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Topic: Omar = OmarFast , bot_bomb = bot_spe (Read 7191 times) |
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Fritzlein
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Re: Omar = OmarFast , bot_bomb = bot
« Reply #15 on: Jan 4th, 2005, 9:32am » |
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I know you like to play at slower speeds, Mr. Brain, and I appreciate your arguments for having the World Championship games at a slow speed, but it's going a bit too far to call fifteen seconds per move a ludicrous speed for anyone else to like to play at. You know perfectly well that lots of people like to play fast games, and in particular that a large majority of games on the Internet Chess Club are played at time controls even faster than 15 seconds per move.
But in any event, under the logaithmic scheme that I propose, the endpoints are essentially irrelevant. They could be extrapolated to a time control that is indeed ludicrous, without changing anything important.
Maybe the whole idea of having endpoints is just a distraction. As we learn in high school algebra, two points define a line, but you can also define a line via a point and a slope. If the endpoints are point of contention, we could think of slow-fast ratings in point-slope terms instead.
We could define the "normal" time control as one minute per move, and give people a single number as their rating based on that time control. Then we add the assumption that some people benefit more than others from having extra time to think (and equivalently that they are hurt more than others by having less time to think), and use that to define a "slope".
For example, let's say my rating is should be 2000 at one minute per move, and my slope is -50 rating points per doubling the time. At two minutes per move my rating would be 1950 while at 30 seconds per move my rating would be 2050. You may think it is ridiculous to play at 15 seconds per move, but if I actually wanted to play that fast, we would extrapolate that my rating at that speed would be 2100. I would join you in thinking that it is ridiculous to play at 3.75 seconds per move, but if we did, we can guess that my rating would be 2200 at that speed.
Now whether we try to determine two endpoints or try to determine a point and a slope, either way we determine a line. The only way endpoints would be relevant is if people played games beyond the endpoints. If all games were played between 30 seconds per move and two minutes per move, it wouldn't matter practically whether we chose those as our endpoints or 1 second per move and 1 week per move as our endpoints. (Well, it would flatten all the slopes somewhat, but that's just changing the scale, like multiplying everything in the current system by two wouldn't have any practical effect.)
The reason to have endpoints at all would be that we wanted to cap the effect of time on a game. We might reason that beyond giving both players four minutes per move to think, giving extra time isn't going to change the balance of playing strength. By the same token we could say that shortening the time below 15 seconds per move also won't change the relative chances of the two players. I'm not sure that I buy either of these arguments. In particular, I guarantee you from personal experience that there is a significant difference in Bomb's playing strength between 15 seconds per move and 30 seconds per move. To you both time controls are "faster than I want to play", but those of us who are interested in playing that fast need to draw distinctions.
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| « Last Edit: Jan 4th, 2005, 11:18am by Fritzlein » |
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MrBrain
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Re: Omar = OmarFast , bot_bomb = bot_spe
« Reply #16 on: Jan 4th, 2005, 10:24am » |
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That's a very good explanation. But I disagree that you can really fit one's performance linearly onto a time-logarithmic scale. Realistically, there is a limit to performance change at very high speeds, and at very long controls. This means there will be horizontal asymtotes at the ends of a graph of performance vs. time control for any entity. (For a computer program, the fast-end asymtote will be reached more slowly, but there is an asymtote there nonetheless.)
Compare our two schemes. Mine tries to take into account a limit on what a reasonable speed (for a human) is, on both ends. Yours does not. If one was to plot the performance (rating) of most players at different speeds versus the percentages that both you and I have proposed, I would wager that the more linear graph would be with my percentages.
(Is there any way that we can extract performance data from existing games at different controls? This would likely be complicated by the facts that players improve over time, and that they tend to play the same time control repeatedly over short periods.)
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MrBrain
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Re: Omar = OmarFast , bot_bomb = bot
« Reply #17 on: Jan 4th, 2005, 10:30am » |
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on Jan 4th, 2005, 9:32am, Fritzlein wrote:For example, let's say my rating is should be 2000 at one minute per move, and my slope is -50 rating points per doubling the time. At two minutes per move my rating would be 1950 while at 30 seconds per move my rating would be 2050. You may think it is ridiculous to play at 15 seconds per move, but if I actually wanted to play that fast, we would extrapolate that my rating at that speed would be 2100. I would join you in thinking that it is ridiculous to play at 3.75 seconds per move, but if we did, we can guess that my rating would be 2200 at that speed.
