradley K. Sherman
Jan 21, 2015, 8:58:21 PM1/21/15
to
Lucky Day or Unlucky Day?
I've told this story before: I headed to a tournament in Sacramento
(from Berkeley) in the late 70's. On the way I had *two* flat tires.
Luckily I have AAA so after 20 minutes of terror on a freeway overpass
with almost no shoulder, I got towed. I arrived at the tournament
about an hour late (and about 20 minutes into the first match). The
TD said that if I wanted, and my opponent said it was okay, I could
play the 9 point match starting down 5-0 (4-0? Can't remember exactly).
I said okay, he said okay. I won that match and then steamrolled
the field until I got to the finals where I lost to Nack Ballard.
I won about the same amount of money as it cost to repair the car.
To this day I cannot figure out if I was lucky or unlucky.
--bks
I've told this story before: I headed to a tournament in Sacramento
(from Berkeley) in the late 70's. On the way I had *two* flat tires.
Luckily I have AAA so after 20 minutes of terror on a freeway overpass
with almost no shoulder, I got towed. I arrived at the tournament
about an hour late (and about 20 minutes into the first match). The
TD said that if I wanted, and my opponent said it was okay, I could
play the 9 point match starting down 5-0 (4-0? Can't remember exactly).
I said okay, he said okay. I won that match and then steamrolled
the field until I got to the finals where I lost to Nack Ballard.
I won about the same amount of money as it cost to repair the car.
To this day I cannot figure out if I was lucky or unlucky.
--bks
michae...@gmail.com
Jan 22, 2015, 7:35:20 AM1/22/15
to
On Thursday, January 22, 2015 at 3:48:22 AM UTC+2, mu...@compuplus.net wrote:
>
> So, my two conclusions are:
>
> 1- Arguments like "skill creates luck" may occasionally and
> situationally appear to be a valid observation but they are
> mere fallacies within the entirety of the subject.
>
> 2- You can't measure luck by mixing and matching it with skill
> or derive anything meaningful from the results of doing such.
>
> MK
I haven't finished my thoughts about luck in the other topic but here are some extracts from my draft:
>
> So, my two conclusions are:
>
> 1- Arguments like "skill creates luck" may occasionally and
> situationally appear to be a valid observation but they are
> mere fallacies within the entirety of the subject.
>
> 2- You can't measure luck by mixing and matching it with skill
> or derive anything meaningful from the results of doing such.
>
> MK
Let's start from the argument that "skill creates luck". Imo this is true but not to the extend people think of.A doubtful move in a 1 pointer would cost about 2% MWC and a blunder about 4.5% MWC. How many would an average player do in a 1 pointer?? However swings of luck by +- 5% are very common in any single pointer, we even have swings in the range of +-10, 20, 30 and sometime more %. My conclussion out of this is that the more similar the skill of the players is the more the majority of games won by pure luck. For skill to start winning more games than luck, the skill difference must be more than 230 abs.Fibs rating points in a 7 point match. And even at that point luck shares 2/3rds of all matches EQUALLY!! between the stronger and weaker player.(1/3rd gift to each one)
Now the effect of playing inferior moves:
Let's take this example:
GNU Backgammon Position ID: Nts2ABBs2wUABw
Match ID : cAk3AAAAAAAE
+13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
| O O O | | O O X O O | 0 points
| O O O | | O O X O O |
| | | X |
| | | |
| | | |
v| |BAR| | 1 point match (Cube: 1)
| | | |
| | | |
| X | | |
| X | | X X X X | Rolled 56
| X X | | X X X X O | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: Mike
Pip counts : O 103, X 128
The best move here is 21/15 7/2.
The inferior move is 8/2 7/2.
From the luck point of view (on next roll alone) O would prefer X to play 21/15 7/2 because his 62 being among his Lucky rolls would really knock X off ;-)
I have some other conclussions that i'd rather explain in the other topic like for example that "Luck creates more Luck".
Regarding your second conclussion, i must say I haven't made up my mind yet,it's one of the things that I am still thinking about.
