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        Arimaa >> General Discussion >> Opening theory
        
(Message started by: mouse on Jan 18^th, 2005, 5:46am)

Title: Opening theory
Post by mouse on Jan 18^th, 2005, 5:46am

I think that there has not been very much debate on opening theory in Arimaa. A big part of the reason is of course the initial setup is not fixed. But the opening still seems to have some significant importance, since there seems to be a (at least partly) consensus that there is a advantage in playing gold, so silver will have to equalise during the game.

There seems to be some general guidelines according to which most players setup there pieces.

The classical setup:
All rabbits on the back row and camel + elephant in the centre. This opening seems to have lost its appeal in high level games and are being phased out.

The 2 dogs on back row or 99of9 setup:
The classical setup seem to have been almost completely replaced by 2 medium strength pieces on the back row. Usually 2 dogs but also often 2 cats and elephant + camel in the centre.

Experimental setup:
Expect for the 2 mention setup there has been a large variation of setups. One of the more prominent is the 4 double rabbits Fritzlein has used (but apparently not in any top games).

Given the first objective for silver is to equalise golds first mover advantage the first change is to make the best possible response to golds setup. Here I would like to ask opinions on the optimal response for silver in the case with 2 dogs on the back row:

What is the best response to a balanced setup by gold:
1) a balanced setup
2) a setup with the camel on one wing and should it be the same wing as silvers elephant

What is the best response to a unbalanced setup by gold with one horse on the same wing as the elephant and a camel on the other wing?

What is the best response to a unbalanced setup by gold with camel on the same wing as the elephant and a horse on the other wing?

What is the best response to a setup with elephant + camel + horse on the same wing?

For the moment I almost always use a balanced setup, but I doubt this is always the best response as silver.

Title: Re: Opening theory
Post by 99of9 on Jan 18^th, 2005, 9:10am

For the sake of any beginners reading this, I'd like to clarify some of mouse's descriptions.

Gold Classic Setup:

DHCMECHD RRRRRRRR
(or switch the E with the M, but symmetry makes this equivalent)

There is good reason why the Hs are positioned as they are. The Cs behind the traps is so that if they get killed you lose less than if it were Ds behind, but I imagine there might be other advantages from switching the Ds<-->Cs.

Silver Classic Response to Gold Classic:
rrrrrrrr dhcemchd
(the most important thing here is that the e is not opposite the E - that is a typical mistake a beginner makes)

99of9 Setup
RHCMECHR RRRDDRRR

The motivation here was to make me less vulnerable to R dragging - especially the back-central Rs. Of course it makes the wing rabbits a little more vulnerable, but I think not so much as the central ones were in the classic. I also like having extra wing rabbits, because they are usually the ones that win the game.

Others have tried switching the Cs for the Ds here. I'm not sure I ever have - I don't like it. I think they'd be better called by someone else's name :-).

The unbalanced setups mouse is talking about are when you switch an H with the M.

Regarding your questions mouse, I plan to answer them after all my postal games have started. I've done some thinking ;-).

Title: Re: Opening theory
Post by mouse on Jan 18^th, 2005, 9:22am

Tanks for the clarification I will put the rest of the notation in the following.

What is the best response to a balanced setup by gold:
1) a balanced setup
rhcmechr
rrrddrrr
2) a setup with the camel on one wing and should it be the same wing as silvers elephant
rhcehcmr
rrrddrrr
or
rmcehchr
rrrddrrr

What is the best response to a unbalanced setup by gold with one horse on the same wing as the elephant and a camel on the other wing?
RMCHECHR
RRRDDRRR

What is the best response to a unbalanced setup by gold with camel on the same wing as the elephant and a horse on the other wing?
RHCHECMR
RRRDDRRR

What is the best response to a setup with elephant + camel + horse on the same wing?
RCCHEHMR
RRRDDRRR
OR
RHCCEHMR
RRRDDRRR

For the moment I almost always use a balanced setup, but I doubt this is always the best response as silver.

Title: Re: Opening theory
Post by Fritzlein on Jan 18^th, 2005, 10:35am

Actually, I did play four rabbits forward in one top-level game, namely the first game of the 2005 World Championship final! I thought it might take Belbo off guard. The idea is that Silver can respond to "elephant forward 4" with "elephant forward 4", because it will immeidately lose only a rabbit and immediately win back whatever Gold has behind the trap. Although I played the setup with Gold too, I mostly think of it as an attempt by Silver to go on the attack as early as possible against an aggressive Gold player. Unfortunately, however, it turns out mostly to be a tactical trick for use against bots, because humans, given enough time to think about it, will defend their own traps first and later calmly exploit the vulnerability of my trap-defending rabbits. Still, if 99of9 gets the symmetrical back central dogs named after him, then unsound as it is, this should be named the Fritzlein opening setup:

RHREMRHR
RDRCCRDR

Title: Re: Opening theory
Post by 99of9 on Jan 18^th, 2005, 10:53am

Ahhh, now that I look at the Fritzlein setup with some explanation, I can suggest what I think is an improvement which keeps the bot-trap tenable:

CHREMRHC RRRDDRRR

Or did you really want those rabbits on the wings too? (NB, switching the cats for dogs was optional - I think this way around might be slightly better)

Title: Re: Opening theory
Post by mouse on Jan 18^th, 2005, 1:34pm

on 01/18/05 at 10:35:47, Fritzlein wrote:

then unsound as it is, this should be named the Fritzlein opening setup:

RHREMRHR
RDRCCRDR

I think there is a big difference between unsound and experimental. The last thing just means it is still a uncommon setup. Which also was the case with 2 dogs on the back row in the beginning.