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And according to this type of reasoning (not taking into account leveling off of performance), one could incorrectly conclude that given enough time to think, that someone who's slope is steep will be able to beat any player who's slope is not as steep. On the ICC, my chess rating difference between bullet (1 minute) and standard (15 minutes) is about 900 points. Therefore, I could conclude that if I were to play a game against Garry Kasparov with a 1-week-per-move control, I should be able to win the game. This is obviously not the case.
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| « Last Edit: Jan 4th, 2005, 10:32am by MrBrain » |
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MrBrain
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Re: Omar = OmarFast , bot_bomb = bot_spe
« Reply #18 on: Jan 4th, 2005, 10:37am » |
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Well, despite the disagreement here, I still think we're on the right track. If we want to do the "normal" rating with another parameter for rating change per doubling of time, just as a starting point to try it out, I'd not have any problem with that. And by the way, my reference to "ridiculous" and "ludicrous" was not to criticize, but to be a little humorous (i.e. SpaceBalls) and simply to make a point.
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Fritzlein
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Re: Omar = OmarFast , bot_bomb = bot
« Reply #19 on: Jan 4th, 2005, 11:13am » |
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One reason to have a cutoff at the fast end of the time control is that some time is used up by Internet lag, moving the pieces with the mouse, the client displaying the previous move, etc. At some point one is measuring physical reflexes or connection speed or something other than thinking fast about Arimaa. As much as I like fast games, I might want to consider, say, 10 seconds per move as the fastest measurable speed, given the current client, Internet, and server situation.
One reason to have a cutoff at the slow end is that at some point one stops using all the time available. Omar reports that at 3 minutes per move against Bomb, he started doing other things in the middle of the game. When we start the postal tournament at one move per day, I seriously doubt that I will ever spend more than ten or fifteen minutes thinking about a particular move; I expect that usually I will spend less. I guess I could see extending the slow endpoint to 6 or 8 minutes per move at a atretch.
Assuming that a player's strength is linear in the logarithm of time allowed is certainly an approximation, and I agree that we can expect that the approximation gets worse and worse as you go towards the extremes, which is a more general reason for wanting to have a cutoff. It's a model which is guaranteed to break down if you test it rigorously (just like the Elo model of chess performance itself breaks down under scrutiny). The advantage of the proposal is that it does something somewhat reasonable to recognize that fast time controls affect some players more than others (particularly computers versus humans) and yet doesn't need four or five different ratings per person, with abrupt cutoffs between the categories.
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99of9
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Re: Omar = OmarFast , bot_bomb = bot
« Reply #20 on: Jan 4th, 2005, 11:14am » |
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on Jan 4th, 2005, 10:24am, MrBrain wrote:I disagree that you can really fit one's performance linearly onto a time-logarithmic scale. Realistically, there is a limit to performance change at very high speeds, and at very long controls. This means there will be horizontal asymtotes at the ends of a graph of performance vs. time control for any entity. (For a computer program, the fast-end asymtote will be reached more slowly, but there is an asymtote there nonetheless.)
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Please attempt to justify this asymtote hypothesis - I don't believe it.
The depth a computer program can search as a function of time limit is theoretically exactly logarithmic. It's hard to say exactly how depth is related to strength, but it's probably fair to guess that they're basically proportional.
So yes, a computer's performance gets better logarithmically with increasing time controls.
A human's ability changes even more as a function of time (ie a higher gradient on the log plot). This is clear when you consider that when you get down to very short times you become unable to even complete the full 4 steps in time. I'd argue it's not an asymptotic plateau, it's in fact closer to an asymptotic fall away!!!
By the way, we are confusing the issue when we say that computers get "better" at fast time controls. What we mean there is that humans get worse quicker so fall behind.
Unless there is good empirical evidence otherwise, in my opinion it is better to go with Fritzlein's 2-parameter model rather than Brain's 9-parameter model.