There are still people in various fora who think "luck" is a conceptual thing. Certainly Bradley's post falls within that category. However I have to disagree that Luck [in_backgammon] is a conceptual thing. It is not, it is a measurable property.
Paul
Jan 22, 2015, 7:46:26 AM1/22/15
to
I also think you were unlucky to be playing in a country where the chocolate bars taste awful because they don't have any dairy products in them. Of course, if you weren't eating chocolate in between rounds, that may not have been a factor.
Paul
Bradley K. Sherman
Jan 22, 2015, 10:34:59 AM1/22/15
to
<michae...@gmail.com> wrote:
> ...
luck of an opening 3-1 versus an opening 4-2? We could have
XG version N play itself 1,000,000 times to get an empirical
value, but that value would be wrong as soon as XG version N+1
was released.
--bks
> ...
>There are still people in various fora who think "luck" is a conceptual
>thing. Certainly Bradley's post falls within that category. However I
>have to disagree that Luck [in_backgammon] is a conceptual thing. It is
>not, it is a measurable property.
"Measurable" is a conceptual thing. What is the measurable
>thing. Certainly Bradley's post falls within that category. However I
>have to disagree that Luck [in_backgammon] is a conceptual thing. It is
>not, it is a measurable property.
luck of an opening 3-1 versus an opening 4-2? We could have
XG version N play itself 1,000,000 times to get an empirical
value, but that value would be wrong as soon as XG version N+1
was released.
--bks
michae...@gmail.com
Jan 22, 2015, 11:50:12 AM1/22/15
to
On Thursday, January 22, 2015 at 5:34:59 PM UTC+2, Bradley K. Sherman wrote:
> "Measurable" is a conceptual thing. What is the measurable
> luck of an opening 3-1 versus an opening 4-2? We could have
> XG version N play itself 1,000,000 times to get an empirical
> value, but that value would be wrong as soon as XG version N+1
> was released.
>
> --bks
Conceptual in the sense that by the term "luck" different people would mean different things. By the minute we agree to the mathematical definition of luck_in_backgammon though it stops being conceptual and it becomes measurable.
> "Measurable" is a conceptual thing. What is the measurable
> luck of an opening 3-1 versus an opening 4-2? We could have
> XG version N play itself 1,000,000 times to get an empirical
> value, but that value would be wrong as soon as XG version N+1
> was released.
>
> --bks
And we all expect the measure to give us a + or - % MWC. How is that conceptual??
Perhaps you mean the method used to measure it is conceptual,in which case, yes of course I agree, there is no doubt about it.
Bradley K. Sherman
Jan 22, 2015, 11:59:55 AM1/22/15
to
<michae...@gmail.com> wrote:
>On Thursday, January 22, 2015 at 5:34:59 PM UTC+2, Bradley K. Sherman wrote:
>
>> "Measurable" is a conceptual thing. What is the measurable
>> luck of an opening 3-1 versus an opening 4-2? We could have
>> XG version N play itself 1,000,000 times to get an empirical
>> value, but that value would be wrong as soon as XG version N+1
>> was released.
>
>On Thursday, January 22, 2015 at 5:34:59 PM UTC+2, Bradley K. Sherman wrote:
>
>> "Measurable" is a conceptual thing. What is the measurable
>> luck of an opening 3-1 versus an opening 4-2? We could have
>> XG version N play itself 1,000,000 times to get an empirical
>> value, but that value would be wrong as soon as XG version N+1
>> was released.
>
>Conceptual in the sense that by the term "luck" different people would
>mean different things. By the minute we agree to the mathematical
>definition of luck_in_backgammon though it stops being conceptual and it
>becomes measurable.
>And we all expect the measure to give us a + or - % MWC. How is that
>conceptual??
>
>Perhaps you mean the method used to measure it is conceptual,in which
>case, yes of course I agree, there is no doubt about it.
I mean that you're never going to arrive at a "mathematical definition
>mean different things. By the minute we agree to the mathematical
>definition of luck_in_backgammon though it stops being conceptual and it
>becomes measurable.
