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Oct 20, 1998, 3:00:00 AM10/20/98

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Here is a detailed explanation of variables and

calculations I found at a web site about FIBS

rating calculations:

calculations I found at a web site about FIBS

rating calculations:

----------------------------------------------------------------------

What do the variables mean?

n = the length of the match.

P1 = the rating of Player 1.

P2 = the rating of Player 2.

E1 = the experience of Player 1 right before finishing the match.

E2 = the experience of Player 2 right before finishing the match.

PE1 = experience factor for Player 1 (calculated).

PE2 = experience factor for Player 2 (calculated).

D = the difference between the two ratings (calculated).

F = the probability of the favorite winning the match (calculated).

U = the probability of the underdog winning the match (calculated).

How are the Variables calculated?

D = absolute value of P1-P2

U = 1/(10^(D*SQRT(n)/2000)+1)

F = 1-U

PE1 = maximum(1, 5-((E1+n)/100))

PE2 = maximum(1, 5-((E2+n)/100))

How is the rating change calculated?

If Player 1 is higher rated and wins, P1's rating increases by

4*PE1*SQRT(n)*U

If Player 1 is higher rated and loses, P1's rating decreases by

4*PE1*SQRT(n)*F

If Player 1 is lower rated and wins, P1's rating increases by

4*PE1*SQRT(n)*F

If Player 1 is lower rated and loses, P1's rating decreases by

4*PE1*SQRT(n)*U

If Player 2 is higher rated and wins, P2's rating increases by

4*PE2*SQRT(n)*U

If Player 2 is higher rated and loses, P2's rating decreases by

4*PE2*SQRT(n)*F

If Player 2 is lower rated and wins, P2's rating increases by

4*PE2*SQRT(n)*F

If Player 2 is lower rated and loses, P2's rating decreases by

4*PE2*SQRT(n)*U

----------------------------------------------------------------------

Before I make comments, let me make sure of one

thing. Is this the same/currently used formula

that many people describe as "simple", "beautiful",

"stable", "proven to work", "accurate", etc...?

The variable "U" that seems to be the heart of this

formula goes completely above my head. What is that

"2000"...? Why square-root and not cube-root (pun

intended!) of "n"...?

While at it, let me try explaining the formula I had

previously suggested, following the above format:

----------------------------------------------------------------------

What do the variables mean?

M = the length of the match.

P1 = the rating of Player 1.

P2 = the rating of Player 2.

D = the difference between the two ratings (calculated).

W = half of "players rating window" (constant).

How are the Variables calculated?

D = absolute value of P1-P2

W = arbitrarily set by me to 50, as an example.

How is the rating change calculated?

Player 1's rating changes to: P1 & (M+M*((W-D)/abs(W-D)))/2

Player 2's rating changes to: P2 & (M+M*((W-D)/abs(W-D)))/2

& = "+" for the winning player, "-" for the loosing player.

----------------------------------------------------------------------

As is, my above formula will produce a "divide by 0"

error when P1=P2, but I'll let rgb's math majors put

the final touch on it since I'm a little rusty/slow

with devising elegant formulas. In actual programming

it would of course be simpler to use "if" clauses...

In an imaginary range of ratings from 0 to 2000, the

value 50 for W would mean an average 5% inaccuracy;

increasing going down, and decreasing going up the

ratings range. I think this may be an unintentional

but welcome effect of this system. Any comments on

this...?

I also would like to revise my initial suggestion

about starting new players at an arbitrary rating

like 1000 (or 1500). I think a better approach would

be to start them at the "most common rating" for the

entire system, which can be computed daily or weekly

and rounded to increments of 50, for example. This

approach would speed up the process of finding one's

place better than the existing adjustments based on

experience or suggested modifications similar to the

chess rating systems. After starting at wherever the

biggest bulge may occur in the ratings distribution,

the majority will get to where they belong faster

than from any other arbitrary point and/or using any

other means of expediting the process. Also, if the

rating range shifts up or down as a whole (because

more beginner or expert players flowing in, or even

because all players getting better in time, etc.)

that entry point would also shift along dynamicly.

I hope not everybody lost interest in this subject

and I'm not talking to myself... :)

MK

Oct 20, 1998, 3:00:00 AM10/20/98

to

Despite the complexity, the formula is fairly simple in that....

1) A certain number of points are at stake in each match - that number

is 4 times the square root of the length of the match

2) There is a calculation as to the relative likelihood of the two

players winning. The odds of the favorite winning increase as the

length of the match increases.

3. The point split is based on the odds of winning. If you play a

4-point match (I know no one does, but it makes the numbers come out

more even) there are 8 points at state. If you are a 62.5% favorite

to win, you will either win 3 points or lose 5.

4. For the first 400 games you play, your rating moves more quickly.

I would like to see some emprical analysis of the relative likelihood

of winning and losing - but other than that - the formula seems pretty

sensible to me.

Oct 20, 1998, 3:00:00 AM10/20/98

to

hankyou...@home.com (Hank Youngerman) writes:

> I would like to see some emprical analysis of the relative likelihood

> of winning and losing - but other than that - the formula seems pretty

> sensible to me.

> I would like to see some emprical analysis of the relative likelihood

> of winning and losing - but other than that - the formula seems pretty

> sensible to me.

Careful what you wish for, you just might get it :-)

I performed an experiment testing these three hypotheses:

* That the basic Elo system could accurately describe the distribution

of backgammon game results, if matches were all of the same length.

* That the FIBS implementation of the Elo system accurately describes

the distribution of backgammon game results, for matches of all

lengths.

* That the FIBS implementation of the Elo system systematically

overestimates the underdog's chances in shorter than average matches,

and overestimates the favourite's chances in longer than average

matches.

The details are written up at:

http://www.cs.arizona.edu/~gary/backgammon/elo.html

but the bottom line is that my data (several thousand one-pointers that

Abbott played against opponents ranging from 1280-1880) showed no evidence

refuting _any_ of the three hypotheses above. I was going to go into

more detail (graphs of observed winning probabilities vs. FIBS-predicted

winning probabilities vs. best-fit Elo predicted winning probabilities

specifically fitted to the match length, etc.) but once I got as far as

what's on that web page, I'd pretty much satisfied my own curiosity so I

think it's pointless going any further.

(The one thing I would be interested in is performing the same kind of

analysis on longer length matches, if anybody has data available.

Unfortunately the chi-squared test I used needs LOTS of data; preferably

over 1000 matches of identical length. If they all involve the same

player, that's even better; if that player is a bot and so we know their

ability didn't change while the data were being collected, that's better

still.)

My current opinion is that the Elo system can be a very good predictor

of backgammon game distributions; that the FIBS implementation (with

the ratings difference scaled by the square root of the match length)

is flawed but adequate; and that FIBS systematically overestimates

the underdog's chances in short matches and overestimates the favourite's

chances in long matches. As I said, I've satisfied my own curiosity and

am now going to shut my mouth on this topic (bet you thought you'd never

hear me say that :-)

Cheers,

Gary.

--

Gary Wong, Department of Computer Science, University of Arizona

ga...@cs.arizona.edu http://www.cs.arizona.edu/~gary/

Oct 21, 1998, 3:00:00 AM10/21/98

to

In <wtbtn79...@brigantine.CS.Arizona.EDU> Gary Wong wrote:

>I performed an experiment testing these three hypotheses:

> * That the basic Elo system could accurately describe the distribution

> of backgammon game results, if matches were all of the same length.

> * That the FIBS implementation of the Elo system accurately describes

> the distribution of backgammon game results, for matches of all

> lengths.

> * That the FIBS implementation of the Elo system systematically

> overestimates the underdog's chances in shorter than average matches,

> and overestimates the favourite's chances in longer than average

> matches.

>The details are written up at:

> http://www.cs.arizona.edu/~gary/backgammon/elo.html

>but the bottom line is that my data (several thousand one-pointers

>that Abbott played against opponents ranging from 1280-1880) showed

>no evidence refuting _any_ of the three hypotheses above.

