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Author Topic: Isotropish Leaderboard (alternative to Goko Pro)  (Read 144078 times)

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ragingduckd

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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #200 on: April 05, 2014, 05:00:17 pm »
+1

TL;DR: Isotropish and Isotropic use an identical updating algorithm, but with different parameters values.  I think it's these different values that give Isotropic lower uncertainties.

I haven't looked at your code, but you said previously that you just used the vanilla TrueSkill algorithm, which does increase the variance (by GAMMA^2) once for each game:

Quote from: http://research.microsoft.com/en-us/projects/trueskill/faq.aspx
So, what is going on here? Between any two games of a gamer, the TrueSkill ranking system assumes that the true skill of a gamer, that is, μ, can have changed slightly either up or down; this property is what allows the ranking system to adapt to a change in the skill of a gamer. Technically, this is achieved by a small increase in the σ of each participating gamer before the game outcome is incorporated.

Quote
sigma=sqrt(pl.skill[1] ** 2 + GAMMA ** 2)

...

(Bold by me.) So you apply GAMMA once per game, while Doug (according to qmech's quote above) ended up applying it only once per day, not per game.

I understand now.  I think our confusion is Microsoft's fault. ;)



This is Vanilla TrueSkill updating as described on Microsoft's TrueSkill detail page.  So I think what Microsoft means by the rather misleading "... small increase in the σ of each participating gamer before the game outcome is incorporated" is that the scaling factor c is not just the sum of the players' variances, but also includes 2β².  That's the sense in which the variance is increased.  The variable itself isn't increased by β², but its effect on the updating is.

Okay, I'm not sure I'd believe me either if I read that, so here's evidence that dougz and I are doing the exact same updating.  Attached are scripts that do an example ratings update in two different ways: Isotropish's and dougz's.  Note that the 3rd party package I use in isotropish.py has the same name as dougz's ("trueskill") even though it's entirely different code.  You can run these yourself if you download those packages: for isotropish and for dougz.

Output (identical for both scripts):
Code: [Select]
Before the game:
Alice: 25.0000 +/- 8.3333
Bob: 33.3333 +/- 8.3333

After Alice wins:
Alice: 26.8396 +/- 8.1911
Bob: 31.4937 +/- 8.1911

So we really are running the same algorithm for updating after individual games.  I've discovered, however, that there are some differences between my parameters and those that dougz used.  See updated version of the OP for details.  I suspect that it's actually these that account for the difference in our variance floors.
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Kirian

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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #201 on: April 05, 2014, 05:51:40 pm »
0

I understand now.  I think our confusion is Microsoft's fault. ;)

Fucking Microsoft.  Figures.

:)
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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #202 on: April 05, 2014, 06:12:12 pm »
+2


I've always been a bit skeptical about this whole idea that colors make things easier to understand, but this is some convincing shit.
« Last Edit: April 05, 2014, 06:16:21 pm by SheCantSayNo »
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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #203 on: April 05, 2014, 07:25:16 pm »
+2

Seeing c^2 as a denominator in a big equation makes me think they probably took this from some physics model.
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Holger

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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #204 on: April 05, 2014, 07:38:00 pm »
+2

TL;DR: Isotropish and Isotropic use an identical updating algorithm, but with different parameters values.  I think it's these different values that give Isotropic lower uncertainties.

I haven't looked at your code, but you said previously that you just used the vanilla TrueSkill algorithm, which does increase the variance (by GAMMA^2) once for each game:

Quote from: http://research.microsoft.com/en-us/projects/trueskill/faq.aspx
So, what is going on here? Between any two games of a gamer, the TrueSkill ranking system assumes that the true skill of a gamer, that is, μ, can have changed slightly either up or down; this property is what allows the ranking system to adapt to a change in the skill of a gamer. Technically, this is achieved by a small increase in the σ of each participating gamer before the game outcome is incorporated.

Quote
sigma=sqrt(pl.skill[1] ** 2 + GAMMA ** 2)

...

