Arimaa Forum
        (http://arimaa.com/arimaa/forum/cgi/YaBB.cgi)
      

        Arimaa >> General Discussion >> Game lengths increasing?
        
(Message started by: Fritzlein on Sep 16th, 2004, 12:02pm)
Title: Game lengths increasing?
Post by Fritzlein on Sep 16th, 2004, 12:02pm
99of9 has suggested that Arimaa games are gradually getting longer as the level of play improves.  Since Omar has made the game database available (Thanks Omar!) one can do a quick calculation of average game length for various subsets of the data.  It turns out that the average number of moves per game is

26.1  over all 7957 games
31.2  over the most recent 1961 games
34.1  over all 1316 games with both players rated over 1600
36.6  over the most recent 265 games with both players rated over 1600

So clearly the games are getting longer over time, but also it clearly has more to do with the level of play being higher than it does to do with the mere passage of time.

-Karl
Title: Re: Game lengths increasing?
Post by 99of9 on Sep 16th, 2004, 3:21pm
How cool.  Good to be proven right too :-)
Title: Re: Game lengths increasing?
Post by 99of9 on Sep 18th, 2004, 11:24am
This might give you an idea of how fast players are improving with time:

I've split the years that arimaa has been going into 3 approx equal sections, counted only the games where players had ratings within 100 ratings points of each other, and excluded games ending on time or resignation.

Here are the average game lengths (according to which colour won)

Period 1: [1037000000 - 1057000000]
w: 21.1 (187 games)
b: 21.5  (185 games)

Period 2: [1057000000 - 1077000000]
w: 30.7  (376 games)
b: 29.5  (402 games)

Period 3: [1077000000 - 1097000000]
w: 39.5  (272 games)
b: 37.7  (267 games)


Question:  why does it take white longer to win than black?  (this gap seems to be getting bigger!)


Note also that contrary to our other discussions, white doesn't appear to be particularly dominant over black in games between fairly equally rated opponents.
Title: Re: Game lengths increasing?
Post by omar on Sep 21st, 2004, 4:01pm
Very interesting results.  It am curious to see how these will change as time goes on.
Title: Re: Game lengths increasing?
Post by Fritzlein on Sep 24th, 2004, 8:03pm
More notes on game length:

Longest game:
251 moves (game 6956) firsttry loses to Arimaazilla on time.  Oddly enough, although they were stuck in circles from about move 80 to 120, and again from about 130 to 205, the game at the end was very much alive, and firsttry had real winning chances.

Longest game decided by rabbit reaching goal:
180 moves (game 6978) firsttry defeats Arimaazilla.  Similar to the game above, stuck from move 40 to 90, but Arimaazilla, although behind, breaks the pattern, perhaps to avoid repetition.

Longest game involving a human:
115 moves (game 7983) speedy loses to Fritzlein.  I framed a horse on move 28, but I just shuffled pieces until move 38 before I realized I needed to rotate out my camel from being a framer to being active on offense.  Then I went and got rabbits methodically.  Until move 88 I followed a slow formula, discovered by trial and error in past games, in which I knew speedy would not abandon the framed horse for counter-attack.  Often I shuffled pieces to wait for a mistake.  When the game broke open, I played poorly, prolonging the conversion of my material advantage.

Longest game involving two humans:
73 moves (game 2868) naveed loses to omar.  Defensive play by both sides.  Thank goodness for rabbit pulls!  Rabbits exchanged on move 35 and again on move 48.  Game finally breaks open on move 58 with advantage to omar.

Percentage of bot v. bot games over 80 moves: 2.5%
Percentage of bot v. human games over 80 moves: 0.4%
Percentage of human v. human games over 80 moves: 0%

And while I'm at it, some shortest game statistics:

Shortest rabbit-to-goal victory:
6 moves (game 1627) ShallowBlue loses to naveed

Shortest rabbit-to-goal victory human vs. human:
9 moves (game 1409) Magrathean defeats Greytle

Shortest human-playing-gold defeats Arimaazilla:
10 moves (game 5091) tomcstein

Shortest human-playing-silver defeats Arimaazilla:
11 moves (game 5092) tomcstein

Shortest human-playing-gold defeats Arimaanator:
13 moves (game 3332) omar

Shortest human-playing-silver defeats Arimaanator:
14 moves (game 5092) Belbo
Title: Re: Game lengths increasing?
Post by omar on Sep 26th, 2004, 3:24pm
That's interesting. I didn't know that there hasn't been any
human vs human game that has gone ove 80 moves.

