Welcome, Guest. Please Login or Register.
Dec 2nd, 2022, 8:52pm

Home Home Help Help Search Search Members Members Login Login Register Register
Arimaa Forum « Measure stereotyped openings »


   Arimaa Forum
   Arimaa
   General Discussion
(Moderator: supersamu)
   Measure stereotyped openings
« Previous topic | Next topic »
Pages: 1 2 3 4 5  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print
   Author  Topic: Measure stereotyped openings  (Read 15115 times)
chessandgo
Forum Guru
*****



Arimaa player #1889

   


Gender: male
Posts: 1244
Re: Measure stereotyped openings
« Reply #30 on: Apr 12th, 2008, 12:06pm »
Quote Quote Modify Modify

on Apr 12th, 2008, 10:58am, Fritzlein wrote:

 
Is it true that Go players, by convention rather than by rule, always play the first stone in the same corner?  

 
yeah, even 1/8th of the board, thanks to diagonal symmetry Smiley
IP Logged

lightvector
Forum Guru
*****



Arimaa player #2543

   


Gender: male
Posts: 197
Re: Measure stereotyped openings
« Reply #31 on: Apr 12th, 2008, 12:13pm »
Quote Quote Modify Modify

According to Go etiquette, when playing black against another opponent, you place the first stone in the upper right corner (relative to you). I'm not exactly sure on the why/how of this custom, but supposedly you are offering the upper left corner to your opponent, since that is the corner closest to his/her right hand. The least polite spot is to place a stone in the upper left corner.
 
However, with online Go, both players typically view the board in the same orientation, which twists things around in an interesting way. Still, the typical play is in the upper right corner, even online, although most won't care if you choose the first move differently.
IP Logged
Fritzlein
Forum Guru
*****



Arimaa player #706

   
Email

Gender: male
Posts: 5928
Re: Measure stereotyped openings
« Reply #32 on: Jun 27th, 2010, 6:17pm »
Quote Quote Modify Modify

on Apr 10th, 2008, 6:30am, woh wrote:
The entropy after each turn is:
1w     5.6121         (max 11.87)
1b     9.4795         (max 11.87)
2w    10.4058         (max 11.87)
2b    11.2211         (max 11.87)
3w    11.6808         (max 11.87)
3b    11.8120         (max 11.868 )
4w    11.8451         (max 11.8634)
4b    11.8559         (max 11.8607)

Woh, if there is some rainy day when you have nothing better to do, I would be curious to know whether the recent EHH revolution has increased the entropy of openings in the last couple of years.  My expectation is that if you were to measure again, the entropy after both setups would now be higher than 9.5.
 
Of course the entropy for later moves will have increased, because it rapidly approaches 100% unique positions, such that we don't have enough games to measure how random it is.  For the setup moves themselves, though, entropy could already be decreasing if we were all standardizing on the 99of9 setup.  So measuring entropy for the setup moves would give us a solid measurement of what is otherwise just a qualitative impression that openings have gone haywire.
IP Logged

JoeHead
Forum Full Member
***



Arimaa player #4979

   


Gender: male
Posts: 24
Re: Measure stereotyped openings
« Reply #33 on: Jun 28th, 2010, 9:21pm »
Quote Quote Modify Modify

I love this arimaa analysis threads by Fritzlein. He is so eloquent in highlighting pluses of the game.
Oh my, what would it be if there was 1 000 000 rated players worldwide. With chessbase like software with games and analysis. With Rybka-like engines. With hundreds of book describing ancient origin of game and strategy, tactics and opening analysis... Oh my, let those times come
IP Logged
woh
Forum Guru
*****



Arimaa player #2128

   


Gender: male
Posts: 252
Re: Measure stereotyped openings
« Reply #34 on: Jul 1st, 2010, 3:15am »
Quote Quote Modify Modify

on Jun 27th, 2010, 6:17pm, Fritzlein wrote:

Woh, if there is some rainy day when you have nothing better to do, I would be curious to know whether the recent EHH revolution has increased the entropy of openings in the last couple of years.  My expectation is that if you were to measure again, the entropy after both setups would now be higher than 9.5.
 
Of course the entropy for later moves will have increased, because it rapidly approaches 100% unique positions, such that we don't have enough games to measure how random it is.  For the setup moves themselves, though, entropy could already be decreasing if we were all standardizing on the 99of9 setup.  So measuring entropy for the setup moves would give us a solid measurement of what is otherwise just a qualitative impression that openings have gone haywire.