(Bold by me.) So you apply GAMMA once per game, while Doug (according to qmech's quote above) ended up applying it only once per day, not per game.

I understand now.  I think our confusion is Microsoft's fault. ;)

I agree, but in another way, I think.   :P

Quote


This is Vanilla TrueSkill updating as described on Microsoft's TrueSkill detail page.  So I think what Microsoft means by the rather misleading "... small increase in the σ of each participating gamer before the game outcome is incorporated" is that the scaling factor c is not just the sum of the players' variances, but also includes 2β².  That's the sense in which the variance is increased.  The variable itself isn't increased by β², but its effect on the updating is.

I don't think this interpretation of β is correct; according to DougZ's code documentation, β is a measure of how random the game is, and is clearly distinct from gamma:

Quote
  beta is a measure of how random the game is.  You can think of it as
  the difference in skill (mean) needed for the better player to have
  an ~80% chance of winning.  A high value means the game is more
  random (I need to be *much* better than you to consistently overcome
  the randomness of the game and beat you 80% of the time); a low
  value is less random (a slight edge in skill is enough to win
  consistently).  The default value of beta is half of INITIAL_SIGMA
  (the value suggested by the Herbrich et al. paper).

  [...]
 
  gamma is a small amount by which a player's uncertainty (sigma) is
  increased prior to the start of each game.  This allows us to
  account for skills that vary over time; the effect of old games
  on the estimate will slowly disappear unless reinforced by evidence
  from new games.

Now the Microsoft formulas quoted don't even mention gamma. On the Details page, they seem to imply that the increase in uncertainty happens before these formulas are used: "Before starting to determine the new skill beliefs of all participating players for a new game outcome, the TrueSkill ranking system assumes that the skill of each player may have changed slightly between the current and the last game played by each player."
So I think they just neglected to give the corresponding equations for the uncertainty increase, and only give the more "interesting" change based on the game's outcome.

I also notice that DougZ does talk about an uncertainty increase per game here; so if qmech was right, this would be DougZ' old TrueSkill implementation, before he switched to an uncertainty increase per day. If this is the case, it's not so surprising that it leads to the same output as your script, because both implementations do it once per game...
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ragingduckd

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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #205 on: April 05, 2014, 08:02:21 pm »
+1

I don't think this interpretation of β is correct; according to DougZ's code documentation, β is a measure of how random the game is, and is clearly distinct from gamma:

...

Now the Microsoft formulas quoted don't even mention gamma.

Ah, okay.  I follow now.  You're quite right about beta vs gamma.  And gamma isn't in Microsoft's docs because they call it tau.  I don't know why they didn't just conform to dougz's notation.  Nope.  It looks like most of the Microsoft researchers also call it gamma.  Some of their researchers and sublee call it tau though.

Quote
I also notice that DougZ does talk about an uncertainty increase per game here; so if qmech was right, this would be DougZ' old TrueSkill implementation, before he switched to an uncertainty increase per day. If this is the case, it's not so surprising that it leads to the same output as your script, because both implementations do it once per game...

And now I understand what you're saying here too.  Yeah, I suppose it's possible that dougz set tau=0 and compensated with a daily increase in sigma.  Using tau=0 would certainly drive the uncertainty through the floor... I just tried a random sample of 5000 games, and Banker Bot was down to sigma=0.9 by the end.  So maybe with the daily increase it could work out to sane-looking but small values sigmas.
« Last Edit: April 07, 2014, 04:50:53 am by ragingduckd »
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WanderingWinder

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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #206 on: April 06, 2014, 07:58:18 am »
0

I don't think this interpretation of β is correct; according to DougZ's code documentation, β is a measure of how random the game is, and is clearly distinct from gamma:

...

Now the Microsoft formulas quoted don't even mention gamma.

Ah, okay.  I follow now.  You're quite right about beta vs gamma.  And gamma isn't in Microsoft's docs because they call it tau.  I don't know why they didn't just conform to dougz's notation.