>And we all expect the measure to give us a + or - % MWC. How is that
>conceptual??
>
>Perhaps you mean the method used to measure it is conceptual,in which
>case, yes of course I agree, there is no doubt about it.
of luck_in_backgammon" except by fiat. If one's opponent makes a
bad move, that can be a *very* lucky event. It can be the difference
between winning and losing a tournament, say. Good luck measuring it.
--bks
michae...@gmail.com
Jan 22, 2015, 1:54:47 PM1/22/15
to
On Thursday, January 22, 2015 at 6:59:55 PM UTC+2, Bradley K. Sherman wrote:
>
> I mean that you're never going to arrive at a "mathematical definition
> of luck_in_backgammon" except by fiat. If one's opponent makes a
> bad move, that can be a *very* lucky event. It can be the difference
> between winning and losing a tournament, say. Good luck measuring it.
>
> --bks
The mathematical definition of luck of a roll is how much +- of MWC % it delivers compared with the average of all rolls of that specific throw. There you are without a fiat. ;-)
>
> I mean that you're never going to arrive at a "mathematical definition
> of luck_in_backgammon" except by fiat. If one's opponent makes a
> bad move, that can be a *very* lucky event. It can be the difference
> between winning and losing a tournament, say. Good luck measuring it.
>
> --bks
In all occasions you would wish your opponent had make a bad move because that would not only increase your chances to get a lucky roll but at the same time increase your MWC more that it would otherwise.
The luck of both rolls is still measurable and the bots can show it to you.
Good luck in playing bad moves.
Bradley K. Sherman
Jan 22, 2015, 3:35:42 PM1/22/15
to
<michae...@gmail.com> wrote:
> ...
That's an algorithm, not a definition, and one that will change with
whatever prodedure you employ to determine MWC%. I think you'll find
that the phrase "average of all rolls" only makes the matter worse.
I don't see the point of this, but if it makes you happy, carry on.
--bks
> ...
>The mathematical definition of luck of a roll is how much +- of MWC % it
>delivers compared with the average of all rolls of that specific throw.
>There you are without a fiat. ;-)
> ...
>delivers compared with the average of all rolls of that specific throw.
>There you are without a fiat. ;-)
That's an algorithm, not a definition, and one that will change with
whatever prodedure you employ to determine MWC%. I think you'll find
that the phrase "average of all rolls" only makes the matter worse.
I don't see the point of this, but if it makes you happy, carry on.
--bks
michae...@gmail.com
Jan 22, 2015, 4:45:18 PM1/22/15
to
On Thursday, January 22, 2015 at 10:35:42 PM UTC+2, Bradley K. Sherman wrote:
You are mixing apples with oranges. Algorithm is the way the bots use to measure it.You may claim it's inaccurate, you may claim whatever you like, it doesn't change one iota on how it's defined.
Just like you can't change the definition of time by measuring it with clock, a pendulum, half life of radioactive elements, or simply looking at the position of the sun.
The point of the discussion are the two questions asked by Murat and I am not seeing anyone spending even 1 mg of gray matter to respond.
You are mixing apples with oranges. Algorithm is the way the bots use to measure it.You may claim it's inaccurate, you may claim whatever you like, it doesn't change one iota on how it's defined.
Just like you can't change the definition of time by measuring it with clock, a pendulum, half life of radioactive elements, or simply looking at the position of the sun.
The point of the discussion are the two questions asked by Murat and I am not seeing anyone spending even 1 mg of gray matter to respond.
Michael Petch
Jan 22, 2015, 4:50:08 PM1/22/15
to
On 2015-01-22 2:45 PM, michae...@gmail.com wrote:
> The point of the discussion are the two questions asked by Murat and I am not seeing anyone spending even 1 mg of gray matter to respond.
If you'd been on here for over a decade you'd probably know the reason.
> The point of the discussion are the two questions asked by Murat and I am not seeing anyone spending even 1 mg of gray matter to respond.
michae...@gmail.com
Jan 22, 2015, 4:53:52 PM1/22/15
to
On Thursday, January 22, 2015 at 11:50:08 PM UTC+2, Michael Petch wrote:
>
> If you'd been on here for over a decade you'd probably know the reason.