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| « Last Edit: Jan 4th, 2005, 11:17am by 99of9 » |
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Fritzlein
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Re: Omar = OmarFast , bot_bomb = bot
« Reply #21 on: Jan 4th, 2005, 11:25am » |
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on Jan 4th, 2005, 11:14am, 99of9 wrote:
The depth a computer program can search as a function of time limit is theoretically exactly logarithmic. It's hard to say exactly how depth is related to strength, but it's probably fair to guess that they're basically proportional.
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Actually, I believe that there have been studies done on the playing strength of chess programs which conclude that their rating (using a fixed time control and humans as a yardstick) is roughtly linear in search depth. This would suggest that a variable time control has an effect on computers proportional to the logarithm of search time. However, I read this long ago, before chess computers were World Championship caliber, so I wouldn't be surprised if there has been some asymptotic falling off at the high end.
[Edit] A quick Google search gave me this link, which disputes the notion of asymptotic falling off, and implies that a linear relation between search depth and playing strength may well hold indefinitely:
http://supertech.lcs.mit.edu/~heinz/dt/node49.html
[Further Edit] 99of9 points out that my proposal would over time give everyone a different slope, but that the varying slopes would only be relative. Computers would have negative slopes, not because they get worse at higher speeds, but because humans get better faster.
An alternative would be to use computer self-play to fix their own positive slope, (which might be around 100 points per doubling of search time) and thusly anchor the slopes of the entire system in a way similar to the plan for using computers to anchor the ratings in another thread. Presumably then fixed-depth searchers like Arimaazilla would have a zero slope and Humans would have a steep slope of 200 or more points per doubling of time.
As first blush, my intuition is that computers would actually be more accurate in anchoring the scale of the slopes than in anchoring the scale of the ratings, because I expect any computer with any reasonable time management to have approximately the same slope.
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| « Last Edit: Jan 4th, 2005, 11:54am by Fritzlein » |
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MrBrain
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Re: Omar = OmarFast , bot_bomb = bot_spe
« Reply #22 on: Jan 4th, 2005, 12:30pm » |
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Don't confuse search depth with rating. Yes, a computer can think more ply, but so can its opponent, human or mechanical. Again, if you compare two players, and there's a slope difference between the two at a certain speed, common sense dictates that that slope difference cannot continue indefinitely. Just look at my chess example to see why. And as was correctly pointed out, there are limits for humans (interface, boredom). These same limits may not apply for computers, since they can move much faster and don't get bored. But regardless, I still think we should have some limit that approximates what happens in reality.
As for the asymtotes, a simple example should suffice: If we play a game with a 10-day limit per move, player A should expect a certain win % versus player B. If we make it a 20-day limit, is this really going to change the % by as much as 1-minute versus 2-minutes? Of course not. Why? It's leveling out. There's some limit to how good a player can be, regardless of how much time per move is alotted. Again, I'm never going to beat Kasparov, even if I had a year to think about each move. Why? Because the rating gain I get by going from 1 to 15 minutes for the game cannot hold up indefinitely.
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| « Last Edit: Jan 4th, 2005, 12:32pm by MrBrain » |
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omar
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Re: Omar = OmarFast , bot_bomb = bot
« Reply #23 on: Jan 5th, 2005, 1:29am » |
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Great discussion.
I was contemplating about what times to use for the boundaries between the different catagories of speed and also how many speed catagories to have. This method of using two ratings with percent contributions solves those problems.
I think we have to keep in mind that the pace of the game is not just controled by time per move, but also the starting reserve. So we might need to do something like divide the number of seconds in the starting reserve by some number like 45 that represents the average number of moves per game and add that to the time per move (in seconds). Also I know from experience that having a higher max reserve limit makes the game feel more slower (ie 1/2/100/5 feels slower than 1/2/100/2) but Im not sure how to incorporate that.
One other thing to keep in mind is that maybe some humans play best at say a pace of 1 min per move but get worse as speeds get faster or slower than that. A line may not be the best model for humans. So in this case maintaining different speed catagories would model the situation better (the more catagories the better it can be modeled). Or maybe with the other method we can model it with two line or a more complex function. For computers though I think a single line model is a pretty good fit.
The catagory division method has the advantage that we don't have to predetermine how to model the effects of speed on ratings. Also we can have more catagories if we want the model to be better. But it also has a lot of disadvantages; like having to maintain a lot of rating numbers and predetermining boundries between the catagories.