Quote
I also notice that DougZ does talk about an uncertainty increase per game here; so if qmech was right, this would be DougZ' old TrueSkill implementation, before he switched to an uncertainty increase per day. If this is the case, it's not so surprising that it leads to the same output as your script, because both implementations do it once per game...

And now I understand what you're saying here too.  Yeah, I suppose it's possible that dougz set tau=0 and compensated with a daily increase in sigma.  Using tau=0 would certainly drive the uncertainty through the floor... I just tried a random sample of 5000 games, and Banker Bot was down to sigma=0.9 by the end.  So maybe with the daily increase it could work out to sane-looking but small values sigmas.


Holger seems to get this stuff. I don't think you are (I don't mean this as an insult - it's an incredibly daunting, technical wall of text). If you look here, they do talk about both Gamma and Tau. Gamma is about halfway down page 2. They don't explicitly give an equation for its effect - it's in words "an additive variance component" (of gamma squared) "in the subsequent prior" - i.e. you are literally adding gamma squared to the player's stored uncertainty every "so often". They say at the bottom that in what they did for Halo on Xbox live is use a Gamma squared = (Sigma_initial/100)^2. It's not clear how often this update is accruing though.

Tau is not the same thing - they are using Tau for the Precision-adjusted mean, Mu*Pi = Mu/(sigma^2), as they say in the first few lines after the box of equations on page 5. This is because they're working with inverse space a lot, as it's convenient for a lot of things they want to do.

I don't know what parameter values DougZ used, or if they'd be correct.

Oh, a few other notes - you are saying you are trying to figure out the best parameter values, and I applaud you for this. My question is how - assuming you can figure out how to actually measure what their effect is on past data, what error/accuracy metric are you using? I would suggest maximum likelihood - effectively this means log likelihood. Also, you have in your OP right now that the Initial Ratings have sigma = 25, but that should be sigma^2 = 25/3. He's also using Beta^2 = 25/6, not just 25, if I am reading the code right (this also jives with what I remember) - this is also the exact same as the value you say it is much different than - I mean, I think Doug just remembered a little wrong when he sent that message.

I am sure the biggest, maybe the only differences between your system and DougZ's are in the updating - i.e. the Gamma updating which could occur per-game or per-time, and you clearly aren't doing the same. I think it's a bit misleading to say that what you're doing is exactly the same, because while it's technically right to say that "it's the same with parameter values", lots of systems are going to be true by that - the parameter values are REALLY important.

Anyway, I hope it goes well for you. I might look at cracking into some of this stuff later on (maybe even today) if I have some time, but I don't know how long it's going to take me, and I probably wouldn't proceed under a TS framework.

ragingduckd

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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #207 on: April 06, 2014, 12:04:36 pm »
0

Holger seems to get this stuff. I don't think you are (I don't mean this as an insult - it's an incredibly daunting, technical wall of text). If you look here, they do talk about both Gamma and Tau. Gamma is about halfway down page 2. They don't explicitly give an equation for its effect - it's in words "an additive variance component" (of gamma squared) "in the subsequent prior" - i.e. you are literally adding gamma squared to the player's stored uncertainty every "so often". They say at the bottom that in what they did for Halo on Xbox live is use a Gamma squared = (Sigma_initial/100)^2. It's not clear how often this update is accruing though.

Tau is not the same thing - they are using Tau for the Precision-adjusted mean, Mu*Pi = Mu/(sigma^2), as they say in the first few lines after the box of equations on page 5. This is because they're working with inverse space a lot, as it's convenient for a lot of things they want to do.

Microsoft doesn't mention either gamma or tau on their details page, which I believe is what Holger was referring to.  I believe dougz is following Herbrich in using gamma as the dynamics factor.  Moser and sublee use tau in place of gamma, possibly following Dangauthier et al, 2008.

