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Topic: Measure stereotyped openings (Read 16114 times) |
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Fritzlein
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Re: Measure stereotyped openings
« Reply #15 on: Apr 10th, 2008, 1:53pm » |
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on Apr 10th, 2008, 12:52pm, aaaa wrote:| Which is exactly what makes me wonder whether it's fair to compare chess and Arimaa on a per half-move basis in the first place. I think what we should look for in a game is how little relative compression is possible of a typical database of games. |
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It certainly isn't fair to chess to compare it to Arimaa, because Arimaa is a much better game.  If a high branching factor in Arimaa means that it does have more variety in practice than chess can have in theory, then it supports my hypothesis that we don't have to worry about stereotyped openings in Arimaa just because it is a problem that has bedeviled chess. Right now people may expect that the variety of openings exists in Arimaa just because it is a new game and we don't yet know how to play well, but I rather expect that the variety is intrinsic, and we can list it among Arimaa's inherent advantages over chess.
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aaaa
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Re: Measure stereotyped openings
« Reply #16 on: Apr 10th, 2008, 2:05pm » |
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As a thought experiment, imagine a chess game where one plays a move and then also gives a list of conditional moves based on every possible reply of the opponent. If we could call this a "move" instead, then the entropy per move would obviously be higher, but one would be hard-pressed to call this a fundamentally different game.
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mistre
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Re: Measure stereotyped openings
« Reply #17 on: Apr 10th, 2008, 2:42pm » |
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on Apr 10th, 2008, 1:08pm, aaaa wrote:| Go to Settings, Game Client and change the client to version 2. |
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I guess I am one of the hold-outs that still use Version 1. I have no problems with it like I used to have. While I like some of the new features of version 2, the graphics aren't up to par of version 1.
So enlighten me. Why does the default set-up not matter in Version 2?
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Fritzlein
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Re: Measure stereotyped openings
« Reply #18 on: Apr 10th, 2008, 2:47pm » |
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Since a game of Arimaa takes about as many moves as a game of chess, and we allow about the same thinking time per move, and the experience of playing a move in each game is similar, I think it is in fact illuminating to compare the two on the basis of standard moves in each game. Sure, as a thought experiment one could redefine what a chess move is. But that wouldn't change the percentage of the game that the players are in book. If it takes 26 moves of a 40-move game before the game reaches a position that is not familiar to both players, then the openings are sadly stereotyped. Redefine "move" so that it takes 13 moves of a 20-move game to see something new, and the magnitude of the problem has not changed.
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Fritzlein
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Re: Measure stereotyped openings
« Reply #19 on: Apr 10th, 2008, 2:51pm » |
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on Apr 10th, 2008, 2:05pm, aaaa wrote:| As a thought experiment, imagine a chess game where one plays a move and then also gives a list of conditional moves based on every possible reply of the opponent. If we could call this a "move" instead, then the entropy per move would obviously be higher, but one would be hard-pressed to call this a fundamentally different game. |
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The game would be so fundamentally different from chess, you would be hard pressed to get two chess players to play under these rules at all. You would have succeeded in minimizing one difference between Arimaa and chess (branching factor) by introducing a much bigger difference (committing to conditional choices)
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| « Last Edit: Apr 10th, 2008, 2:52pm by Fritzlein » |
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aaaa
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Re: Measure stereotyped openings
« Reply #20 on: Apr 10th, 2008, 3:04pm » |
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on Apr 10th, 2008, 2:42pm, mistre wrote:| So enlighten me. Why does the default set-up not matter in Version 2? |
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You have to choose the square for each major piece one by one.
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aaaa
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Re: Measure stereotyped openings
« Reply #21 on: Apr 10th, 2008, 3:55pm » |
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on Apr 10th, 2008, 2:47pm, Fritzlein wrote:| Since a game of Arimaa takes about as many moves as a game of chess, and we allow about the same thinking time per move, and the experience of playing a move in each game is similar, I think it is in fact illuminating to compare the two on the basis of standard moves in each game. Sure, as a thought experiment one could redefine what a chess move is. But that wouldn't change the percentage of the game that the players are in book. If it takes 26 moves of a 40-move game before the game reaches a position that is not familiar to both players, then the openings are sadly stereotyped. Redefine "move" so that it takes 13 moves of a 20-move game to see something new, and the magnitude of the problem has not changed. |
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But now you're no longer following your criterion of entropy per move. You had to take into account another factor, namely that the two games tend to have the same amount of moves per game. Conversely, by your criterion, Arimaa would have to be categorized as being more stereotyped in nature if we go for Omar's per-piece setup, which I doubt is your intention.