If we restrict ourselfs to just the human vs human games
do we still see a pattern of increasing game length ?
Title: Re: Game lengths increasing?
Post by Fritzlein on Sep 30th, 2004, 10:26am
There are 449 human versus human games in my database of all types, i.e. unrestricted by playing strength, type of termination, or rated/unrated.  Of those games

The average length of the of the first 147 games was 19.8
The average length of the of the next 148 games was 24.6
The average length of the of the last 154 games was 32.2
Title: Re: Game lengths increasing?
Post by Fritzlein on Oct 27th, 2004, 11:46pm
Well, there's a new record for the longest human-vs-human game, but only because I am not good at finishing off a game and naveed fought it out to the bitter end.  75 moves in game 8972.
Title: Re: Game lengths increasing?
Post by Fritzlein on Nov 24th, 2004, 10:46pm
This thread deserves a note that the new record for longest game (in terms of number of moves) is game 9842, speedy defeats speedtrap in 316 moves.  As far as I know, speedtrap is the only bot so far designed specifically to win by having the higher score, according to formula, at the end of eight hours.  Unfortunately for the experiment, Fotland was able to tweak speedy's code midgame to increase aggression and break out of the pattern.
Title: Re: Game lengths increasing?
Post by Fritzlein on Feb 6th, 2005, 11:10pm
http://www.math.umn.edu/~juhn0008/Game_length.png

A picture should make everything clear.  I've calculated a moving average for the length of all games terminating in "g", "m", or "p".  I included both rated and unrated games.

The purple line is for all games, and the orange line is for games in which both players were rated over 1700.  I started the former out at 20 and the latter at 30, which seemed low to me, but it looks like both actually dipped a bit before rising.

The "over 1700" stat may be a bit misleading as it includes a bunch of games versus speedy, but I still think it is useful to give a general idea of what is going on.
Title: Re: Game lengths increasing?
Post by PMertens on Feb 16th, 2005, 11:00am
new record for human vs human ...

and no not defensive :-)

http://arimaa.com/arimaa/gameroom/replayFlash.cgi?gid=12053&s=w&client=1
Title: Re: Game lengths increasing?
Post by omar on Feb 25th, 2005, 6:50pm
I've been spending most of my Arimaa time on the postal games and haven't read the forum in a few weeks. Looks like there's been a lot of postings. I'll try to catch up this weekend.

I was quite suprised to see that some of the postal games have ended in under 40 moves; even among 1700+ players. I was expecting them to be much longer. It will be interesting to see how the postal games compare to the interactive ones once the tournament is over.
Title: Re: Game lengths increasing?
Post by Fritzlein on Feb 26th, 2005, 1:27pm

on 02/25/05 at 18:50:38, omar wrote:
[...] haven't read the forum in a few weeks. Looks like there's been a lot of postings.


I'm excited the that forum seems to have reached a level of activity where it makes sense to check it every day.


on 02/25/05 at 18:50:38, omar wrote:
I was quite suprised to see that some of the postal games have ended in under 40 moves; even among 1700+ players. I was expecting them to be much longer. It will be interesting to see how the postal games compare to the interactive ones once the tournament is over.


I expect the average game length will be about the same for the postal games as for the interactive games, not shorter, not longer.  The results so far are not all that anomalous given that the finished games are the shortest of the crop.
Title: Re: Game lengths increasing?
Post by Fritzlein on Mar 11th, 2005, 4:39pm
To update, there is a new record for human versus bot, game 12432: lightning loses to PMertens in 122 moves.

(It's weird to get a "record" for being bad at finishing off a won position, but then again, my previous record of 115 moves against speedy happened for the same reason.  Some day someone will intentionally draw out a game for 500 moves just to get the record...)

Also there is a new record for human versus human (already noted elsewhere), game 11732: robinson loses to Paul in 80 moves.

There was a brief dip in game lengths when attacking play became more popular, but I think we are due for another, further rise as we see attacking games in which at least one wing of the board gets totally clogged up.
Title: Re: Game lengths increasing?
Post by Fritzlein on Mar 21st, 2005, 1:27pm
Game 13011, Belbo beats Paul in 95 moves, is the new record.  It happened in a postal game, but fortunately Paul averaged only 12 hours per move, and Belbo just over 2 hours per move!
Title: Re: Game lengths increasing?
Post by Fritzlein on Apr 15th, 2005, 8:21am
96 moves is quite a long game, but you'll notice in a previous post in this thread that PMertens beat lightning in 122 moves once.  It's sort of a silly record, because someone could intentionally prolong a game where they are winning, but I don't think any of the longest games show that behavior so far.  We'll see what people do in the future...
Title: Re: Game lengths increasing?
Post by Fritzlein on Apr 16th, 2005, 2:18pm

on 04/16/05 at 04:18:15, Arimanator wrote:
What if the game length between two humans starts to augment dramatically because of increasing knowledge of the game or the emergence of new tactics reinforcing the power of the losing side to ward off defeat indefinitely.


