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Topic: average captures (Read 2814 times) |
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knarl
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Arimaa player #1648
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average captures
« on: Jul 12th, 2006, 8:26pm » |
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Gday everyone,
I was just wondering what the average number of captures for a game is? It's probably been discussed already, but I didn't look through past posts because I had another request anyway...
I'd really appreciate it if one or two knowledgable players might look at my game 34660 and add some comments. I played as silver and ended up winning by goal with only one rabbit capture total. I'm sure there's a point when I could have easily put more pressure on the bot, but where?
Cheers,
knarl.
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knarl
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Arimaa player #1648
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Re: average captures
« Reply #1 on: Jul 12th, 2006, 9:43pm » |
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thanks for the comments jbd, I replied to them.
knarl.
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Fritzlein
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Arimaa player #706
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Re: average captures
« Reply #2 on: Jul 12th, 2006, 9:48pm » |
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I once calculated from the game archive that an average game of Arimaa has 8 captures. I forget how I did it, and what my methodology was. I may try to do it again, limiting my set of games to rated human vs. human encounters.
I also calculated from the database that 3% of Arimaa steps are captures. I wanted to compare the capture density to that of chess, but I couldn't find via Google search what percentage of chess moves are captures. Today, just by coincidence (I mean, before I read your post) I decided to calculate the density of capture in chess. Based on a sample of 60 games, I got that 19% of chess moves are captures, and that an average game of chess has 17 captures.
Now it is true that if 3% of Arimaa steps are captures, then about 12% of Arimaa moves are captures. However, I think the 3% to 19% comparison is more relevant than the 12% to 19% comparison, because most Arimaa bots use step-based search, and not many steps will cause alpha-beta cutoffs based on captures, in comparison to the percentage of chess moves that cause alpha-beta cutoffs.
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| « Last Edit: Jul 12th, 2006, 11:02pm by Fritzlein » |
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Fritzlein
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Arimaa player #706
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Re: average captures
« Reply #3 on: Jul 13th, 2006, 1:42pm » |
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I just recalculated it. In 1689 rated human vs. human games, there were an average of 7.89 captures. This includes all types of terminations. If we limit it to games ending in goal or immobilization there are 1184 games with an average of 9.06 captures. The games left out of the second calculation are 326 time losses, 176 resignations, 2 repetitions, and 1 abort.
In the Wikipedia article I'm going to stand by the 8 captures per game figure in comparing to the chess average of 17 captures per game, because the majority of chess games aren't played out to conclusion on the board, so it seems like a fairer comparison to include all Arimaa games too.
By the non-tournament rules, it's possible for a game to have 32 captures and therefore end in a draw. In games where each side is playing to win, 31 captures must be the theoretical limit. The record so far in human games is 27, twice achieved.
http://arimaa.com/arimaa/gameroom/replayFlash.cgi?gid=7371
http://arimaa.com/arimaa/gameroom/replayFlash.cgi?gid=22999
In the former game should be considered the true record-holder, because if 99of9 had been thinking about posterity, I'm sure he would have suicided his elephant on the final play to secure a record 28 captures. 
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Fritzlein
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Arimaa player #706
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Re: average captures
« Reply #4 on: Jul 13th, 2006, 2:05pm » |
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I have no idea what this proves, but here is the average number of captures per game broken down by player. Only rated games against humans and terminating in "g" or "m" are counted.
10.4 blue22
10.3 Adanac
10.3 99of9
10.2 robinson
10.2 Fritzlein
10.0 Belbo
9.8 jdb
9.4 PMertens
9.4 Ryan_Cable
8.9 omar
8.6 chessandgo
8.4 naveed
8.3 Swynndla
8.2 OLTI
8.0 seanick
I think this is a random stat with no bearing whatsoever on anything.
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seanick
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SeaNICK
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Re: average captures
« Reply #5 on: Jul 16th, 2006, 5:08am » |
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I think it shows agressiveness and/or the play strength to act on that aggressiveness. maybe agression is the wrong word. destructiveness? I don't know. but anyway ones tendency to try to kill pieces, as opposed to try to goal.
I think that makes perfect sense, because my aim is usually to try to goal (so therefore my aggressiveness is listed in last place). lately I have learned to be more agressive, especially about rabbits, since PMertens suggested the rabbit-pull exercise against bomb2005p2 which proved both challenging and very helpful. not coincidentally, I have also won a couple more human vs. human games recently.
The only factor that complicates the possible statistical significance of that number, is that it does not take into account the style and skill level of the opponent that each game was against. obviously that would have an effect on the number of captures.
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DorianGaray
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Arimaa player #1210
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Re: average captures
« Reply #7 on: Jul 16th, 2006, 9:23am » |
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on Jul 13th, 2006, 1:42pm, Fritzlein wrote:| ...By the non-tournament rules, it's possible for a game to have 32 captures and therefore end in a draw... |
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I am sorry but I don't think it should be a draw but a win by no move as it is the case when you capture all of an opponent's pieces. The first player who's turn it is and has no pieces loses by no move.
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Fritzlein
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Arimaa player #706
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Re: average captures
« Reply #8 on: Jul 16th, 2006, 9:43am » |
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on Jul 16th, 2006, 9:23am, DorianGaray wrote:
I am sorry but I don't think it should be a draw but a win by no move as it is the case when you capture all of an opponent's pieces. The first player who's turn it is and has no pieces loses by no move. |
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Well, we might have to ask Omar for clarification. He has said in the past that a player who suicides his last piece doesn't lose instantly. That player loses only on the next turn, because it isn't until next turn that that player has no move. The opponent gets one more move in the mean time. See game 22999 for example.