It's your "lg(20^2)" argument I take issue with, not the claim that Arimaa allows for more varied play than chess; I'm sure this will be born out if we use the aforementioned criterion of comparing the relative compression of a typical database of games. Additionally, it would also allow us to better compare Arimaa with other games that have different typical numbers of moves, like Go.
This is in fact all just a rephrasing of the discussion where a game falls in the tactical-strategic spectrum. No game can be strategic without also being tactical, which means it must have its share of obvious and nonsensical moves and Arimaa is no different in that respect.
on Apr 10th, 2008, 2:51pm, Fritzlein wrote:
The game would be so fundamentally different from chess, you would be hard pressed to get two chess players to play under these rules at all. You would have succeeded in minimizing one difference between Arimaa and chess (branching factor) by introducing a much bigger difference (committing to conditional choices) |
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I agree that there are additional complexities arising here due to the intricacies of human thought processes, but it's telling that engines would be able to perform fundamentally the same without changing any of the domain knowledge.
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Fritzlein
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Re: Measure stereotyped openings
« Reply #22 on: Apr 10th, 2008, 4:24pm » |
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on Apr 10th, 2008, 3:55pm, aaaa wrote:| Conversely, by your criterion, Arimaa would have to be categorized as being more stereotyped in nature if we go for Omar's per-piece setup, which I doubt is your intention. |
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On the contrary, I would agree that Omar's per-piece setup would make the opening more stereotyped and by extension more boring. My objection to his proposed setup procedure was that it would add playing time and rules complexity for no benefit. Breaking up one move into four moves with the same total "action" just makes the opening of the game dull; if the entropy per move turned out to be 1/4 as much as the current setup (because people don't actually use the decision opportunities to deviate, but rather end up with the 99of9 setup four moves later) that would serve to confirm that a good metric of the inherent interest of the opening is the number of moves (relative to the length of the whole game) that it takes to max out the entropy.
Yes, if chess and Arimaa didn't take about the same number of moves per game, they wouldn't be as directly comparable. I am more interested in what proportion of the game is spent "in book" than I am interested in the absolute number of moves spent in book. I take your theoretical point against entropy-per-move. I was merely confused by your two thought experiments about rule changes, both of which seemed to confirm rather than refute that Arimaa openings are not stereotyped as chess openings (and therefore more interesting in my opinion.)
The general thrust of your comments appeared to me to be that the measurements woh has made are arbitrary and meaningless. Your implication was that if you change the way you look at it, chess openings are no more stereotyped than Arimaa openings. I still disagree with that claim, if in fact it is what you were claiming. I apologize if I misinterpreted the point of your remarks.
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| « Last Edit: Apr 10th, 2008, 4:47pm by Fritzlein » |
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woh
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Re: Measure stereotyped openings
« Reply #23 on: Apr 10th, 2008, 4:57pm » |
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on Apr 10th, 2008, 12:03pm, Fritzlein wrote:| I didn't know you had implemented your own position hash function. |
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Well, I haven't. I used a standard hash function on the board position.
on Apr 10th, 2008, 12:03pm, Fritzlein wrote:| Are you sure that you counted it as a duplicate if the same setup was reached in a different order of steps? |
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I am pretty sure since board positions were used and not moves. I will double check it. But I will only have time for this after the week-end.
When the same board position is reached after some move, it is still counted as duplicate even if the board position after one of the previous moves was different.
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Fritzlein
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Re: Measure stereotyped openings
« Reply #24 on: Apr 10th, 2008, 4:59pm » |
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on Apr 10th, 2008, 12:52pm, aaaa wrote:| I think what we should look for in a game is how little relative compression is possible of a typical database of games. |
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Shannon's original definition of entropy was very much motivated by studying data compression. In fact, he proved precisely that the greater the entropy of data, the less it can be compressed. It would be ironic to object to entropy as a metric merely to embrace possible compression, since the two are exactly inversely related in theory. Fundamentally it's the same metric.