The statistics seem to support the idea that the games get longer as the players get better.  It isn't clear whether this trend will continue indefinitely, though.  Perhaps we will discover new offensive strategies that shorten games considerably.  If I had to guess at the moment, though, I would say that top-level games will continue to get longer and longer on average.   Let me guess that a year from now the average game between two 1700+ players will be 55 moves.
Title: Re: Game lengths increasing?
Post by Fritzlein on May 4th, 2005, 1:49pm
Not 300, just 252.  They broke the old record by one move!  Personally I think they agreed to play just long enough to get the record.  That's all they were after.  But we'll make note of it anyway for posterity: Game 14356 bot_Loc2005P2 defeats bot_GnoBot2005P2.

Contrast this do-nothing game to the previous record game.  In that one it looked like they only needed another 20 moves or so to reach a conclusion, whereas in this one nothing happened after move 10.
Title: Re: Game lengths increasing?
Post by Fritzlein on Aug 6th, 2005, 2:08pm
Because it is relevant to the discussion about time control for the World Championship, I thought I would update my graph which shows a moving average of game length.  I counted only games which ended in "g", "p", or "m".  I further restricted the games based on whether both players were human, and whether both players were rated 1700 or over.

http://www.math.umn.edu/~juhn0008/GameLength.png

I think the yellow line is the most relevant, as it shows the average length of all human versus human games.  It hasn't been declining recently, contrary to my claim elsewhere, and it now sits around 38 moves per game.  The average for strong human games has held fairly steady, and sits around 45.  My hunch is that the lengthening of human vs. human games overall has a lot to do with there being more strong humans around.

The pink line is composed mostly of games involving a strong human and some version of Bomb, so its progress depends on what methods are currently most popular for Bomb-bashing.
Title: Re: Game lengths increasing?
Post by 99of9 on Aug 6th, 2005, 9:57pm
Thanks for the update, I always take great interest in these plots.

I'd say the light blue line is the most relevant to the tournament, since we're trying to select a champion, and s/he should presumeably be rated over 1700.
Title: Re: Game lengths increasing?
Post by Fritzlein on Aug 6th, 2005, 11:01pm
You are right, the light blue line is the most relevant to the World Championship time controls.  Just FYI, it consists of 264 points.  These days there are quite a few over-1700 human vs. human matchups, enough to start doing statistics and such.
Title: Re: Game lengths increasing?
Post by Fritzlein on Sep 2nd, 2005, 10:58pm
One question we asked ourselves (but neglected to answer) was whether postal games would take more moves on average than live games.  It makes sense that a reduction in blunders would prolong games somewhat on average, but also one can finish won games more efficiently.

It turns out that among the 80 games of the postal tournament, 20 were decided by timeout or resignation, and the other 60 averaged 43 moves per game.  That is slightly longer than the average human vs. human game, but not by much, as expected.
Title: Re: Game lengths increasing?
Post by Fritzlein on Sep 9th, 2005, 9:03am
To update, there is a new record for human versus bot, game 19278: Bomb2005Blitz loses to Adanac in 143 moves.
Title: Re: Game lengths increasing?
Post by Fritzlein on Dec 2nd, 2005, 6:51pm
Game 22068, Megamau defeats Belbo in 96 moves, is the new record longest human versus human game.
Title: Re: Game lengths increasing?
Post by Ryan_Cable on Mar 9th, 2006, 10:33pm
Clueless2006P1 drew Clueless2006Fast on score after move 600w.
http://arimaa.com/arimaa/gameroom/comments.cgi?gid=25959

This is a hint that all BvB games should have a G factor.
Title: Re: Game lengths increasing?
Post by Fritzlein on Mar 9th, 2006, 11:30pm
Now we'll have to keep a separate record for the longest game decided on the board.  Obviously two bots that never go on offense could play a million-move game, assuming they are careful to avoid repetition.
Title: Re: Game lengths increasing?
Post by omar on Mar 10th, 2006, 11:12am
I might need to change the bot matching script to avoid games between different versions of Clueless2006 :-)
Title: Re: Game lengths increasing?
Post by Fritzlein on Aug 7th, 2006, 4:00pm
Since some previous longest-game records went here, I'll add game 36476, H_Bobbletoff vs. seanick, which seanick won in 138 moves.  It's interesting that the only HvH game of over 100 moves should be way over 100 moves.  I think that's what they call a "statistical outlier".
Title: Re: Game lengths increasing?
Post by seanick on Aug 7th, 2006, 11:57pm
http://arimaa.com/arimaa/gameroom/replayFlash.cgi?gid=34855&s=w&client=1

seanick vs. bot_bomb2005p2: seanick wins as gold in 223 moves.

I blame it on Paul, and he blames it on me not paying attention to what he said.

either way that was fairly long.  


Arimaa Forum » Powered by YaBB 1 Gold - SP 1.3.1!
YaBB © 2000-2003. All Rights Reserved.