Meanwhile both sides running out of rabbits seems to kick in instantly. So after the first player suicides his last piece, the second player has a turn to suicide his last piece (a rabbit, or it would have been drawn before all 32 captures), and the server declares it a draw before checking on the next turn for a loss by immobilization.
Note that to me it makes more sense for a player to lose the game by immobilization as soon as soon as he loses his last piece. The next move should not be necessary. But I believe Omar has set it up differently than my intuition would expect, so I think a 32-capture draw is indeed theoretically possible according to the official rules.
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Fritzlein
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Arimaa player #706
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Re: average captures
« Reply #9 on: Jul 16th, 2006, 9:53am » |
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Thanks for the link to previous discussion, 99of9. I had totally forgotten about it. Re-reading what we said then reminds me that capture density (i.e. captures per move or captures per step) is more interesting to me than captures per game, although both are relevant.
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| « Last Edit: Jul 17th, 2006, 12:26pm by Fritzlein » |
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Fritzlein
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Arimaa player #706
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Re: average captures
« Reply #10 on: Jul 17th, 2006, 12:37pm » |
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OK, I've run the numbers for capture density. The stats include only rated HvH games, but I include time losses and resignations along with goals and immobilization. Since this is captures per 100 steps, it takes the game length out of the equation.
Note that seanick is now high on the list. I think he was low before simply due to shorter games. Given the duration of his games, they tend to be bloodier than most. Also it sort of makes sense that jdb tops the list: his style is to accept trades, even disadvantageous ones, rather than sweat it out in a positional bind.
3.50 jdb
3.21 blue22
3.16 seanick
3.15 clauchau
3.11 Adanac
3.06 Swynndla
3.05 99of9
3.03 Fritzlein
3.01 Ryan_Cable
2.98 OLTI
2.96 megamau
2.90 robinson
2.89 chessandgo
2.84 Belbo
2.84 PMertens
2.83 naveed
2.78 Paul
2.78 Arimanator
2.66 omar
2.44 kamikazeking
Still, I'm not sure what this proves. It doesn't make sense to me that defensive players like Ryan and me are in the middle of the pack. And PMertens, with his wild flooding attacks, is low in capture density. Perhaps it is because he floods to gain control? But these numbers may be mostly just random and/or unenlightening.
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chessandgo
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Arimaa player #1889
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Re: average captures
« Reply #11 on: Jul 17th, 2006, 1:23pm » |
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one might be as well surprised by Kami's last position ... maybe kamikazing one's pieces is not the best way to capture much ? 
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seanick
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SeaNICK
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Re: average captures
« Reply #12 on: Jul 18th, 2006, 12:05am » |
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I think it makes perfect sense that Fritzlein at least is closer to the middle or high end of the capture density- for being a defensive player, it sure seems like he subscribes to the "the best defense is a good offense" school of thought. Kind of like some so-called "defensive" or reactive martial arts.... use the opponents attack to deliver their own strength plus your own into a crushing counterattack. like the second game I played against him, about move 10w: http://arimaa.com/arimaa/gameroom/replayFlash.cgi?gid=31540&s=b& client=1.
that was a learning experience. and didn't strike me as all that defensive, though I realize now that itwas just reactive.
anyway. I didn't realize I was so bloody, I thought I had trouble killing pieces. or are those mostly my pieces that are getting killed?
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Fritzlein
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Arimaa player #706
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Re: average captures
« Reply #13 on: Jul 18th, 2006, 2:21pm » |
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Now that I think about it, seanick, it's not too weird that my capture density is middle of the road. I'm a defensive player, true, but I'm very capture-oriented. When I have an advantage, I don't try to use it to force goal, I use it to try to take pieces. Unlike goal-oriented people, I wait until I have accumulated a large material advantage before I try to force a win. And even when I'm behind material, it takes a lot to induce me to launch a desperation goal attack. Instead I usually try to catch up on material in any way possible. So my general reluctance to launch a goal attack ever probably drives up my capture numbers overall.
I guess the aggressive/defensive distinction is not the same as the goal/capture distinction. For example, I refer to Adanac and PMertens as aggressive players. Both are eager to take the fight to the opposing half of the board, rather than having it on their own side. But both are materialistic, compared to Robinson and Blue22. I wonder if the following categorizations are fair:
aggressive/goal: robinson, blue22
aggressive/capture: Adanac, PMertens
defensive/goal: Belbo
defensive/capture: Fritzlein, Ryan_Cable
It's a bit weird to think of a defensive player being focused on goal, since you can't threaten a goal without taking the fight to the other side of the board in some way, but I think it reasonably describes Belbo's penchant for worming through a rabbit without necessarily making a bunch of captures on the way.
Sadly, this doesn't help much to explain capture density. For that maybe other axes are more useful, along the lines of "comfortable with elephants apart" vs. "comfortable with elephants together". JDB is at the former extreme of the scale, whereas I tend to gravitate more towards the latter.
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| « Last Edit: Jul 18th, 2006, 2:32pm by Fritzlein » |
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Adanac
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Re: average captures
« Reply #14 on: Jul 19th, 2006, 8:29am » |
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on Jul 17th, 2006, 12:37pm, Fritzlein wrote:
3.50 jdb
3.21 blue22
3.16 seanick
3.15 clauchau
3.11 Adanac
3.06 Swynndla
3.05 99of9
3.03 Fritzlein
3.01 Ryan_Cable
2.98 OLTI
2.96 megamau
2.90 robinson
2.89 chessandgo
2.84 Belbo
2.84 PMertens
2.83 naveed
2.78 Paul
2.78 Arimanator
2.66 omar
2.44 kamikazeking
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Most of my HvH games have been against players in the middle of the list, but comparing top vs. bottom I've definitely played more games against the high-capture players rather than low-capture players. I'm sure that's one of several reasons that I have a higher than average score.
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