 
Fritz, you're quite right. It is higher than 9.5 after 1s.  
 
movgamdisdupmaxsinSSmax
1g6175 93752381249 676 5.899512.5922
1s617533132862 256281910.221412.5922
2g617541032072 121361311.156712.5922
2s617549791196  43454511.950012.5922
3g61735728 445  15546912.407412.5918
3s61556000 155   5588112.531712.5875
4g61256073  52   3602612.562912.5805
4s61076088  19   2606912.570012.5762

 
mov: move
gam: number of games that lasted that long
dis: number of distinct positions after that move
dup: number of duplicate positions
max: number of games with the most frequent position
sin: number of games with a position occurring only once
 
IP Logged

Fritzlein
Forum Guru
*****



Arimaa player #706

   
Email

Gender: male
Posts: 5928
Re: Measure stereotyped openings
« Reply #35 on: Jul 1st, 2010, 3:29am »
Quote Quote Modify Modify

Thanks, woh.  Your research is excellent.
 
We can now officially say that Arimaa has more variety of openings than Chess960.   What's more, our variety is voluntarily chosen by players trying to win, not arbitrarily imposed by dice.  Therefore we have the best of both worlds: the lack of randomizers (like chess) and the lack of memorized openings (like Chess960).
IP Logged

woh
Forum Guru
*****



Arimaa player #2128

   


Gender: male
Posts: 252
Re: Measure stereotyped openings
« Reply #36 on: Jul 1st, 2010, 3:33am »
Quote Quote Modify Modify

The top 10 gold setups are now:
 
1. (2) 1249
RHDMEDHR
RRRCCRRR
 
2. (1) 1172
RHCMECHR
RRRDDRRR
 
3. (3) 405
HDCMECDH
RRRRRRRR
 
4. (4) 250
DHCMECHD
RRRRRRRR
 
5. (-) 160
RHRMERHR
RCRDDRCR
 
6. (-) 157
RHDMECHR
RRRCDRRR
 
7. (5) 111
RHRMERHR
RDRCCRDR
 
8. (9) 82
RMDHEDHR
RRRCCRRR
 
9. (6) 73
RHCMECHR
RDRRDRRR
 
10= (-) 65
RHDMEDHR
RCRRRRCR
 
10= (9) 65
DHCCEDMH
RRRRRRRR
 
The setup with 4 rabbits upfront and the the dog in the center makes an impressive entry in the top 10. It is now more popular than the same setup but with the cats in the center.
IP Logged

Fritzlein
Forum Guru
*****



Arimaa player #706

   
Email

Gender: male
Posts: 5928
Re: Measure stereotyped openings
« Reply #37 on: Jul 1st, 2010, 5:49am »
Quote Quote Modify Modify

I wonder how long until some variation of the double flank horse breaks into the top ten, or whether it ever will.  One thing holding it back is that when the symmetry is broken, it becomes less obvious what to do with the remaining pieces, so there are more sub-variations.
 
I notice that the top four from two years ago remained the top four, but all of them lost mind share.  Still, it would take some doing for any other setup to compete.
 
« Last Edit: Jul 1st, 2010, 5:57am by Fritzlein » IP Logged

Sconibulus
Forum Guru
*****



Arimaa player #4633

   


Gender: male
Posts: 116
Re: Measure stereotyped openings
« Reply #38 on: Jul 1st, 2010, 2:02pm »
Quote Quote Modify Modify

Woh, does that list of top openings include mirrored positions? Also, what's the time frame? The top positions seem very high, while those around 10 seem really low...
 
Oh, also, would it be possible to ignore bots playing as gold? Since most of those are probably from the ladder, they don't change, and therefor will keep human variance from showing up as readily.
IP Logged

Fritzlein
Forum Guru
*****



Arimaa player #706

   
Email

Gender: male
Posts: 5928
Re: Measure stereotyped openings
« Reply #39 on: Jul 2nd, 2010, 1:38am »
Quote Quote Modify Modify

Only woh can answer authoritatively, but based on what he said last time:
1) Mirror setups are counted separately.
2) The time frame is Arimaa's entire history.
3) The disparity between the top positions is real, because if one doesn't do the 99of9 or interface default setup, there is little standardization.
4) Bots are ignored.  These stats are from rated human vs. human games only.
« Last Edit: Jul 2nd, 2010, 9:55am by Fritzlein » IP Logged

Hippo
Forum Guru
*****




Arimaa player #4450

   


Gender: male
Posts: 883
Re: Measure stereotyped openings
« Reply #40 on: Jul 2nd, 2010, 2:46am »
Quote Quote Modify Modify

Yes "symmetrical setups" tend to be more frequent. It is not only from historical reasons, but as well as there are much less options to make the setup symmetric.  
I am playing mostly the Ef2 Hg2 Hh2 setup now, but I am not sure how often the full setup repeats.
 