>.....My current opinion is that the Elo system can be a very good

>predictor of backgammon game distributions; that the FIBS

>implementation (with the ratings difference scaled by the square

>root of the match length) is flawed but adequate

Gary, after reading these, I went back to your page

where you have the log of the last 1000 games played

by Abbott. As you did in your above analysis, I did

eliminate players with less than 400 experience and

ended up with 815 matches of which Abbot had won 435

and lost 380. The average rating of its opponents was

1615.79 and its winning rate was 53.37%.

Then I logged on to FIBS to see what rating difference

would give me 53.37% chance of winning and found out

that it's about 120 points (my rating at this time was

1668). Looking at the table in your web page mentioned

above, (given that you mentioned R=1505 for Abbott), I

could see that it would have that same winning chance

against opponents rated at around 1400, which gives

approximately the same ratings difference also.

Abbott's current rating on FIBS is 1552. I believe at

the time we were talking about those last 1000 matches

(in the thread "loosing streaks" about a week ago or

so) it was well below 1500 but let's just stick with

the higher number here and say 1550. If I understand

all this rating stuff correctly, for Abbott to have a

53.37% winning chance against opponents rated at 1615,

its own rating would have to be around 1735... That's

a whopping discrepency of almost 200 points.

Let's stress that even the higher number above (1550)

that I picked would be its end rating not its average

rating. Considering it won 435 out of the 815 games I

included in my analysis, its starting rating and/or

average rating must have been lower than that. I think

while talking about loosing streaks its rating was

around 1460's(?) and at that time its average rating

during those 1000 logged matches may have been around

1450's. So, we may be talking here about a discrepency

that's possibly as high as 250 points or even higher.

Unless I'm misunderstanding/misinterpreting things

and way off in my above numbers, I would conclude

that FIBS current rating system may not be just

slightly flawed and still adequate; but actually

grossly inaccurate...

MK

BTW, looking at the "wwllwll..." sequences that you

had posted in the thread about loosing streaks and

looking at the log of those 1000 matches by just

scrolling it up and down for a few minutes, I had

come to the conclusion (which I posted in response

to your article) that Abbott had lost a lot of its

games to much higher rated opponents and that it had

done better than expected overall. It looks like a

more careful examination of that log confirms what

I had quickly observed then.

Oct 21, 1998, 3:00:00 AM10/21/98

to

In <362c044d.5390690@news> hankyou...@home.com wrote:

>Despite the complexity, the formula is fairly simple in that....

Complex=simple...? :)

>1) A certain number of points are at stake in each match - that

>number is 4 times the square root of the length of the match

What is this based on? Why 4 times? Why square root?

Please don't take my questions personally and/or feel

obligated to answer, but I'm really making an effort

to understand all this.

>4. For the first 400 games you play, your rating moves more quickly.

This is a minor issue, but where did 400 came from?

>I would like to see some emprical analysis of the relative

>likelihood of winning and losing - but other than that - the

>formula seems pretty sensible to me.

I would like to see such data also but preferably from

different sources than the ones using the said formula

to begin with. Otherwise, I'm not sure if any analysis

done on the data based on ratings produced by a formula

in order to see if that same formula works could be

considered valid...

MK

Oct 21, 1998, 3:00:00 AM10/21/98

to

Gary Wong wrote:

>

> I performed an experiment testing these three hypotheses:

>

> * That the basic Elo system could accurately describe the distribution

> of backgammon game results, if matches were all of the same length.

>

> * That the FIBS implementation of the Elo system accurately describes

> the distribution of backgammon game results, for matches of all

> lengths.

>

> * That the FIBS implementation of the Elo system systematically

> overestimates the underdog's chances in shorter than average matches,

> and overestimates the favourite's chances in longer than average

> matches.

>

> The details are written up at:

>

> http://www.cs.arizona.edu/~gary/backgammon/elo.html

>

> but the bottom line is that my data (several thousand one-pointers that

> Abbott played against opponents ranging from 1280-1880) showed no evidence

>

> I performed an experiment testing these three hypotheses:

>

> * That the basic Elo system could accurately describe the distribution

> of backgammon game results, if matches were all of the same length.

>

> * That the FIBS implementation of the Elo system accurately describes

> the distribution of backgammon game results, for matches of all

> lengths.

>

> * That the FIBS implementation of the Elo system systematically

> overestimates the underdog's chances in shorter than average matches,

> and overestimates the favourite's chances in longer than average

> matches.

>

> The details are written up at:

>

> http://www.cs.arizona.edu/~gary/backgammon/elo.html

>

> but the bottom line is that my data (several thousand one-pointers that

> Abbott played against opponents ranging from 1280-1880) showed no evidence

> refuting _any_ of the three hypotheses above. I was going to go into

> more detail (graphs of observed winning probabilities vs. FIBS-predicted

> winning probabilities vs. best-fit Elo predicted winning probabilities

> specifically fitted to the match length, etc.) but once I got as far as

> what's on that web page, I'd pretty much satisfied my own curiosity so I

> think it's pointless going any further.

>

> (The one thing I would be interested in is performing the same kind of

> analysis on longer length matches, if anybody has data available.

> Unfortunately the chi-squared test I used needs LOTS of data; preferably

> over 1000 matches of identical length. If they all involve the same

> player, that's even better; if that player is a bot and so we know their

> ability didn't change while the data were being collected, that's better

> still.)

> more detail (graphs of observed winning probabilities vs. FIBS-predicted

> winning probabilities vs. best-fit Elo predicted winning probabilities

> specifically fitted to the match length, etc.) but once I got as far as

> what's on that web page, I'd pretty much satisfied my own curiosity so I

> think it's pointless going any further.

>

> (The one thing I would be interested in is performing the same kind of

> analysis on longer length matches, if anybody has data available.

> Unfortunately the chi-squared test I used needs LOTS of data; preferably

> over 1000 matches of identical length. If they all involve the same

> player, that's even better; if that player is a bot and so we know their

> ability didn't change while the data were being collected, that's better

> still.)

This touches on a question I have been evaluating. I am suspicious of

the fibs rating forumla in the way it accounts for match length. I have

collected a lot of match results and checked empirically whether the

winning probability as predicted by the FIBS rating formula actually

matches the observed winning probability for a given match between

players

of known ratings. I sampled the players ratings before recording any

matches so that the random errors in the ratings would be uncorrelated

with with the outcome of the observed games. Only matches where both

players had at least 1000 experience points were included. Currently

the number of recorded results is as follows:

1 point matches 19926

3 point matches 12036

5 point matches 8621

1, 3, and 5 account for 90% of all matches.

I then took the fibs ratings formula for win probability:

P = 1/(1 + 10^(D*sqrt(N)/2000))

Rather than using the match length for N, I used an effective

match length where the effective match length was chosen so

that the formula gave the best fit with the observed data.

The results were what I expected only more extreme. The effective

match lengths which gave the best fit were as follows:

match length effective match length

---------------------------------------------------------

1 1.6

3 1.6

5 2.1

Due to the limited number of matches recorded, the standard error

on these effective match lengths is about 0.25 . If anyone notices

zbest lurking on fibs, he is collecting more data to try to get

a more accurate fix on these numbers.

These numbers suggest that a 3 point match has exactly the same

skill component as a 1 point match, and a 5 point match only

slightly more.

I am at a loss to explain these numbers, but the implication is

that if you want to increase you rating, play 1 point matches

agains the weakest opponents you can find, and play long matches

against the strongest opponents you can find. It also suggests

that if we want to make backgammon more a game of skill and less

a game of luck, we should eliminate the doubling cube.

