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        Arimaa >> General Discussion >> Material exchanges/control questions
        
(Message started by: JimmSlimm on May 3^rd, 2011, 9:52am)

Title: Material exchanges/control questions
Post by JimmSlimm on May 3^rd, 2011, 9:52am

I am trying to figure out the importance of different units, this is both for a material evaluator used in my bot, and for myself trying to learn.

I wasn't sure wether to post in bot development or here in general discussion.

1. How many rabbits would you give up for killing opponent elephant? 5? 6? 7!?

2. When luring bots into killing one of my animals for the purpose of "freezing" its elephant, is it worth to sacrifice the camel? If no, horse?
2b. If the bot is very very good except the weakness that it falls for this trick, is it still worth to sacrifice the camel to "freeze" the bots elephant?

3. Is it worth to sacrifice a camel if you kill:
2 enemy dogs?
1 enemy horse+cat?
1 enemy horse+dog?

4. How many rabbits is a enemy cat or dog worth?

Any answer is appreciated, thanks!

Title: Re: Material exchanges/control questions
Post by rbarreira on May 3^rd, 2011, 9:58am

Have you seen this page?

http://arimaa.janzert.com/eval.html

It automatically calculates some existing material evaluation functions, and if you click each function it links you to an explanation of how it's calculated.

Title: Re: Material exchanges/control questions
Post by robinz on May 3^rd, 2011, 10:08am

I am far too weak to attempt to give answers to your questions, but from my time on the Arimaa forum it seems clear that even the experts don't agree on the answers to these questions! Or more likely, the only accurate answer is the catch-all "it depends on the position". (For a start, material imbalances involving trading one strong piece for 2 or more weaker pieces depend heavily on what other material is left. After all, a cat is exactly as good as a camel if your opponent has nothing left except for his elephant and some rabbits!)

PS: I forgot to thank rbarreira for providing the link (and Janzert for making the page) - I've not come across it before. (And, while I may be weak, I'm very interested by theoretical questions like these.) Lots of interesting-looking material there! :D

Title: Re: Material exchanges/control questions
Post by rbarreira on May 3^rd, 2011, 10:23am

I would add that while interesting, the first question is very unlikely to matter when playing a game :)

The best evaluators seem to be happy to throw away 7 rabbits for the elephant though.

Title: Re: Material exchanges/control questions
Post by JimmSlimm on May 3^rd, 2011, 10:27am

on 05/03/11 at 09:58:38, rbarreira wrote:

Thanks! It seems like some evaluators even thinks its ok to throw away all rabbits for a elephant, when in reality, it has lost the game if that happens

Title: Re: Material exchanges/control questions
Post by rbarreira on May 3^rd, 2011, 10:30am

on 05/03/11 at 10:27:37, JimmSlimm wrote:

Thanks! It seems like some evaluators even thinks its ok to throw away all rabbits for a elephant, when in reality, it has lost the game if that happens

In my opinion the game terminating conditions like goals and having no rabbits should be handled separately from the material evaluation, and that's probably the reason why some evaluators don't handle it either.

Title: Re: Material exchanges/control questions
Post by Fritzlein on May 3^rd, 2011, 10:48am

We have almost no experience with positions in which one side has an elephant and the other side doesn't. We don't have a good basis for building anything into our material evaluators about the value of the elephant. Even for material evaluators that work reasonably well in "normal" situations, there is scant reason to trust them about the value of the elephant.

The value of an elephant blockade depends on whether it can be broken, and if so at what cost. If it can be easily broken, it isn't worth sacrificing a rabbit for. If it can't be broken, it can be worth more than a horse. I've never seen a situation where it was worth sacrificing a camel to get an elephant blockade.

I think of a dog as worth two rabbits as the first trade, and a cat as worth about a rabbit and a half. That, however, is controversial, as is everything else we are discussing here. IdahoEv showed us statistics that when there was an initial cat-for-rabbit trade, the side that gave up a cat won significantly more often than the side that gave up the rabbit. Thus, even though all bots and all humans except IdahoEv prefer a cat to a rabbit as a first trade, the statistical evidence is that the rabbit is worth more than the cat!

Title: Re: Material exchanges/control questions
Post by Swynndla on May 7^th, 2011, 3:21am

Fritzlein, in another older post, you said (something like) as material is exchanged, the camel hostage is worth less, and Bomb could be tricked into over-valuing the camel hostage towards the end of the game, and so a human player could thus get an advantage. Or perhaps you didn't say as material was exchanged ... but can you explain why the camel hostage is worth less and less towards the end of the game? I don't doubt you, I'm just trying to understand. You were saying that if a camel hostage is worth a dog towards the beginning of the game, it will be worth less than the dog towards the end of the game. Oh, you were probably meaning that the value of a dog increases after material has been exchanged, and so you would no longer give up a dog to take a camel hostage (but Bomb still would)? Or perhaps you were saying that Bomb would go after the camel trying to take it as hostage, when it should have been thinking more about goal threats? Thanks in advance! (And I hope I'm posting this in the appropriate thread.)

