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        Arimaa >> General Discussion >> Game branching factor graphs
        
(Message started by: Janzert on Mar 30th, 2006, 2:29am)
Title: Game branching factor graphs
Post by Janzert on Mar 30th, 2006, 2:29am
I've spent the last little while making a little online app that gives a graph of the branching factor for individual games. It also provides a few other related statistics for the game. This is now online at http://arimaa.janzert.com/gamegraphs/.

There are probably still a few bugs in it, so let me know if something doesn't seem to work.

btw, my other arimaa things (fame calculator, bf study) have moved over to arimaa.janzert.com (http://arimaa.janzert.com/) as well. The old links have redirects that should be there for the foreseeable future so they should continue working fine.

Janzert
Title: Re: Game branching factor graphs
Post by mouse on Mar 30th, 2006, 4:24am
Interesting tool. I tried it on a couple of my old games. The result came as a bit of a supprise to me. In games were I thought I had a clear mobility advantage I sometimes didn't. Hence there most be a big difference between what kind of moves I consider and the actual available number of moves.
Title: Re: Game branching factor graphs
Post by omar on Mar 30th, 2006, 2:25pm
Hey that's really cool, Brian. Thanks for making it available. I have linked it on the Arimaa >> Games page. I also updated the link on the Downloads page use the new URL.
Title: Re: Game branching factor graphs
Post by Ryan_Cable on Mar 30th, 2006, 8:13pm
I think there is a bug in your calculation of geometric mean.  It is often, though not always, identical for silver and gold.

It would be nice if you added links to the games on the Arimaa.com server such as:
http://arimaa.com/arimaa/gameroom/comments.cgi?gid=26741

Also that particular game shows the limited predictive power of available move advantage.  Neither side lost any pieces, and from move 13 to the end, Adanac had 3 to 4 fold more available moves, yet I was clearly winning and won the game on move 19.
Title: Re: Game branching factor graphs
Post by Fritzlein on Mar 30th, 2006, 8:39pm
Thanks for adding the geometric mean, Janzert.  I agree with Ryan, however, that something is fishy.  I looked at a sample of one game (namely game 10000), and although the numbers are different for Silver and Gold, it seems that the wrong one is larger.  Maybe I'm just no good at visually calculating a multiplicative average.  8)
Title: Re: Game branching factor graphs
Post by Janzert on Mar 30th, 2006, 10:19pm
Oops, I should know to recheck stuff that I finish at 3am. Fixed two bugs, one major and one minor, and double checked a couple games on the spreadsheet. Silver means were completely wrong. Should all be working correctly now.

I also added a link to get the raw move numbers, so you can throw them in a spreadsheet and play with them yourself as well.

Janzert
Title: Re: Game branching factor graphs
Post by Fritzlein on Mar 31st, 2006, 3:28pm
Game 25959 seems to have a graph that is not only very crowded, but also has some extraneous lines on it.

Games 6956 and 13011 provide an argument for using a logarithmic scale for the moves axis.  In the latter game Belbo's 117,059 possible moves on 66w dwarf the rest of the graph, so that changes in Paul's endgame mobility are barely visible.

Game 19278 is, I believe, still the longest serious HvB game.  Adanac managed to find a difficult theoretical win over the board in a blitz game!  But anyway the endgame with only a couple of pieces left is impossible to read on a linear scale.
Title: Re: Game branching factor graphs
Post by Swynndla on Mar 31st, 2006, 4:04pm
I was going to ask if there is a "view game" link, where I could put the game ID in and it would open the game (since the game references above aren't linked) ... but then it dawned on me that all I need to do is go to:
http://www.arimaa.com/arimaa/gameroom/replayFlash.cgi?gid=19278&s=b&client=1

Sorry for being a slow learner, and figuring out what is obvious to the rest of you.

There may even already be a "view game" link, and if so, then that's something else I've missed!
Title: Re: Game branching factor graphs
Post by Janzert on Mar 31st, 2006, 4:49pm

on 03/31/06 at 16:04:52, Swynndla wrote:
There may even already be a "view game" link, and if so, then that's something else I've missed!


Select Games from the lefthand navigation frame, there will be a view game and plan game link. Either one can be used to enter a game number to view a game.

I personally like using the plan game link better, because it will open the game in a new window instead of resizing the current window. But only the view game will show you who won and lost the game.

Janzert
Title: Re: Game branching factor graphs
Post by Janzert on Mar 31st, 2006, 5:04pm

on 03/31/06 at 15:28:54, Fritzlein wrote:
Game 25959 seems to have a graph that is not only very crowded, but also has some extraneous lines on it.


I agree, trying to graph a 600 move game with a 640x480 image doesn't work terribly well. ;) I'm not positive I understand what you mean by extraneous lines though. I'm assuming you mean the turns for Gold (P1) that went over ~17000 possible moves. I double checked peaks at 140w, 277w, 278w and 346w with the official move generator and they all matched the number displayed in the graph. They just happen to be positions that have more options than the others.


Quote:
Games 6956 and 13011 provide an argument for using a logarithmic scale for the moves axis.  In the latter game Belbo's 117,059 possible moves on 66w dwarf the rest of the graph, so that changes in Paul's endgame mobility are barely visible.