And that would be an excuse to divert all discussions to irrelevant issues??
>
> If you'd been on here for over a decade you'd probably know the reason.
Message has been deleted
Bradley K. Sherman
Jan 22, 2015, 7:47:46 PM1/22/15
to
<michae...@gmail.com> wrote:
>On Thursday, January 22, 2015 at 11:50:08 PM UTC+2, Michael Petch wrote:
>
>>
>On Thursday, January 22, 2015 at 11:50:08 PM UTC+2, Michael Petch wrote:
>
>>
>> If you'd been on here for over a decade you'd probably know the reason.
>
>
>And that would be an excuse to divert all discussions to irrelevant issues??
Correction: *Away* from irrelevant issues.
--bks
Tim Chow
Jan 22, 2015, 9:12:36 PM1/22/15
to
On Thursday, January 22, 2015 at 1:54:47 PM UTC-5, michae...@gmail.com wrote:
> The mathematical definition of luck of a roll is how much +- of MWC % it
> delivers compared with the average of all rolls of that specific throw. There
> you are without a fiat. ;-)
But insisting that this is *the* mathematical definition of luck is fiat.
> The mathematical definition of luck of a roll is how much +- of MWC % it
> delivers compared with the average of all rolls of that specific throw. There
> you are without a fiat. ;-)
One could, for example, define luck to be the number of rolls that are better than average, minus the number of rolls that are worse than average. This would be a mathematical definition. I don't think it's as good as your definition, but you can't rule it out except by fiat.
---
Tim Chow
Paul
Jan 23, 2015, 3:54:17 AM1/23/15
to
With this definition of luck, we would not have the apparent paradox of better players consistently being "luckier".
Speaking personally, I prefer such skill-independent metrics although the one I just said is probably a worse idea than mixing coffee and tea in the same cup and serving it in a fancy hotel. The reason the idea is probably bad is that I only just thought of it and a better skill-independent definition would require some work.
Paul
mu...@compuplus.net
Jan 23, 2015, 12:42:30 PM1/23/15
to
google archive has my articles from even 1996-1998) you
would see what a nice and polite person I was... :)
I guess one adapts over time... :(
MK
Tim Chow
Jan 23, 2015, 8:03:39 PM1/23/15
to
On Friday, January 23, 2015 at 3:54:17 AM UTC-5, Paul wrote:
> With this definition of luck, we would not have the apparent paradox of
> better players consistently being "luckier".
The paradox can be removed even with the current definition of luck, if we agree to say that the "luckier" player is the one with the higher *mean* luck overall, rather than the player who has *more* luck in a particular match.
> With this definition of luck, we would not have the apparent paradox of
> better players consistently being "luckier".
In fact I'd argue that this is a better way to define "luckier." If I'm a little bit luckier than you are most of the time, and you're a lot luckier than I am the rest of the time, then it seems reasonable to me to say that we're equally lucky overall. In contrast, I don't think it should be surprising to get seemingly paradoxical results if we focus solely on the fact that I'm luckier than you are *in more matches*, while ignoring *how much luckier* I am in those matches.
But perhaps you still find it disturbing that different players can have different luck distributions.
---
Tim Chow
michae...@gmail.com
Jan 24, 2015, 6:00:09 AM1/24/15
to
On Friday, January 23, 2015 at 7:42:30 PM UTC+2, mu...@compuplus.net wrote:
> And if you go a little further back than that (I think
> google archive has my articles from even 1996-1998) you
> would see what a nice and polite person I was... :)
>
> I guess one adapts over time... :(
>
> MK
You stilled remained a thinker. There is only one way to check your thoughts, get conclusions, clear misconceptions, or pass correct ideas to others: Discuss them with other thinkers without planting bombs that could kill their responses ;-)
> And if you go a little further back than that (I think
> google archive has my articles from even 1996-1998) you
> would see what a nice and polite person I was... :)
>
> I guess one adapts over time... :(
>
> MK
0 new messages