So as you can probably tell, Im still contemplating which method to use.
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| « Last Edit: Jan 5th, 2005, 1:30am by omar » |
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MrBrain
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Re: Omar = OmarFast , bot_bomb = bot_spe
« Reply #24 on: Jan 5th, 2005, 7:22am » |
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In general, I don't feel that starting reserve is a big issue, but it does come into play at the start of the game (e.g. Omar vs. Brain 2004 WC).
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clauchau
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Re: Omar = OmarFast , bot_bomb = bot_spe
« Reply #25 on: Jan 6th, 2005, 1:31pm » |
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Yes, interesting discussion. One improvement with the available time controls is needed in any case I think - the gameroom should allow the two players to play according to distinct time controls.
Firstly because otherwise we are getting isolated groups of players -- one group for each speed -- and their ratings may be going to get relatively wrong between different groups. Let's get accurate by allowing two different time settings for each opponent.
Secondly because I'd like to play at 1 min per move against bots playing at 15 sec per move.
Then, as the current discussion hints at, we might update the ratings accordingly, taking the times into account. The lightning bots ratings wouldn't decrease much against slow-playing humans.
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omar
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Re: Omar = OmarFast , bot_bomb = bot
« Reply #26 on: Jan 12th, 2005, 4:05pm » |
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Hi Claude,
I think you are suggesting that with each game we maintain two seperate time controls; one for each player. We can then use this when computing the ratings. I kind of like the idea, but implementation wise its going to require a lot of changes at all levels; database, game server and game clients.
Let me throw out another proposal that trys to acheive the same thing, but a little differently.
After a game is over, we can calucluate from the event log the average number of seconds each player took to make the move. If you open up a recently played game and scroll down the chat area you will see the average move times that were calculated from the event log.
I could much more easily record these numbers with each game in the database. A program could be written to fill in these numbers for the older games. We could then use these numbers in calculating the ratings.
Remember that with each game we also record what each players rating was going into the game.
Our current rating system uses something like this:
myRatingAfter = rating(myRatingBefore, oppRatingBefore, didIWin)
With the new performance rating system that we had discussed earlier a players rating is calculated on the fly using the players complete game history and not just the rating after the previous game. It uses something like this:
myRatingAfterGameX = rating(oppRatingFromGameX, didIWinGameX, weightOfGameX, oppRatingFromGameX-1, didIWinGameX-1, weightOfGameX-1, ... up to Game1)
Notice that only the opponents ratings are used in computing our rating. Also weights are used to give varying amount of importance to the games. We discussed a lot about how to set the weights based on factors such as how many unique opponents you have played, how old the game is, etc.
I suppose we could also use the performance rating system to ask a question like 'what is my rating at 20 seconds per move'. To answer such a question we could adjust the weights of the games so that games where the player used exactly 20 seconds per move (average move time) are given a full weight of 1 and games that are farther (time wise) from the time in question are given a lesser wight (down to a limit of 0). These weights are multiplied by the weights that would otherwise be used. We could also compute some uncertianty of the rating at the given time, based on the average of the weights. So if the uncertianty was 1 then it would mean that in all the games used in computing the rating the player happend to have a time per move that is the same as the time in question.
The rating of a player that we store with the game is computed based on the average time per move the player took in that game. For example if a player took 52 seconds per move in this game then we use the performance rating of that player computed for 52 seconds per move. We might also compute and store the rating uncertianty with the game and could also use the uncertianty when determining the weight of the game.
So we don't need to store any ratings with each player. Rather we just compute them on the fly from the players game history. We should also be able to compute what the players rating would be at a given time per move speed. When computing the rating of a player that is displayed in the gameroom it is computed without regard to any times associated with past games; thus the time component of all the weights is 1. When comuting the rating of a player that is stored with the game we use the average time per move the player took in that game to bias the rating to give more weight to previous games where the player took similar time.
We could have a form where given the player name and average time per move it shows what the players rating is at that speed along with the uncertianty at that speed. For example if a player has played all the games at 60 second per move and we ask what the players rating would be at 30 seconds per move, it would be the same rating, but the uncertianty would be higher. The uncertianty would be higher still if we asked what the rating would be at 15 seconds per move; the rating would still be the same.