For the entire analysis there is nothing to change, but I would be interested on seeing top ten openings with both horses on the same half of board.
 
And may be separate counts of symmetrical/assymetrical gold setup.
« Last Edit: Jul 2nd, 2010, 2:48am by Hippo » IP Logged

woh
Forum Guru
*****



Arimaa player #2128

   


Gender: male
Posts: 252
Re: Measure stereotyped openings
« Reply #41 on: Jul 2nd, 2010, 12:40pm »
Quote Quote Modify Modify

on Jul 1st, 2010, 2:02pm, Sconibulus wrote:
Woh, does that list of top openings include mirrored positions? Also, what's the time frame? The top positions seem very high, while those around 10 seem really low...
 
Oh, also, would it be possible to ignore bots playing as gold? Since most of those are probably from the ladder, they don't change, and therefor will keep human variance from showing up as readily.

 
Sconibulus, like Fritzlein already pointed out, those results are based on all HvH games ever played. Games with bots are ignored.
 
In my original post mirrowed positions were counted separately but I have changed that since. They are now considered the same.
 
For comparison here are the results with mirrowed positions counted separately:
 
mov gam dis dup max sin S   Smax
1w 6175 1058 5117 1121 754 6.3538  12.5922
1b 6175 3492 2683 234 2998 10.4251 12.5922
2w 6175 4252 1923 120 3770 11.2903 12.5922
2b 6175 5090 1085 43  4684 12.0180 12.5922
3w 6173 5768 405 14  5524 12.4258 12.5918
3b 6155 6017 138 5  5909 12.5381 12.5875
4w 6125 6081 44  3  6040 12.5658 12.5805
4b 6107 6093 14  2  6079 12.5717 12.5762

 
Obviously the entropy is higher.
After Gold's setup the difference is about 0.45 and after both player's setup 0.2
IP Logged

woh
Forum Guru
*****



Arimaa player #2128

   


Gender: male
Posts: 252
Re: Measure stereotyped openings
« Reply #42 on: Jul 2nd, 2010, 12:48pm »
Quote Quote Modify Modify

on Jul 2nd, 2010, 2:46am, Hippo wrote:
... but I would be interested on seeing top ten openings with both horses on the same half of board.

 
Hippo, there are 492 games in which Gold's horses are setup in the same half of the board. This is 8% of all HvH games.
 
There are 227 distict such setups.
The most frequent ones are:
 
21. 34
RHCHECMR
RRRDDRRR
 
29. 23
HHCEDRMR
RRRDRRCR
 
31. 19
DHCHECMD
RRRRRRRR
 
32. 17
RMCDDEHH
RRRRRCRR
 
35. 16
RHDHEDMR
RRRCCRRR
 
37. 15
RMREHRHR
RCRDDRCR
 
38. 15
RHHEMDDR
RRRCCRRR
 
52. 9
HHECCDMR
RRDRRRRR
 
60. 8
HECDDCMR
RHRRRRRR
IP Logged

Fritzlein
Forum Guru
*****



Arimaa player #706

   
Email

Gender: male
Posts: 5928
Re: Measure stereotyped openings
« Reply #43 on: Jul 4th, 2010, 2:37am »
Quote Quote Modify Modify

on Jul 2nd, 2010, 12:48pm, woh wrote:
Hippo, there are 492 games in which Gold's horses are setup in the same half of the board. This is 8% of all HvH games.

Nice.  It will be interesting to see whether that 8% share goes up in the next couple of years.
 
Quote:
37. 15
RMREHRHR
RCRDDRCR

I wonder how many of those fifteen were me.  I know I tried it for a while, but I forget how long exactly.
 
Thanks again, woh, for compiling such interesting and illuminating statistics.
IP Logged

FireBorn
Forum Guru
*****



Arimaa player #1832

   


Gender: male
Posts: 123
Re: Measure stereotyped openings
« Reply #44 on: Jul 4th, 2010, 9:40am »
Quote Quote Modify Modify

I think I've tried that one a few times too
IP Logged
Pages: 1 2 3 4 5  Reply Reply Notify of replies Notify of replies Send Topic Send Topic Print Print

« Previous topic | Next topic »

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