Game 19278 is, I believe, still the longest serious HvB game.  Adanac managed to find a difficult theoretical win over the board in a blitz game!  But anyway the endgame with only a couple of pieces left is impossible to read on a linear scale.


I'm hoping to add an option to switch between a log and linear view. But I'm going to be out of town on a business trip for most of next week so I may not get it done for a couple weeks.

Janzert
Title: Re: Game branching factor graphs
Post by Fritzlein on Mar 31st, 2006, 5:11pm

on 03/31/06 at 17:04:17, Janzert wrote:
I agree, trying to graph a 600 move game with a 640x480 image doesn't work terribly well. ;) I'm not positive I understand what you mean by extraneous lines though.

On my graph there are four lines, two green and two red, which are more horizontal than vertical.  They seem to connect a point near (550, 17000) with points near (170, 12000), (170, 17000), (170, 18000), and (170, 20000) respectively.  Maybe they don't appear on your screen?

Thanks for considering the log option for the moves axis.
Title: Re: Game branching factor graphs
Post by Janzert on Mar 31st, 2006, 5:47pm
Hmm, no I don't think I'm seeing that. Do they show in any/all of these versions png (http://arimaa.janzert.com/25959.png), gif (http://arimaa.janzert.com/25959.gif) or bmp (http://arimaa.janzert.com/25959.bmp)? The png should be the same as the dynamic page the others were converted from the original in gimp.

Also what browser do you use and can you tell if it might be resizing the image to fit on your screen?

Janzert

Oops, nevermind. I just took a look at the online version and I see the extra lines. I'm guessing it's a gnuplot bug in the version that I have on the server. I'll see what I can do with it.

Janzert
Title: Re: Game branching factor graphs
Post by Janzert on Mar 31st, 2006, 6:53pm
Ok, nevermind again. :P It was a bug in my code. Should be working correctly now.

Janzert
Title: Re: Game branching factor graphsG
Post by Swynndla on Mar 31st, 2006, 8:01pm

on 03/31/06 at 16:49:38, Janzert wrote:
Select Games from the lefthand navigation frame, there will be a view game and plan game link. Either one can be used to enter a game number to view a game.


Call me slow (go on) but I don't see a "Games" link on the left side of anywhere ... from the gameroom I have such things as:
Start Game
Invite Friend
Practice Games
Live Games
etc etc

... but no "Games"?
Title: Re: Game branching factor graphs
Post by Ryan_Cable on Mar 31st, 2006, 8:44pm
He means the left frame of the main page (to the left of this forum).
Title: Re: Game branching factor graphs
Post by Janzert on Mar 31st, 2006, 8:47pm
Hmm, when you arrive at http://www.arimaa.com/arimaa/ the left side should be a navigation frame. A little less than halfway down is the Game link.

Janzert
Title: Re: Game branching factor graphs
Post by Janzert on Mar 31st, 2006, 10:51pm
It doesn't remember your setting, but there is now an option to view a log scaled graph.

Janzert
Title: Re: Game branching factor graphs
Post by Fritzlein on Mar 31st, 2006, 11:06pm

on 03/31/06 at 22:51:36, Janzert wrote:
It doesn't remember your setting, but there is now an option to view a log scaled graph.

Thanks for the log option!  It really brings out the endgames, without quashing the midgame too much, IMHO.

Also thanks for fixing that other bug thingy, although that 600-move game is never going to look good.  You rock.
Title: Re: Game branching factor graphs
Post by Swynndla on Mar 31st, 2006, 11:50pm

on 03/31/06 at 20:47:03, Janzert wrote:
Hmm, when you arrive at http://www.arimaa.com/arimaa/ the left side should be a navigation frame. A little less than halfway down is the Game link.


Ahhhh ... I never go to http://www.arimaa.com/arimaa/ ... I always go to http://www.arimaa.com/arimaa/gameroom/ ... I know what you mean now.

Ryan, I open the forum from the gameroom, so I don't have that link to the left of the forum, but I have it now.

... thanks to you people for putting up with my lack of knowledge!
Title: Re: Game branching factor graphs
Post by Janzert on Apr 15th, 2006, 9:36am
Just a note that I've now added FAME graphs to this page (http://arimaa.janzert.com/gamegraphs/) as well.

Janzert
Title: Re: Game branching factor graphs
Post by Fritzlein on Apr 15th, 2006, 10:33am
Majorly cool, thanks!

Has something gone wrong with the line that displays the outcome?  It seems that every game has the winner winning in two moves.  Also the max and min number of moves is always on move two.

Most FAME graphs are pretty boring: they say at zero for a while, then go only in one direction from there.  This shows that material advantage is a pretty good indicator of who is winning.  There are, however, some dramatic mid-game reversals in FAME score, such as game 25959.
Title: Re: Game branching factor graphs
Post by Janzert on Apr 15th, 2006, 3:07pm
yes, should be fixed now.

Also added links to view the game or comments and a cookie to remember your preference of a log or linear move graph.

Janzert
Title: Re: Game branching factor graphs
Post by Fritzlein on Apr 15th, 2006, 4:26pm
Thanks some more.  The log cookie is very convenient (cutting my page loads in half) and it's nice to be able to jump straight to the comments when a graph looks interesing for whatever reason.


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