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| « Last Edit: Jan 12th, 2005, 4:20pm by omar » |
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Fritzlein
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Re: Omar = OmarFast , bot_bomb = bot
« Reply #27 on: Jan 18th, 2005, 3:23am » |
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Omar, I'm suspicious of rating the game based on how much time each player actually uses, rather than on how much time was allotted. I just now played Bomb/2004 at 3 minutes per move, but once I got a strong position I didn't need to use all my time, so I moved faster. By your proposal this would affect my rating at a faster speed, not my rating at 3 minutes per move. I could win a half dozen games against Bomb and they would all count towards my (let's say) 90 second rating, but then one time when I get in trouble and have to use up my entire time and lose anyway, that loss would be the only game counting towards my 3-minute rating. Your proposed system might well conclude that the slower I play the worse I am, when the causality is in fact reverse.
I like the idea of allowing games with a time handicap. However, that would force us to try to create a system where the ratings at different time controls were on the same scale. Presumably then both bots and humans would have ratings that increased steadily with time allowed.
On the other hand, I don't like the notion of having to calculate a player's rating at a given speed from scratch for every single speed. If I understand what you were proposing, Omar, the calculated rating at each speed, if plotted on a graph, wouldn't necessarily be linear or any reasonable curve. To keep the calculation time sane, I would strongly suggest making the assumption of a linear increase in rating with the logarithm of time allowed. Then we can pay attention to the endpoints only.
Incorporating this into the other changes to the rating system we had talked about would then involve only adding one extra saved parameter per player per game. Instead of saving each player's rating for each game, you would save each player's "lightning rating" and "postal rating". If you wanted to also save the "effective rating" for each player for that game you could do so, but it wouldn't be necessary since it could be inferred from the time control and the saved endpoint ratings.
If I understand how your testratings perl script worked (for the new system, pre-time-control-dependent), you just tried different ratings until you found the best match for the game history as weighted. To add a time control dependency, you would instead have to be testing pairs of endpoint ratings (rather than a single rating) to find the best fit. Unfortunately the best fit can no longer be insured by making the total wins match expected wins, since more than one pair of endpoints will do that exactly. To sop up the extra degree of freedom you would have to divide the actual wins into fast wins and slow wins by the proportionality suggested earlier, and also have the expected wins be thusly divided, and then make both sides match.
One potential problem is that if every single game a player has played is at the same time control, there will be no way to get a handle on the slope. I suggest solving that by having one of our fictitious draws be at lightning speed and the other at postal speed.
Is it clear what I'm suggesting overall? If I'm not mistaken the formulas I'm suggesting could be retroactively applied to our archived data. The results might be somewhat weird because most bots play at one time control only, but I'm curious what numbers would pop out nonetheless.
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| « Last Edit: Jan 20th, 2005, 7:05pm by Fritzlein » |
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omar
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Re: Omar = OmarFast , bot_bomb = bot
« Reply #28 on: Jan 22nd, 2005, 11:23am » |
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That's a really good point Karl. Humans do tend to play a bit faster when they are in a winning position and take more time to think when they are losing. It would tend to be a bit misleading. However, I don't think the distortion will be too much and maybe we can even compensate for it by adding 10% more to the time when the player wins and subtracting 10% when the player loses.
Regardless of what system we eventually go with, we first need to implement it and test it out. I will eventually provide the code for any system that I propose. That way people can try it out, check the code for any bugs and get familiar with it. I will also provide a condensed version of the games database so we can run the systems on the real data.
This way we can try out all the proposed systems before selecting one.
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99of9
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Re: Omar = OmarFast , bot_bomb = bot
« Reply #29 on: Jun 8th, 2005, 8:05pm » |
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I've done some simulations.
Although it's possible that there are still a bug or two in my code (let me know if you want the code to help look for them!), I wanted to share the early results.
I used Fritz's fast/slow interpolation method, with cutoffs at 15s on the fast side, and 8 minutes on the slow side. The 8 minute thing is as a concession to MrBrain's argument's in this thread. I agree with him that a 4 minute game is different to a postal game. Correspondence players could reasonably argue that they feel "rushed" in a 4 minute game.
Because this simulation just uses the game results, it does not include things like:
1) Rating Uncertainties increasing 1 point per week.