Of course, in practice data compression would be influenced by how wasteful the game notation is in the first place. Arimaa games could be much compressed by omitting the first of the four characters in every step as entirely redundant. I assume you would want to measure possible compression at a more abstract level that doesn't depend on notational efficiency.
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| « Last Edit: Apr 10th, 2008, 5:05pm by Fritzlein » |
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Fritzlein
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Re: Measure stereotyped openings
« Reply #25 on: Apr 10th, 2008, 5:01pm » |
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on Apr 10th, 2008, 4:57pm, woh wrote:| When the same board position is reached after some move, it is still counted as duplicate even if the board position after one of the previous moves was different. |
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Excellent! Sorry that I suspected the numbers were too good to be true. I'm willing to accept that there has been far more experimentation with the Gold setup than I had guesstimated. Indeed, I'm thrilled that I underestimated the actual variation.
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| « Last Edit: Apr 10th, 2008, 5:03pm by Fritzlein » |
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woh
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Re: Measure stereotyped openings
« Reply #26 on: Apr 10th, 2008, 5:18pm » |
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on Apr 10th, 2008, 12:54pm, mistre wrote:
Can you continue this list down to at least the top 10? I am curious. |
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Sure.
5. 62 times
RHRMERHR
RDRCCRDR
6. 60 times
RHCMECHR
RDRRDRRR
7. 51 times
RMCRREHR
RHDRRCDR
8. 49 times
RHDEMDHR
RRRCCRRR
9= 48 times
RMDHEDHR
RRRCCRRR
9= 48 times
DHCCEDMH
RRRRRRRR
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aaaa
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Re: Measure stereotyped openings
« Reply #27 on: Apr 10th, 2008, 5:27pm » |
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I guess what I'm trying to say here is that to me a move is just a means of branching out in the game tree and that it isn't so much the strategic freedom per move which interests me, but the overall one. So I would want to take a look at the relative entropy at each move, not the absolute one, and see how it changes with every move. What is such an indictment of chess is that the number of acceptable openings at a given ply is so little when compared to all possible moves.
If you took an arbitrary game and then start adding different moves that directly lose the game to the rules, then that would degrade it by relative, but not absolute measurement. In fact, it would actually increase if you start including random players.
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woh
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Re: Measure stereotyped openings
« Reply #28 on: Apr 10th, 2008, 5:29pm » |
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After Silver setup the most popular positions are:
1. Gold 99of9 with dogs behind the traps vs Silver 99of9 with cats behind the traps: 195 times
2. Gold 99of9 with cats behind the traps vs Silver 99of9 with dogs behind the traps: 188 times
3. Gold 99of9 with cats behind the traps vs Silver 99of9 with cats behind the traps: 178 times
4. Gold 99of9 with dogs behind the traps vs Silver 99of9 with dogs behind the traps: 143 times
5. Gold standard setup vs Silver 99of9 setup with cats behind the traps: 45 times
In all the 5 board position the silver elephant is in the same file as the gold camel.
More results later.
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| « Last Edit: Apr 10th, 2008, 5:35pm by woh » |
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Fritzlein
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Re: Measure stereotyped openings
« Reply #29 on: Apr 12th, 2008, 10:58am » |
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on Apr 10th, 2008, 5:18pm, woh wrote:5. 62 times
RHRMERHR
RDRCCRDR
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Mostly played by me?
Quote:6. 60 times
RHCMECHR
RDRRDRRR
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Mostly played by chessandgo
Quote:7. 51 times
RMCRREHR
RHDRRCDR
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Exclusively played by blue22
It goes to show that some of the entropy comes not from players experimenting, but from players disagreeing and stubbornly sticking with pet openings that others never adopt.
Quote:8. 49 times
RHDEMDHR
RRRCCRRR
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Aha, so mirror reflections are counted as distinct! I wonder how much entropy comes from that. The Gold setup is the only point at which symmetry comes into play, since the Gold elephant itself breaks symmetry thereafter. One could eliminate this one symmetry by reflecting the entire game if Gold sets up with the elephant west of the midline. But that's probably more trouble than it's worth.
Is it true that Go players, by convention rather than by rule, always play the first stone in the same corner? Maybe Arimaa players will eventually adopt the convention of always setting up the Gold elephant in the eastern half of the board.
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