Oct 21, 1998, 3:00:00 AM10/21/98

to

mu...@cyberport.net (Murat Kalinyaprak) writes:

> >.....My current opinion is that the Elo system can be a very good

> >predictor of backgammon game distributions; that the FIBS

> >implementation (with the ratings difference scaled by the square

> >root of the match length) is flawed but adequate...> >.....My current opinion is that the Elo system can be a very good

> >predictor of backgammon game distributions; that the FIBS

> >implementation (with the ratings difference scaled by the square

>

> Gary, after reading these, I went back to your page

> where you have the log of the last 1000 games played

> by Abbott. As you did in your above analysis, I did

> eliminate players with less than 400 experience and

> ended up with 815 matches of which Abbot had won 435

> and lost 380. The average rating of its opponents was

> 1615.79 and its winning rate was 53.37%.

I took a look just now and got exactly the opposite results (ie. Abbott

lost 435 and won 380). Note that a "w" in the 3rd column means _Abbott_

won, and an "l" means _Abbott_ lost. 53.37% is the _loss_ rate; the

observed win rate is 46.6%. In a sample of this size, the standard error

works out to 1.7%.

> Then I logged on to FIBS to see what rating difference

> would give me 53.37% chance of winning and found out

> that it's about 120 points (my rating at this time was

> 1668).

Yes, FIBS predicts this win rate at a difference of 117 points (the

loss rate naturally means a difference of -117). Since there's some

sampling error in the 53.37% figure, we should really be more

conservative and give this figure with the standard deviation, which

is unfortunately a whopping 60 points.

> Abbott's current rating on FIBS is 1552. I believe at

> the time we were talking about those last 1000 matches

> (in the thread "loosing streaks" about a week ago or

> so) it was well below 1500 but let's just stick with

> the higher number here and say 1550.

Yes, 1550 is certainly too high. The best estimates I have of Abbott's

true ability are 1503 or 1478, in that those ratings most closely predict

the observed win rate distributions (1503 using the best-fit Elo parameters

to observed 1-point matches; 1478 using the FIBS "d sqrt(n) / 2000" method

which I believe overestimates the underdog's chances for 1 point matches).

Unfortunately these are MLEs (maximum likelihood estimators; ie. they are

obtained numerically by observing that higher or lower values than 1503 or

1478 respectively predict the observed data less accurately) and I do not

know how to measure the uncertainty in this value. In any case, if you

want a figure to use with the FIBS variant of the Elo system, the best

estimate I can give you is 1478.

> If I understand

> all this rating stuff correctly, for Abbott to have a

> 53.37% winning chance against opponents rated at 1615,

> its own rating would have to be around 1735... That's

> a whopping discrepency of almost 200 points.

Since it really _lost_ 53.37% of games, our estimation is in fact 1615

_minus_ 117, or 1498. This estimate is again subject to a standard error

of 60 points.

> Unless I'm misunderstanding/misinterpreting things

> and way off in my above numbers, I would conclude

> that FIBS current rating system may not be just

> slightly flawed and still adequate; but actually

> grossly inaccurate...

I don't think there's any discrepancy at all. From the 1000 game sample

we derive an estimated rating of 1498; from the MLE calculations shown on

the web page we get 1478. This disagreement is well within the margin

of error. (If there is anybody out there who observes Abbott's long term

rating, I believe they would trust that these are reasonably accurate

estimates of its true performance as well. It tends to fluctuate anywhere

from the low 1400s to mid 1500s.)

> BTW, looking at the "wwllwll..." sequences that you

> had posted in the thread about loosing streaks and

> looking at the log of those 1000 matches by just

> scrolling it up and down for a few minutes, I had

> come to the conclusion (which I posted in response

> to your article) that Abbott had lost a lot of its

> games to much higher rated opponents and that it had

> done better than expected overall. It looks like a

> more careful examination of that log confirms what

> I had quickly observed then.

I don't understand what you mean here. Losing games to much higher rated

opponents is surely nothing more than we would expect? And I see no

evidence that it has done better than expected overall, either in the

1000 game sample here or the larger sample categorised by opponent strength

on the web page.

Oct 21, 1998, 3:00:00 AM10/21/98

to

In article <362E02...@giga-net.com> Jim Williams <ji...@giga-net.com> writes:

>Rather than using the match length for N, I used an effective

>match length where the effective match length was chosen so

>that the formula gave the best fit with the observed data.

>

>Rather than using the match length for N, I used an effective

>match length where the effective match length was chosen so

>that the formula gave the best fit with the observed data.

>

>The effective match lengths which gave the best fit were as follows:

>

> match length effective match length

>---------------------------------------------------------

> 1 1.6

> 3 1.6

> 5 2.1

>

>Due to the limited number of matches recorded, the standard error

>on these effective match lengths is about 0.25 .

>

> match length effective match length

>---------------------------------------------------------

> 1 1.6

> 3 1.6

> 5 2.1

>

>Due to the limited number of matches recorded, the standard error

>on these effective match lengths is about 0.25 .

Wow. Great work Jim (and Gary). This is cool stuff.

I'm only a little surprised by the results for 1 and 3 pointers,

since I've long thought that 1 point matches were underrated and

3 point matches overrated.

However, theoretically it seems entirely implausible that 1 and 3

should be equivalent. A 3 point match will always have a game

played to conclusion (like a 1 pointer), and will have many other

decisions in earlier games. So I'm certain that there is more

skill in a 3 pointer than in a 1 pointer.

Besides the uncertainty due to the amount of data, it could well

be that people play 3 pointers so bad that this fact is obscured.

I think most people play 3 pointers really badly, especially at

-2:-3.

I'm very surprised by the results for 5 pointers.

Could you make your data publicly available? I would like to

try some alternative analyses.

David Montgomery

mo...@cs.umd.edu

monty on FIBS

Oct 21, 1998, 3:00:00 AM10/21/98

to

Jim Williams <ji...@giga-net.com> writes:

> Gary Wong wrote:

> > (The one thing I would be interested in is performing the same kind of

> > analysis on longer length matches, if anybody has data available.

> > Unfortunately the chi-squared test I used needs LOTS of data; preferably

> > over 1000 matches of identical length. If they all involve the same

> > player, that's even better; if that player is a bot and so we know their

> > ability didn't change while the data were being collected, that's better

> > still.)

>

> [snip]

> Currently the number of recorded results is as follows:

>

> 1 point matches 19926

> 3 point matches 12036

> 5 point matches 8621

> Gary Wong wrote:

> > (The one thing I would be interested in is performing the same kind of

> > analysis on longer length matches, if anybody has data available.

> > Unfortunately the chi-squared test I used needs LOTS of data; preferably

> > over 1000 matches of identical length. If they all involve the same

> > player, that's even better; if that player is a bot and so we know their

> > ability didn't change while the data were being collected, that's better

> > still.)

>

> Currently the number of recorded results is as follows:

>

> 1 point matches 19926

> 3 point matches 12036

> 5 point matches 8621

Wow, that's exactly the data I would have liked in the first place! :-)

> The results were what I expected only more extreme. The effective

> match lengths which gave the best fit were as follows:

>

> match length effective match length

> ---------------------------------------------------------

> 1 1.6

> 3 1.6

> 5 2.1

>

> Due to the limited number of matches recorded, the standard error

> on these effective match lengths is about 0.25.

This is very encouraging! My result of d/1634 for the MLE exponent for

1-point matches (instead of the d sqrt(n)/2000 = d/2000 that FIBS

predicts) works out to an effective match length of 1.5, which is well

within the margin of error for agreement with your value of 1.6.

(I'd like to know how you measured the standard error on those quantities.

The 1634 figure I got was a chi-squared minimum parameter, but tacking a

variance onto that takes way more estimation theory than I understand.)

> I am at a loss to explain these numbers,

I don't think we need much more explanation than we already have, do

we? We expect that gammons and the cube lead to significant

dependence between points in a multi-point match; with a bit of

hand-waving (see previous articles) we see that these effects mean

that "effective match length" increases LESS than linearly with "real

match length". (Loosely speaking, these two will be equal at the

"average match length", which seems to be between 1 and 3.)