We're all talking about the same thing though:

Herbrich & Graepel:




Moser:


dougz:
https://github.com/dougz/trueskill/blob/master/trueskill.py#L347

sublee:
https://github.com/sublee/trueskill/blob/master/trueskill/__init__.py#L316
https://github.com/sublee/trueskill/blob/master/trueskill/factorgraph.py#L99

Quote
Oh, a few other notes - you are saying you are trying to figure out the best parameter values, and I applaud you for this. My question is how - assuming you can figure out how to actually measure what their effect is on past data, what error/accuracy metric are you using? I would suggest maximum likelihood - effectively this means log likelihood.

Yes, I find max likelihood compelling.  Herbrich and Graepel use "prediction error (fraction of teams that were predicted in the wrong order before the game)," which also seems reasonable and maybe easier to understand.

Quote
Also, you have in your OP right now that the Initial Ratings have sigma = 25, but that should be sigma^2 = 25/3. He's also using Beta^2 = 25/6, not just 25, if I am reading the code right (this also jives with what I remember) - this is also the exact same as the value you say it is much different than - I mean, I think Doug just remembered a little wrong when he sent that message.

The OP now correctly shows what Isotropish is actually doing and what I now believe that dougz was doing.  Isotropish really is still using σ0=25, though that will change soon.  I'm assuming those "^2"s are just typos, but where are you reading dougz's leaderboard code or seeing beta=25/6? 
« Last Edit: April 06, 2014, 12:05:57 pm by ragingduckd »
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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #208 on: April 06, 2014, 12:43:42 pm »
+1

Stuff

Okay, all this makes sense now. I think we're on the same page.

The reason I like maximum likelihood over  the 'fraction of teams that were predicted in the wrong order before the game' is that scale is really important. Under prediction error, predicting that X has a 50.1% chance of winning against Y is the same as predicting that X has a 93% chance of winning against Y, and I really think you want to scale there. Basically, I want rating more than just ranking.

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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #209 on: April 06, 2014, 12:49:17 pm »
+6

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ragingduckd

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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #210 on: April 06, 2014, 12:57:17 pm »
+9



... yelled the online Dominion tournament organizer.
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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #211 on: April 06, 2014, 02:31:09 pm »
+4



... yelled the online Dominion tournament organizer.

You know it's serious when that's the guy calling you a nerd.
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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #212 on: April 15, 2014, 09:57:52 pm »
+1

Just noticed that the Isotropish Leaderboard has not recorded any new games now for over 4 hours, so it probably needs some attention.

Just curious - when this happens, will the games that finished during this period will eventually be posted to the leaderboard, or is some of the data lost?

Also - Is there somewhere else where I should report issues like this rather than on this forum topic?  I don't have a GitHub ID, but I could certainly get one if that is the better place to report issues with the non-Goko software.

Thanks.
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ragingduckd

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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #213 on: April 15, 2014, 10:33:57 pm »
+3

Just noticed that the Isotropish Leaderboard has not recorded any new games now for over 4 hours, so it probably needs some attention.

Thanks.  I restarted it.  Someday I will definitely figure out why that happens.

Just curious - when this happens, will the games that finished during this period will eventually be posted to the leaderboard, or is some of the data lost?

Everything gets posted... eventually.

Almost everything gets posted when I restart the downloader, but I've encountered some rare bugs that cause a game to get skipped (recorded but not rated).  In such cases, the game doesn't show up until the next time I regenerate the leaderboard from scratch (i.e. starting from game one in May 2013).  I'd like to claim that that can't happen anymore, but you probably shouldn't trust a programmer who 100% guarantees his code to be bug-free.

There's also a MF/Goko bug that can result in a game log not getting created at all.  Or there was in recent months anyway.

Also - Is there somewhere else where I should report issues like this rather than on this forum topic?  I don't have a GitHub ID, but I could certainly get one if that is the better place to report issues with the non-Goko software.