Title: Re: Opening theory
Post by Fritzlein on Jan 18^th, 2005, 1:43pm

on 01/18/05 at 10:53:47, 99of9 wrote:

CHREMRHC
RRRDDRRR

Or did you really want those rabbits on the wings too?

It's an interesting idea, probably just as good and I think both Omar and naveed have already tried it, but without the rabbits on the wings, you don't have "Fritz rabbits" (TM). ;-) One reason I like a rabbit better than a cat on the flanks is that I would rather have my rabbit pulled than my cat pulled if I am going to play hyper-aggressive. Taking over opposing traps is helped along by advanced rabbits, so if that's the way I'm going to play, I want my rabbits forward and my cats and dogs back.

It gets back to a question someone posed earlier: To support an elephant-horse attack is it best to have a rabbit, several rabbits, a small piece, some combination, or nothing at all? If it turns out that the elephant/horse attack could be usefully supported by a cat, I'd put the cat forward instead of the rabbit.

Title: Re: Opening theory
Post by Fritzlein on Feb 5^th, 2005, 8:03pm

The postal tournament can provide us some statistics on the opening theory as it stood in late January of 2005. Of course I had to lump things into broad categories to do statistics, but it still gives us some idea. Of the 160 opening setups:

126 had six rabbits back
- 89 of these had the forward rabbits on the flanks
- 37 of these had the forward rabbits behind the traps
23 had all eight rabbits on the back rank
9 had seven rabbits back
- 4 of these had the forward rabbit on a flank
- 5 of these had the forward rabbit behind a trap
2 had four rabbits back

To judge our penchant for symmetry, I considered the elephant and camel to be identical. If the two sides of the midline were mirror images, I called it a symmetrical setup. If the two halves had equal forces but not in mirror image I called it a balanced setup. If the two halves didn't have equal forces (e.g. both horses on one side, or camel and elephant on the same side) I called it an unbalanced setup. Of the 160 opening setups:

91 were symmetrical
36 were balanced
33 were unbalanced

I also tried to categorize the opening moves, but it quickly gets hard to define irregular openings. Of the 80 first moves by Gold:

55 moved the elephant up 4 steps
9 moved the elephant up 3 steps and over 1
5 moved the elephant up 3 steps and another piece up 1
3 moved the elephant up 2 steps and two pieces up 1
3 moved each of four pieces up one step
5 were in categories of two or fewer occurances

Beyond the first move it totally gets out of control in trying to make categories. I'm not sure opening theory in Arimaa will ever resemble opening theory in chess.

Title: Re: Opening theory
Post by mouse on Feb 6^th, 2005, 5:39am

I think the opening in Arimaa is far more complex than the opening game in chess. Hence it is unlikely that we will ever see opening theory covering the first 20 moves as is the case for some chess openings.

But I think there is some scope for exploring what will be silvers best reply to golds initial setup and first move. That would limit the opening in an Arimaa game to 2 moves (at least for the moment).

I find your statistic of the setup very interesting. I just have a couple of questions for clarification. What is the reaction of the silver player to the different setup by gold. So if gold have a symmetrical setup how will the silver player make the initial setup. And the same statistic for the other categories.

Title: Re: Opening theory
Post by Fritzlein on Feb 6^th, 2005, 8:13am

I didn't try to track the corresondence between Silver's opening and Gold's, but offhand I didn't notice any relation at all. Maybe it would be best if people who did adjust their silver setups on the basis of the gold setup would expain what they changed and why. My only adjustment was to not put my silver elephant directly across from the gold elephant.

By the way, there were also about three setups that didn't have the elephant in the center, maybe all by jdb. I didn't track having the elephant centeral because I thought it would be 160 of 160, and only afterwards realized that that is another important area of experimentation.

Title: Re: Opening theory
Post by mouse on Feb 19^th, 2005, 5:52am

In three (3,7 and 8) of the challenge games Belbo used a initial setup with:

RHMEDDHR
RRRCCRRR

He won all of these games - and it was the 3 wins in fewest moves. So the results off the games were a big success for Belbo.

But was the fast wins because of the initial setup or despite the initial setup?

In my opinion the setup work alright in the 3. and 7. game. Because Belbo got a Elephant Horse attack on the diagonal trap and the camel were well placed for the rest of the game. But in the last game he got a Elephant Horse attack on the wing with the camel (west wing). So after move 5w I thought the position was a bit awkward for Belbo with his camel stuck behind the south west trap.

Obviously from the result Bomb didn't take advantage of this and it ended in a safe win. But still I have some doubt about the setup which I think actually put Belbo in a bit of a disadvantage. What do other people think about this setup?