This is more or less the suspicion I think we've had all along (the

earliest reference I can find is an article by David Montgomery in

1995, at http://www.bkgm.com/rgb/rgb.cgi?view+44).

The fact that 1 and 3 point matches seem to yield the same effective

match length is probably meaningless considering the margin of error.

(Assuming the standard error decreases with the square root of the

number of samples, then the effective match length for 1-pointers

from the total of our data is 1.56 with standard error 0.21.)

Also, Peter Fankhauser found in an analysis of the Big Brother

database (http://www.bkgm.com/rgb/rgb.cgi?view+139) that the favourite

expected to gain a tiny fraction of a point (0.011) in 3 point matches,

suggesting that the effective match length in that case was just _over_

3. However, that was from a sample of only 185 games and only

measured highly ranked players, so may be subject to considerable

sampling error (especially when applied to the entire FIBS population).

> but the implication is

> that if you want to increase you rating, play 1 point matches

> agains the weakest opponents you can find, and play long matches

> against the strongest opponents you can find.

Yup. And drop when you're losing, and use Jellyfish to select your

moves, and use more than one account, and...

> It also suggests

> that if we want to make backgammon more a game of skill and less

> a game of luck, we should eliminate the doubling cube.

Oh dear, them's fighting words ;-) My OPINION (I won't attempt to

substantiate this) is that the cube can add a significant amount of

skill to the game by creating the opportunity for costly cube errors

(which will naturally tend to be made more often by less skilled

players). In matches of constant _length_, a match played with no

cube and no gammons be will more of a game of skill purely because more

matches will be played and the variance in the result will be lower;

however, in matches of constant _time_, I suspect (hope? :-) that

cubeful games will be more skillful. In the time that it takes to

play a 15-point match, you might only be able to fit in (say) a

5-point cubeless, gammonless match. My guess is that the cubeful

match is a better test of skill. Whether it is or not, I also

believe it's the most interesting.

So much for my promise from a couple of days ago to shut up about this

topic ;-)

Oct 22, 1998, 3:00:00 AM10/22/98

to

In <362E02...@giga-net.com> Jim Williams wrote:

>These numbers suggest that a 3 point match has exactly the same

>skill component as a 1 point match, and a 5 point match only

>slightly more.

>I am at a loss to explain these numbers...... It also suggests

>that if we want to make backgammon more a game of skill and less

>a game of luck, we should eliminate the doubling cube.

Without quoting the entire article, what you presented

was indeed very interesting, and I must say that your

last sentence is music to my ears... :)

MK

Oct 22, 1998, 3:00:00 AM10/22/98

to

In <wtaf2pa...@brigantine.CS.Arizona.EDU> Gary Wong wrote:

>mu...@cyberport.net (Murat Kalinyaprak) writes:

>I took a look just now and got exactly the opposite results

>(ie. Abbott lost 435 and won 380). Note that a "w" in the

>3rd column means _Abbott_ won, and an "l" means _Abbott_ lost.

>53.37% is the _loss_ rate; the observed win rate is 46.6%.

Oops, I got it backwards... The numbers I ended up

with sure had looked like they could be way off to

the point that I had felt a need to say something

about such a possibility in my last paragraph...

>> Then I logged on to FIBS to see what rating difference

>> would give me 53.37% chance of winning and found out

>> that it's about 120 points

>Yes, FIBS predicts this win rate at a difference of 117

>points (the loss rate naturally means a difference of -117).

>> Abbott's current rating on FIBS is 1552. I believe at

>> the time we were talking about those last 1000 matches

>> (in the thread "loosing streaks" about a week ago or

>> so) it was well below 1500

>In any case, if you want a figure to use with the FIBS variant

>of the Elo system, the best estimate I can give you is 1478.

Sounds reasonable to me. Around the days I was looking

at those 1000 matches, I think it was fluctuating

between 1540's and 1560's...

>> If I understand

>> all this rating stuff correctly, for Abbott to have a

>> 53.37% winning chance against opponents rated at 1615,

>> its own rating would have to be around 1735... That's

>> a whopping discrepency of almost 200 points.

>Since it really _lost_ 53.37% of games, our estimation is in

>fact 1615 _minus_ 117, or 1498. This estimate is again subject

>to a standard error of 60 points.

Thanks for correcting my "whopping mistake"...

>> Unless I'm misunderstanding/misinterpreting things

>> and way off in my above numbers, I would conclude

>> that FIBS current rating system may not be just

>> slightly flawed and still adequate; but actually

>> grossly inaccurate...

>I don't think there's any discrepancy at all. From the 1000

>game sample we derive an estimated rating of 1498; from the

>MLE calculations shown on the web page we get 1478. This

>disagreement is well within the margin of error.

More than close enough for me and nothing next to

the "discrepency" that had emerged from my wrong

figures. As my numbers were coming out drasticly

different than even what I would expect, I had

started to wonder if the analysys I was trying to

do made any sense at all. I was trying to derive

a rating for Abbott based on its opponents ratings

but we don't know how those players had attained

their ratings (i.e. were they mostly multi-point

match players who happen to play occasional 1-pt

matches against others including Abbott, or were

they 1-pointers especially seeking to play against

players like Abbott)? Am I wrong to think that this

process may get highly circular and produce skewed

results beyond satandard/acceptable...?

>> BTW, looking at the "wwllwll..." sequences that you

>> had posted in the thread about loosing streaks and

>> looking at the log of those 1000 matches by just

>> scrolling it up and down for a few minutes, I had

>> come to the conclusion (which I posted in response

>> to your article) that Abbott had lost a lot of its

>> games to much higher rated opponents and that it had

>> done better than expected overall. It looks like a

>> more careful examination of that log confirms what

>> I had quickly observed then.

>I don't understand what you mean here. Losing games to much

>higher rated opponents is surely nothing more than we would

>expect? And I see no evidence that it has done better than

>expected overall, either in the 1000 game sample here or the

>larger sample categorised by opponent strength on the web page.

My mistaking 53% vs 46% win rates led me to attempt

such a link; but even without this error it would be

a meaningless thing to say anyway because the context

was different. As oppesed to this time, at that time

I was focusing on Abbott's losses and your "wwllwll..."

sequence was in front of me then, and I had the "w"s

and "l"s straight. The point then was that Abbott had

won almost just as much against stronger players than

it lost to weaker players, and that there was no signs

of constantly huge/long series of losses that could be

called "loosing streaks" (and/or related to opponents'

streghts at the same time). Ignoring players with less

than 400 experience this time is another thing that

makes such a link/comparison meaningless also. Doing

the same might have well led to different clustering

of "l"s and "w"s at that time also. In short, never

mind that last paragraph...

MK

Oct 22, 1998, 3:00:00 AM10/22/98

to

In <wt90i9a...@brigantine.CS.Arizona.EDU> Gary Wong wrote:

>Jim Williams <ji...@giga-net.com> writes:

>> that if we want to make backgammon more a game of skill and less

>> a game of luck, we should eliminate the doubling cube.

>Oh dear, them's fighting words ;-) My OPINION (I won't attempt to

>substantiate this) is that the cube can add a significant amount of

>skill to the game by creating the opportunity for costly cube errors

>(which will naturally tend to be made more often by less skilled

>players).

Am I the only one actually trying to substantiate my

view on the cube, at the expense of compromizing my

potentially higher/precious :) FIBS rating...? Where

are all the other Turks/Greeks/Armenians/Iranians/etc.

who would assumendly have stronger checker player and

weaker cube skills, to tell us about their experiences

and opinions on this subject...?

What I'm doing on this is different than my saying

that I beat JF in my living room, at which you would

have to take or not take my word for it. This time

it's all happening on the FIBS and in the open. Since

I'm making the effort there, let me also tell a little

more about it here:

1- My current experience is reaching 1300 and after

the first 100 or so games, I have been playing 5 point

cubeful matches almost exclusively.