Probably just sending me an e-mail or PM is best.
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Blueswan

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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #214 on: April 20, 2014, 09:28:19 am »
0

Any idea why one would be massively higher rated on Isotropish than on Goko? I'm currently #587 on Goko, but #229 on Isotopish. Infact, I always seem to be higher rated on Isotropish.
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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #215 on: April 20, 2014, 10:15:06 am »
0

Any idea why one would be massively higher rated on Isotropish than on Goko? I'm currently #587 on Goko, but #229 on Isotopish. Infact, I always seem to be higher rated on Isotropish.
Perhaps because your uncertainity is high, which means that Goko drops your rating more than Isotropish does.
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Holger

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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #216 on: April 20, 2014, 11:43:49 am »
0

Any idea why one would be massively higher rated on Isotropish than on Goko? I'm currently #587 on Goko, but #229 on Isotopish. Infact, I always seem to be higher rated on Isotropish.
Perhaps because your uncertainity is high, which means that Goko drops your rating more than Isotropish does.

No, Blueswan has Isotropish uncertainty of only 10.2, close to the lowest uncertainty of 9.x. The 1 sigma difference between the two ratings is unlikely to ever be the cause of such a difference, since Isotropish gives you a massively higher starting uncertainty - you start at 1000 points in Goko, but at level -50 (!) in Isotropish.

The most probable reason is that Blueswan plays very few games per day/week, so Goko's daily increase in uncertainty dominates the rating. It's the same for me.

Edit: Some bots (and one player) now have uncertainties <9. Was the algorithm changed in the meantime, or is this a rare coincidence?
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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #217 on: April 20, 2014, 12:03:12 pm »
0

Any idea why one would be massively higher rated on Isotropish than on Goko? I'm currently #587 on Goko, but #229 on Isotopish. Infact, I always seem to be higher rated on Isotropish.
Perhaps because your uncertainity is high, which means that Goko drops your rating more than Isotropish does.

No, Blueswan has Isotropish uncertainty of only 10.2, close to the lowest uncertainty of 9.x. The 1 sigma difference between the two ratings is unlikely to ever be the cause of such a difference, since Isotropish gives you a massively higher starting uncertainty - you start at 1000 points in Goko, but at level -50 (!) in Isotropish.

The most probable reason is that Blueswan plays very few games per day/week, so Goko's daily increase in uncertainty dominates the rating. It's the same for me.

Edit: Some bots (and one player) now have uncertainties <9. Was the algorithm changed in the meantime, or is this a rare coincidence?
The last few days I've been playing quite a bit, but up until a couple of weeks ago I pretty much hadn't played in 6 months or so. Still trying to find my groove. Getting better today even if my Goko rating is still fairly mediocre.

I don't know if it could have anything to do with the fact that the vast majority of my games are against Conqueror Bot.
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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #218 on: April 20, 2014, 12:12:29 pm »
0

The last few days I've been playing quite a bit, but up until a couple of weeks ago I pretty much hadn't played in 6 months or so. Still trying to find my groove. Getting better today even if my Goko rating is still fairly mediocre.
That explains it then. Isotropish froze your rating from 6 months ago, while Goko probably increased your uncertainty by a factor >4 as "punishment" for not playing that long; it will take lots of games to reduce it to its previous value. That's why I prefer Isotropish ratings...

Quote
I don't know if it could have anything to do with the fact that the vast majority of my games are against Conqueror Bot.
You'd need a few more games against weaker opponents to increase your rating/reduce your uncertainty, but it shouldn't matter too much.
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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #219 on: April 22, 2014, 11:07:07 pm »
+1

Before you ask, yes, something is definitely wrong.  I'm looking into it.

Edit: fixed.
« Last Edit: April 23, 2014, 10:22:33 am by ragingduckd »
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Hugovj

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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #220 on: April 23, 2014, 04:04:02 pm »
+1

My leaderboard is stuck at 830 minutes ago. Don't know if that was what you were trying to fix, but I don't think it is fixed...

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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #221 on: April 23, 2014, 05:12:46 pm »
+1

My leaderboard is stuck at 830 minutes ago. Don't know if that was what you were trying to fix, but I don't think it is fixed...

You're right.  I broke something else with my previous fix.