2) Bots inserted into the system with a rating matching that of their "parent". All new players are given a rating of 1500.
Other technical issues:
3) Abandoned games do not count in these ratings at all, they're treated like unrated games.
4) I agree with omar that the initial time reserve matters. It has been shared out over the number of moves in the game to determine the effective number of seconds per move. As has the 60s for the first move (minus the normal time per move which is not awarded on the first move).
5) Results are sorted according to "Slow" (8 minute+) rating.
6) I left out anyone who didn't play any rated games.
I will save my commentary on the actual ratings for a subsequent post. For now, here they are:
SLOW FAST NAME
2111 2130 Fritzlein
2036 1608 Belbo
2000 1610 omar
1963 1972 99of9
1896 1832 bot_speedy
1853 1706 bleitner
1830 1625 bot_Bomb2004CC
1815 1529 clauchau
1813 1913 robinson
1813 1742 mouse
1791 1649 RonWeasley
1781 1683 Adanac
1777 1709 bot_bomb
1745 1625 Paul
1725 1797 omarFast
1717 1529 fotland
1709 1586 BlackKnight
1690 1619 ytri
1678 1561 naveed
1677 1805 PMertens
1677 1450 bot_firsttry
1672 1574 OLTI
1652 1638 Ryan_Cable
1647 1541 bot_clueless
1641 1590 bot_Bomb2005CC
1636 1520 schmoe
1634 1578 bot_IIIT
1630 1582 bot_Arimaanator
1624 1550 Hannibal
1616 1518 dtj
1612 1594 bot_Bomb2005Fast
1598 1539 deselby
1597 1452 CeeJay
1596 1584 DorianGaray
1594 1534 Groumpf
1594 1522 inylong
1589 1547 Asturianuco
1587 1517 qsasha
1585 1454 Tore
1581 1531 xabiron
1577 1522 jdb
1576 1484 bot_Occam
1573 1639 bot_Bomb2005Blitz
1573 1527 adsyed01
1573 1521 camperman
1573 1516 TheMadHair
1572 1541 YunK
1570 1528 Keitam
1562 1566 ajedrezDude2
1561 1785 bot_lightning
1556 1521 Jonked
1556 1487 kissl
1556 1470 rajah
1555 1490 88of8
1554 1521 tj1777
1552 1532 TheUglyDog
1552 1508 travis
1549 1519 Paranoia
1546 1528 bot_Clueless2005CC
1546 1510 kerdamdam
1545 1559 spela
1543 1517 pikachamp
1541 1496 bot_Clueless2005Fast
1541 1479 arvindn
1539 1541 Jonathan
1537 1523 BLooodyANgel
1536 1537 mohabbatse
1535 1514 Jojo
1533 1462 trevor
1533 1412 boris_toplak
1531 1557 NativeOne
1531 1521 zman
1529 1482 blue22
1529 1461 Darkenrahl
1529 1438 jemicobel
1528 1511 fdailey
1527 1517 Agt
1526 1538 bot_Bomb2005P2
1526 1510 Guest1637
1526 1363 bot_Clueless2005Blitz
1525 1517 Booyah
1524 1515 KovirWyttcliffGerra
1521 1513 Tobi
1518 1478 bot_GnoBot2005Blitz
1517 1478 Threlicus
1514 1509 domi6
1514 1509 Simon
1514 1509 someone
1514 1505 msz
1513 1508 ktartandude
1512 1536 Yusei
1512 1514 bot_Clueless2005P1
1509 1509 Ander
1509 1506 Mauret
1509 1469 Spunk
1508 1505 eyvin
1508 1503 Josh
1507 1504 ntroncos
1505 1510 dbriggs
1504 1538 PatoGuy
1503 1491 sutzli
1502 1519 bot_Aamira
1502 1501 Miki
1502 1485 novacat
1499 1496 CraigS
1499 1463 Vinvin
1498 1499 bot_Clueless2005P2
1497 1503 Renaissance
1497 1498 bot_Loc2005P2
1497 1497 chess77
1497 1491 UltraWeak
1494 1494 jurc
1493 1521 gsyed
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| « Last Edit: Jun 8th, 2005, 8:06pm by 99of9 » |
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