2- Although I don't feel good about rejecting invitations

from lower rated players, for at least the last 700-800

games I have almost exclusively played against higher

rated players, just to avoid arguments about my picking

on lesser players. Despite my rating not going up and

getting any closer to theirs, it seems like it's getting

easier and easier for me to get matches with higher rated

players (maybe because they remember/recognise my name

more).

3- I refuse to read up on using the cube and learn to

compute probabilities, etc. Occasionally I ask feedback

from my opponents (after the fact of course:) on how I

did with my doubling or taking the cube. But all I want

to hear back is whether I did right or wrong. Although I

appreciate if they try to get detailed with numbers, etc.

I either don't understand or not even try to understand

those details. The intent in this is to validate that I

can indeed do quite well with the cube if I try hard

enough (even if based on my own criteria) and that when

I do a bad take I'm most likely doing it knowingly.

4- When I try to use the cube "right", it's based on

mostly nothing more than what I would base my checker

play on (i.e. a much simpler/casual observation on how

the board "looks" at what stage in the game, etc.) Its

only the magnitude of the consequences are different

(i.e. taking a chance with leaving blots is much less

risky than losing more points after a bad take). When

I use the cube "knowingly wrong" it's based on the same

criteria also (i.e. based on probably sound criteria but

for the wrong reason of stubbornly going against it)...

5- I may be considering the match score much more than

what other players would perhaps do, but not necessarily

claiming that I do it right, and only in certain cases.

For example, if one doubles when I'm 3-0 or 3-1 ahead,

I'll most likely take unless things look really bad. My

reasoning is that, if he looks like he's kind of winning

anyway, giving an extra free point doesn't worry me next

to the possibility that with things turning around by a

little bit I may win the match. I may do the same at 3-2

although more conservatively but still surely way too

often to be considered right.

6- Occasionally I get comments back that indicate a little

irritation/resentment about the fact that I may have made

wrong cube decisions and ended up winning anyway. I also

wonder if I'm getting repeat matches beacause the other

players want to prove back to me that their way is indeed

right and that in the long run I'll be the loser with my

current attitude/approach.

7- My rating is still staying around 1670's or so and

not taking a dive as of yet...

What I'm doing must certainly be visible to at least some

players who played against me and the result is visible

also. There must be something little that one can deduct

from all this, isn't there...?

>however, in matches of constant _time_, I suspect (hope? :-) that

>cubeful games will be more skillful. In the time that it takes to

>play a 15-point match, you might only be able to fit in (say) a

>5-point cubeless, gammonless match. My guess is that the cubeful

>match is a better test of skill. Whether it is or not, I also

>believe it's the most interesting.

Can I argue the exact opposite?:) Remember our recent

match where we kept doubling as the game turned around

time and again incredibly, to finally end with 1 pip

difference? The cube was just sitting next to the board,

while the dice and checkers were doing all the trick,

which we both had found interesting. If we were playing

for money, at a much earlier stage either one of us would

have had too many butterflies in the stomach in proportion

to dollar bills in the pocket and would have dropped.

Then we would have never seen the rest of the interesting

stuff (we both had admitted that we kept doubling and

going on because it wasn't even a rated match which would

cost FIBS rating points).

The most boring part of any game is the beginning where

opening moves are made almost roboticly, etc. Often it

only gets interesting much later in the game. Too many

games never get past that boring early stages because

of the cube... So, talking about constant time vs match

length, with the cube one would end up playing 15 short,

less interesting games vs. 5 long more interesting ones.

I see it as a matter of quantity vs. quality. I think

cube adds much less to the game or even takes away from

it when played as a pass-time than when played for points

or money. Also, based on my own experiments, I'm coming

to believe more and more that the effect of the cube can

be dampened/neutralized to a much greater extent that

one may expect (although certainly not completely)...

MK

Oct 22, 1998, 3:00:00 AM10/22/98

to

>>Jim Williams <ji...@giga-net.com> writes:

>

>>> that if we want to make backgammon more a game of skill and less

>>> a game of luck, we should eliminate the doubling cube.

>

>

>>> that if we want to make backgammon more a game of skill and less

>>> a game of luck, we should eliminate the doubling cube.

>

I've said before that I am Armenian, have been playing since I was 9, and my

father, who is 86 is just a terrific BG player. He and his friends play

without the cube, and generally play 5 game matches for a buck a game. Gammons

count, backgammons are meaningless. The winner of the original dice throw

picks up the dice and throws them again for the opening roll.

He and the folks he plays with don't consider the cube part of the game. As a

result, having "skill" in the cube is not something they think is part of BG

skill.

It seems to me that this is the point. There is no question that cube

decisions involve skill -- but if you are a player who is used to playing

without the cube, that skill doesn't seem like its a skill associated with the

game, but rather an outside skill that affects the game.

Oct 23, 1998, 3:00:00 AM10/23/98

to

In <19981022073836...@ng143.aol.com> EdmondT wrote:

>>>Jim Williams <ji...@giga-net.com> writes:

>>>> that if we want to make backgammon more a game of skill and

>>>> less a game of luck, we should eliminate the doubling cube.

>It seems to me that this is the point. There is no question

>that cube decisions involve skill -- but if you are a player

>who is used to playing without the cube, that skill doesn't

>seem like its a skill associated with the game, but rather

>an outside skill that affects the game.

This is well said and may need a slight clarification

that the effect it has on the game doesn't really alter

how the game is played but rather how the score is kept.

I hope nobody will say that given a certain board and

a dice roll, they would play differently based on the

current value of the cube, etc. We know that the much

worshipped robots don't do that...

In a world where people gamble on whose frog will jump

farther, it's no wonder that bg is used as a gambling

tool and the cube is not much more than the primitive

stake-jacking practice of "double or nothing", which

may predate the invention of the wheel. The cube could

be and is indeed used in many other games. If a couple

of scientists could concoct some formulas to calculate

the odds, equity, etc. in it, we could even talk about

how much skill it would take to use a cube in multi-hop

frog jumping contests...

The argument that cube skill has nothing to do with

what is/should be called "backgammon" could be shown

by the fact that people can use the cube in relation

to bg without even having the least bit of knowledge

about playing bg. Joe and I could sit in a room and

"play cube" based on a match being played by two bg

players playing in another room. All we would need is

for someone to calculate and report to us after each

move the numbers used in double/take/drop decisions.

Even with as little knowledge about the cube as having

a little cheat-sheet in our hand, (telling us what's

the appropriate action at which values), using those

numbers we could "skill the cube out of each other"

without knowing the "b" about "backgammon"...

During some past discussions, people had argued that

players with higher checker-play skills would reach

the cube point sooner and/or more often, etc. And I

had in return offered that I would be willing to play

(for FIBS points) any player higher rated than me who

would be willing to double invariably after "N" moves

during each game. The "N" here would be determined by

"predicting" how soon the more skilled player would

reach the cube point based on the difference in our

ratings. If no scientist can concoct a formula to make

such a prediction, I wouldn't care if they pulled some

number out of the air. So far nobody argued against me

on this nor has anybody taken me up on my offer.

I reserve the right to double back, but had kind of

hoped that someone would propose to limit me to always

take and never redouble (as this was part of a point I

had tried to make in another context), because I had

wanted to drive home the point that in that case it

wouldn't matter if the doubling took place before the

first move, "N'th" move or the very last move... The

end result would have been nothing more than playing

cubeless and counting each point two instead of one...

Certainly there must be lots of players on FIBS with

stronger checker-player skills than mine. Since the

argument had included the claim that they would reach

the cube point "more often" (i.e. >50% of the time),

they should have nothing to lose but much to gain. So,

I was a little disappointed that nobody volunteered to

participate in this potentially fun experiment...

Way back when, some people had even claimed that if

they had ran into me on a train and didn't know my

name (and/or my face), they would feel confident that

they could beat me. Where are they to miss out on such

a chance to rake up FIBS points two by two, (and dunk

my rating)...? I'm still willing to pay the price in

precious FIBS points, if anybody is willing to try to

show me that backgammon (checker-play) skill and cube

skill are in any way linked at all...