Now it's running again, but it skipped all the games from the last 7 hours.  I'm fixing that too, but it'll take an hour or two.  If you played games in the last 7 hours, your rating will "jump" when I switch to the fixed version that incorporates those games.
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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #222 on: April 26, 2014, 12:02:13 pm »
0

Okay, obviously there is something wrong with the new logparsing/leaderboard code I wrote last week.  The weird part is that whenever I regenerate the leaderboard from scratch, this nonsense goes away:

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Salvager Extension | Isotropish Leaderboard | Game Data | Log Search & other toys | Salvager Bug Reports

Salvager not working for me at all today. ... Please help! I can't go back to playing without it like an animal!

LuciferousPeridot

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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #223 on: April 26, 2014, 12:15:26 pm »
+8

Okay, obviously there is something wrong with the new logparsing/leaderboard code I wrote last week.  The weird part is that whenever I regenerate the leaderboard from scratch, this nonsense goes away:



There's me thinking I had lost most of my games recently....
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7string

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Re: Isotropish Leaderboard (alternative to Goko Pro)
« Reply #224 on: April 28, 2014, 05:44:51 pm »
+1

I've been having a number of problems with online games the last few days.  I just posted the following in a Tech Support thread at the Making Fun site where I described the issues.  Note my last concern #5 as it relates directly to the Isotropish Leaderboard.  It just seems out of line that 3 new user id's would pop up at the top of the list of number of games in the last few days, and that all 3 of them would have over 50,000 games, and that Banker Bot would have shot up so much in games.  If the numbers are correct, then either a) Goko/Makingfun is using these ID's to test the system; b) Someone is gaming the Goko/Makingfun system with automated bot programs and that could be why the servers have been slow; or c) Someone is gaming the Isotropish leaderboard.  If there is another possible answer, I can't think of it at the moment...  I don't usually expand the full Iso list, but I have in the past, and these names did not roll to the top of # of games list, so I do not think it is just because they have not played for a while.  2 of the new id's show in the partial list, but elhobb only shows in the full list.  It is also odd that the numbers for the Goko Bots have changed with Banker Bot shooting up so significantly, and if my memory is correct, Conqueror Bot dropping down in # of games, as Conqueror Bot always had notably the most games.

********  Copy of my post on Makingfun site
                (http://forum.makingfun.com/showthread.php?4653-Lots-of-problems-with-games-last-couple-days)

Lots of problems with games last couple days
The last couple days I have had lot of problems with games:

1) Very slow response time, with frequent long lags.

2) Games not starting sometimes after hitting the play button. They just never start and I have to hit the Create button to start a new game.

3) One time where the game started but the whole screen was displayed with dark gray overlay so that I had to hit refresh to go back to home screen.

4) One game where it hung up during the game and never came back. I checked the game log, and it was logged as a Quit against a Bot, but it was not counted as a loss on my loss record. While it doesn't seem quite fair to get a loss when the system hangs up, I think it is important for any game logged as a quit to count as a loss. Otherwise the door is still open for people to game the system and simply quit anytime they are behind to preserve their record without a loss. Especially if this can be done against bots without a quit counting as a loss it will cause the potential for players to be fixing even the pro ratings by just playing bots and quitting any time they are behind to achieve a perfect record.

5) Finally, I noticed in the Isotropish rankings taken from Goko games (http://gokologs.drunkensailor.org/le...rtkey=numgames) that if you sort them by number of games played there has been some radical changes at the top. I could usually sort by # of games to quickly see all the Bots at the top and see what their respective ISO ratings were. Now I see that Banker Bot has gone up by at least 20,000 or 30,000 games in the last week or so. I also see 3 new user names which have never been at the top (frankdom, LuciferousPeridot, and elhobb) - all 3 of these users suddenly show as having over 50,000 games. Now I understand this is a 3rd party site not maintained by Goko/Makingfun, but if the numbers are true, it might indicate that the servers are slow because they are being swamped by some sort of automated programmed bots (who perhaps have been playing Banker Bot?). Perhaps these are Makingfun tests?? Something you probably want to look at.
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