Author |
Topic: Measure stereotyped openings (Read 15862 times) |
|
chessandgo
Forum Guru
Arimaa player #1889
Gender: 
Posts: 1244
|
 |
Re: Measure stereotyped openings
« Reply #30 on: Apr 12th, 2008, 12:06pm » |
 Quote  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 
|
|
 IP Logged |
|
|
|
lightvector
Forum Guru
Arimaa player #2543
Gender:
Posts: 197
|
|
Re: Measure stereotyped openings
« Reply #31 on: Apr 12th, 2008, 12:13pm » |
Quote 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
Gender:
Posts: 5928
|
|
Re: Measure stereotyped openings
« Reply #32 on: Jun 27th, 2010, 6:17pm » |
Quote 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:
Posts: 24
|
|
Re: Measure stereotyped openings
« Reply #33 on: Jun 28th, 2010, 9:21pm » |
Quote 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:
Posts: 254
|
|
Re: Measure stereotyped openings
« Reply #34 on: Jul 1st, 2010, 3:15am » |
Quote 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.
| mov | gam | dis | dup | max | sin | S | Smax | | 1g | 6175 | 937 | 5238 | 1249 | 676 | 5.8995 | 12.5922 | | 1s | 6175 | 3313 | 2862 | 256 | 2819 | 10.2214 | 12.5922 | | 2g | 6175 | 4103 | 2072 | 121 | 3613 | 11.1567 | 12.5922 | | 2s | 6175 | 4979 | 1196 | 43 | 4545 | 11.9500 | 12.5922 | | 3g | 6173 | 5728 | 445 | 15 | 5469 | 12.4074 | 12.5918 | | 3s | 6155 | 6000 | 155 | 5 | 5881 | 12.5317 | 12.5875 | | 4g | 6125 | 6073 | 52 | 3 | 6026 | 12.5629 | 12.5805 | | 4s | 6107 | 6088 | 19 | 2 | 6069 | 12.5700 | 12.5762 |
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
Gender:
Posts: 5928
|
|
Re: Measure stereotyped openings
« Reply #35 on: Jul 1st, 2010, 3:29am » |
Quote 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:
Posts: 254
|
|
Re: Measure stereotyped openings
« Reply #36 on: Jul 1st, 2010, 3:33am » |
Quote 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
Gender:
Posts: 5928
|
|
Re: Measure stereotyped openings
« Reply #37 on: Jul 1st, 2010, 5:49am » |
Quote 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:
Posts: 116
|
|
Re: Measure stereotyped openings
« Reply #38 on: Jul 1st, 2010, 2:02pm » |
Quote 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
Gender:
Posts: 5928
|
|
Re: Measure stereotyped openings
« Reply #39 on: Jul 2nd, 2010, 1:38am » |
Quote 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:
Posts: 883
|
|
Re: Measure stereotyped openings
« Reply #40 on: Jul 2nd, 2010, 2:46am » |
Quote 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:
Posts: 254
|
|
Re: Measure stereotyped openings
« Reply #41 on: Jul 2nd, 2010, 12:40pm » |
Quote 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:
Posts: 254
|
|
Re: Measure stereotyped openings
« Reply #42 on: Jul 2nd, 2010, 12:48pm » |
Quote 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
Gender:
Posts: 5928
|
|
Re: Measure stereotyped openings
« Reply #43 on: Jul 4th, 2010, 2:37am » |
Quote 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:
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:
Posts: 123
|
|
Re: Measure stereotyped openings
« Reply #44 on: Jul 4th, 2010, 9:40am » |
Quote Modify
|
I think I've tried that one a few times too
|
|
IP Logged |
|
|
|
|
Home
Help
Search
Members
Login
Register
Reply
Notify of replies
Send Topic
Print