MK

Oct 23, 1998, 3:00:00 AM10/23/98

to

Murat Kalinyaprak wrote:

> I hope nobody will say that given a certain board and

> a dice roll, they would play differently based on the

> current value of the cube, etc. We know that the much

> worshipped robots don't do that...

I do that ALL THE TIME. I play matches with the cube in play.

Whether ahead or behind or even VASTLY affects my style.

I may be wrong, but I play very risky when a lot behind,

and very conservatively when a lot ahead, with lots of

gradations in between. In bridge, this is called swinging,

or anto-swinging , as the case may be. -12,-6 with the

cube at 1 is vastly different with the cube at 4 and even

different than the cube at 8 and that different when the

cube is at 16.

> The argument that cube skill has nothing to do with

> what is/should be called "backgammon" could be shown

> by the fact that people can use the cube in relation

> to bg without even having the least bit of knowledge

> about playing bg. Joe and I could sit in a room and

> "play cube" based on a match being played by two bg

> players playing in another room. All we would need is

> for someone to calculate and report to us after each

> move the numbers used in double/take/drop decisions.

Using that strategy, we can all make billions every week.

All we need is someone else to calculate and report the

true value of a a stock versus it's market price and we

will manage how much to invest.

Pardon the satire. The correct assessment of the

outcome of a position is a very difficult skill. The

selection of a choice of moves from all legal moves

is a DIFFERENT very difficult skill. What you propose is

two people can read multiplication tables, or log

tables, ... and can play at calculating. What you imply

is that doing elementary calculations is the same as

combining the net outcome of trillions (or sometimes 36)

outcomes for a given position.

> And I

> had in return offered that I would be willing to play

> (for FIBS points) any player higher rated than me who

> would be willing to double invariably after "N" moves

> during each game. The "N" here would be determined by

> "predicting" how soon the more skilled player would

> reach the cube point based on the difference in our

> ratings. If no scientist can concoct a formula to make

> such a prediction, I wouldn't care if they pulled some

> number out of the air.

As I am wont to say when I pontificate on mathematics,

you are mixing apples with grey.

My algorithm goes:

BEGIN

At every turn that I may cube,

before I roll,

Assess the "Net value" of all possible outcomes of

the current position, if I don't double.

Assess the "Net value" of all possible outcomes of

the current position, if I do. double.

Choose the higher "Net Value:

Comment: No mention of move number appears.

Subroutine Assess(Returns Net Value)

<Body>

END

The same position can occur 6 or 12 or 2000000

rolls after the game starts. Why is it better or worse.

You invented a metric (always good) of length from opening.

You argued (this time questionable) that net value monotonically

increases with increase in your metric. You attached a

decision test to that metric

to prove or disprove your argument (always double at

move N even if you are way behind and will drop the

redouble the next roll). The marketplace implicitly voted

on your argument, 2750 to 0, that you are wrong. Now

is the time to either re-market your invention, or replace it.

Good luck!

Oct 23, 1998, 3:00:00 AM10/23/98

to

>Murat Kalinyaprak wrote:

>

>> I hope nobody will say that given a certain board and

>> a dice roll, they would play differently based on the

>> current value of the cube, etc.

>

>> I hope nobody will say that given a certain board and

>> a dice roll, they would play differently based on the

>> current value of the cube, etc.

I doubt there are many people who play the same way regardless of the score.

Oct 23, 1998, 3:00:00 AM10/23/98

to

In article <70pbrn$r9h$1...@news.chatlink.com>,

Murat Kalinyaprak <mu...@cyberport.net> wrote:

>I hope nobody will say that given a certain board and

>a dice roll, they would play differently based on the

Murat Kalinyaprak <mu...@cyberport.net> wrote:

>I hope nobody will say that given a certain board and

>a dice roll, they would play differently based on the

>current value of the cube, etc. We know that the much

>worshipped robots don't do that...

>worshipped robots don't do that...

In money play I don't play differently based on the value of the cube,

except perhaps doubled/undoubled for Jacoby considerations. But I do

play a lot differently based on *ownership* of the cube. That's a

perfectly normal part of backgammon.

In match play, the value of the cube and the match score factor into

my plays.

-Patti

--

Patti Beadles |

pat...@netcom.com/pat...@gammon.com |

http://www.gammon.com/ | "I trust you. It's just

or just yell, "Hey, Patti!" | that I'm scared of you."

Oct 24, 1998, 3:00:00 AM10/24/98

to

In <19981023142220...@ng38.aol.com> EdmondT wrote:

>>Murat Kalinyaprak wrote:

>>> I hope nobody will say that given a certain board and

>>> a dice roll, they would play differently based on the

>>> current value of the cube, etc. We know that the much

>>> worshipped robots don't do that...

> I doubt there are many people who play the same way

> regardless of the score.

I agree but I wasn't equating cube value with score.

In a cubeless 5 point match, if I'm ahead 4-0, I may

play much more relaxed than if I'm behind by 0-4. In

a 5 point cubeful match if the cube has already gone

up to 4 in the second game with me being 0-1 behind,

I would feel the same pressure but I would still see

this as a matter of score, because I can find myself

in that position with or without the cube (i.e. it's

not exclusively a consequence of using the cube)...

BTW: those robots are said to play differently based

on score (match length) also; there would be nothing

to contrast between them and humans on that...

MK

Oct 24, 1998, 3:00:00 AM10/24/98

to

In <pattibF1...@netcom.com> Patti Beadles wrote:

>In <70pbrn$r9h$1...@news.chatlink.com> Murat Kalinyaprak wrote:

>>I hope nobody will say that given a certain board and

>>a dice roll, they would play differently based on the

>>current value of the cube, etc. We know that the much

>>worshipped robots don't do that...

>In money play I don't play differently based on the

>value of the cube, except perhaps doubled/undoubled

>for Jacoby considerations.

Jacoby who...? :) This goes above my head, so I'll

skip...

>But I do play a lot differently based on *ownership* of

>the cube. That's a perfectly normal part of backgammon.

There may be something for me to learn here. Would

you or anybody else care to illustrate this with a

couple of examples...?

>In match play, the value of the cube and the match

>score factor into my plays.

As I myself do it, I have no doubt that others play

differently based on the score. However, within this

context the value of the cube is not an independent

factor. One can look at the cube value as already

lost points plus 1. For example, if the cube is at

4 in a 9 point match and you are 3-5 behind (or 5-3

ahead), you could look at it as though the cube was

at 1 and you were 3-8 behind (or 8-3 ahead)...

I chose these numbers so that ownership of the cube

doesn't get mixed in the same argument. If the score

in my example was 1-3 (or 3-1), then by your above

statement ownership of the cube may be an additional

factor effecting one's play(??) [hopefully I'll get

to see some examples on this]

MK

Oct 24, 1998, 3:00:00 AM10/24/98

to

In <3630B1...@mail.beehive.com> m...@bernstein.com wrote:

>Murat Kalinyaprak wrote:

>> I hope nobody will say that given a certain board and

>> a dice roll, they would play differently based on the

>> current value of the cube, etc. We know that the much

>> worshipped robots don't do that...

>I do that ALL THE TIME. I play matches with the cube in play.

>Whether ahead or behind or even VASTLY affects my style....

Sorry for all the confusion my saying "current

value of the cube" may have caused. What I'm

after, is a factor that exists only because of

the cube. My difficulty is in trying to name

something which I don't even know if it exists.

The effect of score (i.e. being ahead, behind,

even, etc.) is there whether using the cube or

not. One reader mentioned "ownership of cube"

as something causing her to play differently.

That's the sort of things I'm looking for...

>> had in return offered that I would be willing to play

>> (for FIBS points) any player higher rated than me who

>> would be willing to double invariably after "N" moves

>> during each game. The "N" here would be determined by

>> "predicting" how soon the more skilled player would

>> reach the cube point based on the difference in our

>> ratings. If no scientist can concoct a formula to make

>> such a prediction, I wouldn't care if they pulled some

>> number out of the air.

>As I am wont to say when I pontificate on mathematics,

>you are mixing apples with grey.

Just for you and anyone else who may be missing

the point, let me try one more time:

I previously argued that the cube amplifies the

luck factor. Others argued back that it doesn't

because the more skilled player would get to the

cube point with or without luck (i.e. by skill),

and that he would get there sooner and more often

than the less skilled played. I hope this is all

clear to everybody so far...?

"More often" simply means "at least more than 50%

of the time". There should be no problem with it

as it must be easy enough for anyone to understand.

"Sooner" however, lead to questions like "when",

"how soon", etc. Now let's work this through your

algorithm...

>My algorithm goes:

>BEGIN

>At every turn that I may cube,

>before I roll,

>Assess the "Net value" of all possible.......

At the beginning of a game you roll 53, then 22,

then 66, and hit two pieces of your opponent on

top of that. Your algorithm goes bananas: "Beep!

Beep! Double! Double!"....

If that happened, I'd say you got lucky and that

the cube allows you to capitalize on it. I may

also go further on to say that nobody can show

enough skill to reach cube point after only 3 or

6 or "N" moves unless he gets lucky. This isn't

the end of it either. I'll go on to say stronger

stuff further down...

>to prove or disprove your argument (always double at

>move N even if you are way behind and will drop the

>redouble the next roll).

A player rated at 2000 may reach cube point more

often and/sooner against a player rated at 1200,

but after a certain point (let's use my rating

of around 1670) just skill alone will not get

anybody to cube point more often and/or sooner

against his opponent, unless ge gets lucky, no

matter at what stage of a game...! Never...

>The marketplace implicitly voted on your argument,

>2750 to 0, that you are wrong. Now is the time to

>either re-market your invention, or replace it.

"Implicitly voted" meaning nobody argued back or

took me up on my offer...? Here is my conclusion:

the marketplace is made up of a mixture of people

of which some don't even have a clue as to what

I'm talking about, some agree with me and have no

reason to argue against me, some no longer argues

because they changed opinions and some who continue

to argue against me but can't put essence behind

their argument...

Here is my challenge to you all: Determine on your

own by whatever method or formula and come tell me

how many moves would it take for your skill to

start showing in a game at a sufficient degree to

overcome mine and reach the so called "cube point"

on the average. Then comit to playing "X" number

of matches against me, where you will consistently

double after that many moves in each game...

There is nothing special about me in this argument.

I believe that many other players could (and I wish

some joined in to do) make the same offer to anyone

within maybe 300(??) points of their ratings. As I

do, the ones with about 1700 rating should be able

to make a blanket offer to all players on FIBS since

the highest ratings go only to about 2000. I picked

300 (i.e. about 1950-my rating) because I played

such higher rated players (and observed) enough

times to feel fairly confident that most (if not

all) of them wouldn't take me up on this...

Of course, there is no guarantee that the reality

may turn out different than what I predict but I'm

not affraid to find out... Hey, what do we all have

to lose other than some FIBS points...? :)

MK

Oct 26, 1998, 3:00:00 AM10/26/98

to

Reposted due to recent spam problem...

In <19981023142220...@ng38.aol.com> EdmondT wrote:

>>Murat Kalinyaprak wrote:

>>> I hope nobody will say that given a certain board and

>>> a dice roll, they would play differently based on the

>>> current value of the cube, etc. We know that the much

>>> worshipped robots don't do that...

> I doubt there are many people who play the same way

Oct 26, 1998, 3:00:00 AM10/26/98

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Reposted due recent spam problem...

In <pattibF1...@netcom.com> Patti Beadles wrote:

>In <70pbrn$r9h$1...@news.chatlink.com> Murat Kalinyaprak wrote:

>>I hope nobody will say that given a certain board and

>>a dice roll, they would play differently based on the

>>current value of the cube, etc. We know that the much

>>worshipped robots don't do that...

>In money play I don't play differently based on the

Oct 26, 1998, 3:00:00 AM10/26/98

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Reposted due recent spam problem...

In <3630B1...@mail.beehive.com> m...@bernstein.com wrote:

>Murat Kalinyaprak wrote:

>> I hope nobody will say that given a certain board and

>> a dice roll, they would play differently based on the

>> current value of the cube, etc. We know that the much

>> worshipped robots don't do that...

>I do that ALL THE TIME. I play matches with the cube in play.

Oct 27, 1998, 3:00:00 AM10/27/98

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In article <710r79$78r$2...@news.chatlink.com>,

Murat Kalinyaprak <mu...@cyberport.net> wrote:

>Jacoby who...? :) This goes above my head, so I'll

>skip...

Murat Kalinyaprak <mu...@cyberport.net> wrote:

>Jacoby who...? :) This goes above my head, so I'll

>skip...

The Jacoby rule is nearly always used in money play. It says that

gammons and backgammons don't count unless the cube has been turned.

The reason is to speed the game up... it prevents someone from playing

out a position rather than cashing when he has a slight chance of

winning a gammon, and no chance whatsoever of losing.

-Patti

--

Patti Beadles | Not just your average

pat...@netcom.com/pat...@gammon.com | degenerate gambling adrenaline

http://www.gammon.com/ | junkie software geek leatherbyke

or just yell, "Hey, Patti!" | nethead biker.

Oct 29, 1998, 3:00:00 AM10/29/98

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Patti Beadles wrote:

> Murat Kalinyaprak wrote:

> Murat Kalinyaprak wrote:

>>Jacoby who...? :) This goes above my head, so I'll skip...

> The Jacoby rule is nearly always used in money play. It

> says that gammons and backgammons don't count unless the

> cube has been turned. The reason is to speed the game up...

> it prevents someone from playing out a position rather

> than cashing when he has a slight chance of winning a

> gammon, and no chance whatsoever of losing.

Patti, thanks for explaining these. I was also

wishing for a couple of examples on how you play

"a lot differently" based on ownership of cube.

Oh well. Maybe it's your secret weapon that you

don't want your opponents to know...

Does anybody else play differently based on cube

ownership? If they do and don't consider it their

trade secret, I would appreciate a few examples

on how they play even "a little" if not "a lot"

differently based on cube ownership...

Let me also take this opportunity to offer a more

watered down challenge on cube usage.

I recognize that it may be difficult to concoct a

formula to predict how much sooner a more skilled

player will roll a joker (i.e. reach cube point:)

based on rating differences and this may be what

makes it difficult for anyone to take me up on my

offer...

So, I came up with an alternative challenge which

won't require such a formula (although it will be

much more disadvantageous for me). Here it is:

You (genereicly used to address any/all readers)

and I will play "X" number of "N" point matches.

You may double whenever you wish. But after you

double, I'll have these options.

- I may decide to take or drop at that point or

have the option to postpone my decision until

after the next roll. If I elect to postpone it

by one roll, consequences of my decision will

the same as in regular cubed play after that.

If I decide to make a decision right then, I'll

have the following choices:

a-If I decide to drop, nothing else is different.

b-If I take, you will take back your last move,

roll the dice again and we'll proceed normally

as in regular cube play from then on.

I believe this challenge is reasonable because

unless reaching cube point sooner means who'll

roll 66 first, it has to imply the more skilled

player will get to that point progressively...

Since the argument against me is that the cube

doesn't magnify the luck factor, once the more

skilled player reaches the stage one prior to

cube point, whether he rolls a 21, 43, 55 or 66

shouldn't really matter to the degree of making

or braking, should it...? Neither postponing my

decision by one turn should hurt since hopefully

a more skilled player will not run out of skill

in just one more turn...

If you guys think that I dream up stuff like

this in my sleep, you could be wrong. Although

I don't participate in them, I do quietly read

your discussions in other threads about loosing

market, etc. which are full of better arguments

than mine to show that cube play is based on and

magnifies the luck factor. When the next day you

argue to the contrary, I basically take your own

arguments, throw them back at you in different

words and you don't know what to do with it...

So, we'll see if there will be any takers now...

MK

Oct 30, 1998, 3:00:00 AM10/30/98

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In article <363924...@cyberport.net>,

Murat Kalinyaprak <mu...@cyberport.net> wrote:

>So, I came up with an alternative challenge which

>won't require such a formula (although it will be

>much more disadvantageous for me). Here it is:

>

>You (genereicly used to address any/all readers)

>and I will play "X" number of "N" point matches.

>You may double whenever you wish. But after you

>double, I'll have these options.

>

>- I may decide to take or drop at that point or

> have the option to postpone my decision until

> after the next roll. If I elect to postpone it

> by one roll, consequences of my decision will

> the same as in regular cubed play after that.

> If I decide to make a decision right then, I'll

> have the following choices:

>

>a-If I decide to drop, nothing else is different.

>

>b-If I take, you will take back your last move,

> roll the dice again and we'll proceed normally

> as in regular cube play from then on.

>

Murat Kalinyaprak <mu...@cyberport.net> wrote:

>So, I came up with an alternative challenge which

>won't require such a formula (although it will be

>much more disadvantageous for me). Here it is:

>

>You (genereicly used to address any/all readers)

>and I will play "X" number of "N" point matches.

>You may double whenever you wish. But after you

>double, I'll have these options.

>

>- I may decide to take or drop at that point or

> have the option to postpone my decision until

> after the next roll. If I elect to postpone it

> by one roll, consequences of my decision will

> the same as in regular cubed play after that.

> If I decide to make a decision right then, I'll

> have the following choices:

>

>a-If I decide to drop, nothing else is different.

>

>b-If I take, you will take back your last move,

> roll the dice again and we'll proceed normally

> as in regular cube play from then on.

>

Can you explain this more clearly? I'm especially wondering about when

"right then" is and whether you really mean "one roll" or you mean a

turn by both players.

Here's the interpretation that makes the most sense to me:

I roll and move, you roll and move.

I double. You can drop and I win the value of the cube.

You can delay -- I roll and move, then you decide if you want to drop or

take.

Or you can take immediately and we both take back our last moves and

then I roll and play continues.

This looks like it's as much of an edge for you as your previous

challenge, which involved requiring the stronger player to spot you the

cube.

I can't double right after rolling a market losing sequence, since you

can take and make me take back the market losing sequence (essentially

force me to have doubled last turn when I had already decided not to).

I can't take hoping to roll a market losing sequence because you'll

delay and then if I roll the market loser you'll drop (essentially

forcing me to wait a turn to double).

I don't see how giving one player a big advantage with the cube proves

whether the cube magnifies skill or luck. If you really wanted to prove

it you'd take two players of unequal strength and have them play a long

series of games against each other, both with and without the cube, and

analyze the results. Here's one way of analyzing the results:

Play N games both with and without the cube. Don't use the Jacoby rule

for either set of games to minimize any variance caused by it. Count

the total number of points won or lost (total, not net, i.e. it must be

>= N for each set). Assuming the stronger player ended up with a net

positive for both sessions, divide the cubeful points by the cubeless

point to get the actual cube ratio. Divide the total points won or lost

with the cube with the total points on or lost without the cube to get

the theoretical cube ratio. If the actual is greater than the

theoretical, then the cube magnifies skill, otherwise it magnifies luck.

To get statistically valid answers, N might have to be very large, or

the experiement might have to be repeated many times. A statistican

could quantify this for you.

(Here's my theory for why the cube will magnify skill instead of luck:

the games that end with a drop of an initial double will on average have

fewer rolls in them than games in which the initial double is taken.

Since luck tends to average out over time, and skill tends to compound

over time, the longer games favor the more skillful player. So it's

more likely that luck evens out and skill decides the games that have a

higher cube value, and more likely the skill doesn't have many chances

to change the result and luck determines the games that are worth less.)

-Michael J. Zehr

Oct 31, 1998, 3:00:00 AM10/31/98

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In <71bnf1$m...@senator-bedfellow.MIT.EDU> Michael J Zehr wrote:

>In <363924...@cyberport.net> Murat Kalinyaprak wrote:

>Here's the interpretation that makes the most sense to me:

>I roll and move, you roll and move.

>I double. You can drop and I win the value of the cube.

>You can delay -- I roll and move, then you decide if you

>want to drop or take.

>Or you can take immediately and we both take back our

>last moves and then I roll and play continues.

Yes, despite the deficiency in my explaining it, you

interpreted it all correctly.

>This looks like it's as much of an edge for you as your

>previous challenge, which involved requiring the stronger

>player to spot you the cube.

You mean right after the first roll? If so, I would

agree with you. This is a loophole in my challenge,

which I would have to live with, if anybody went as

far to claim that he can show enough skill to reach

the cube point in a single roll/move... :)

In that case, I would suggest that we play 10+ point

matches, always take, never double back and thus turn

it effectively into a cubeless match where simply the

points are counted two by two. This would really work

against me but it would be the best thing I could do

lessen the damage...

Other than this possible situation, I'm not sure if

this modified challenge gives me as much of an edge

as where the stronger player would have to double at

a predetermined number of moves like 10, 15, 20, etc.

Whether I postpone my take/drop decision or make the

stronger player back up by one move, I think he would

still be in somewhat of a better position than having

to double in situations like having 3 men on the bar,

trying to get into a 5-point board, etc.

Actually, I was hoping that somebody would claim that

"N" could be calculated based on *probability* (using

a formula which would divide the rating difference by

the square root of match length and multiplying it by

pi, etc. :) Then, like Jacoby's, John's, Joe's rules,

I was going to propose a "Murat's rule" which would

say that (for the initial doubling) a player has to

wait until after "N" or has to double before "N" (or

loose his right to initial double during that game),

depending on whether we would want to give an edge to

the stronger or the weaker player... :)

>I can't double right after rolling a market losing sequence,

>since you can take and make me take back the market losing

>sequence (essentially force me to have doubled last turn when

>I had already decided not to).

I don't think you would want to double after losing

your market for the exact opposite reason, which is

that I wouldn't make you take your roll/move back

but let you live with it instead...

>I can't take hoping to roll a market losing sequence because

>you'll delay and then if I roll the market loser you'll drop

>(essentially forcing me to wait a turn to double).

I assume you mistyped when you said "I can't take"

because the rules don't effect you taking/dropping

decisions at all. But if I understant it corrently,

you're right. The option to "delay my decision" is

there to prevent you from constantly waiting one

additional turn to double. Otherwise, sometimes you

would lose your market and miss a doubling chance

but at least you wouldn't be forced to make a bad

(retroactively) double .

I realize the rules are harsh from a cube player's

point of view but they are necessary in an argument

about skill vs. one single lucky roll...

>I don't see how giving one player a big advantage with the

>cube proves whether the cube magnifies skill or luck.

Can you look at it as "not giving a big advantage"

to one player but as "taking away the big advantage

a single roll may give" to one player...?

If a player rated 300 points below me dared me to

play a number of 5-point matches without the cube,

where he would get one chance per game to make me

discard a joker and reroll, I would gladly accept.

If taking away one lucky roll from the more skilled

player will ruin him, I would suspect his skill...

>Play N games both with and without the cube...... Divide

>the total points won or lost with the cube with the total

>points on or lost without the cube to get the theoretical

>cube ratio. If the actual is greater than the theoretical,

>then the cube magnifies skill, otherwise it magnifies luck.

I'll have to take time to digest this proposition

before I make any comments on it but it may very

well be one way of going about it.

>(Here's my theory for why the cube will magnify skill instead

>of luck: the games that end with a drop of an initial double

>