Title: Re: Material exchanges/control questions
Post by Fritzlein on May 7^th, 2011, 11:03am

The main reason exchanges make a camel hostage less valuable is that exchanges make the camel itself less valuable. Are you clear on why the camel itself is less valuable after material has been exchanged?

There are two basic ways to play after giving up a camel hostage: swarming the hostage trap and giving up the camel with a well-timed elephant departure. The swarming strategy is harder on an emptier board, but the elephant departure is much, much easier.

If the defending elephant leaves in order to capture material, it doesn't need to get as much material to compensate losing the camel. But more importantly, on an emptier board the elephant has more opportunity to leave in a way that creates a goal threat. If the threat is strong enough, the hostage-holder might not even be able to take the camel immediately. If the defending elephant has a couple of turns to make mischief before his camel is lost, it is all the easier to get sufficient compensation for the lost camel. Of course, the hostage-holding player will realize what is going on and try to play cautiously so that a departing elephant can't do as much immediate damage, but simply being constrained to play more cautiously in this way makes the camel hostage less valuable.

Bomb would do things like give up a rabbit to avoid giving up his camel hostage when the rabbit was far more valuable, or be happy to "win" a camel for two dogs when the two dogs were more valuable, etc. But if I remember correctly, the errors don't start to get noticeable until five or so pieces have been traded, i.e. most games are decided by then anyway.

Title: Re: Material exchanges/control questions
Post by Swynndla on May 7^th, 2011, 4:16pm

Thank you for the very clear explanation Fritzlein - I tend to find this sort of thing a bit confusing.

Playing around with the Arimaa Material Evaluation Scores, I see that camel vs two dogs is better at the start of the game, but not after lots of material has been exchanged:
EMHHCCRRRRRRRR > EHHDDCCRRRRRRRR
but:
EMRRRRRRRR < EDDRRRRRRRR
which surprises me at first, and at second ... after having a think I can see how the camel would tie down one dog, and the other would hopefully be free to do damage and cause goal threats, but I'd still be telling myself "you fool, you're losing!". I guess Bomb tells itself that too, as it thinks both are winning for the side holding the camel. I think I need to play a few M vs dd games to silence my inner voice.

Title: Re: Material exchanges/control questions
Post by 99of9 on May 8^th, 2011, 12:38am

Does it feel better if instead of this:
EMRRRRRRRR < EDDRRRRRRRR
I call it this:
EDRRRRRRRR < ECCRRRRRRRR

Title: Re: Material exchanges/control questions
Post by UruramTururam on May 8^th, 2011, 2:33am

on 05/08/11 at 00:38:31, 99of9 wrote:

Does it feel better if instead of this:
EMRRRRRRRR < EDDRRRRRRRR
I call it this:
EDRRRRRRRR < ECCRRRRRRRR

You may even call it
HDRRRRRRRR < HCCRRRRRRRR
;D

Title: Re: Material exchanges/control questions
Post by Swynndla on May 8^th, 2011, 5:01am

on 05/08/11 at 00:38:31, 99of9 wrote:

Does it feel better if instead of this:
EMRRRRRRRR < EDDRRRRRRRR
I call it this:
EDRRRRRRRR < ECCRRRRRRRR

Good point, the 2nd one is logically the same strength, even though it seems so much more comfortable.
So:
ERRRRRRRR < CCRRRRRRRR
... sac'ing my phant for two cats is sometimes the right thing.

In chess, if you're up in material, exchanges are a good idea, but in arimaa, it looks like if you're up in the number of pieces (not necessarily strength), exchanges are a good idea.

Title: Re: Material exchanges/control questions
Post by UruramTururam on May 8^th, 2011, 9:31am

This leads me to think about the situation I had in one of my on-board games recently. All the pieces were on the board. I had a nice positional advantage, and then I had an opportunity to convert it into material one. I could catch a dog or a camel first both of which were leading to almost-forced sequences of moves. The first option ended in getting MHD for MH. The second one to MH for HD both with no significant positional advantage. Which one of the above would you value more?

During the game I decided to exchange MH and get an additional dog.

Title: Re: Material exchanges/control questions
Post by Fritzlein on May 8^th, 2011, 10:54am

on 05/08/11 at 09:31:43, UruramTururam wrote:

The first option ended in getting MHD for MH. The second one to MH for HD both with no significant positional advantage. Which one of the above would you value more?

I would prefer MH for HD, leaving myself with the deputy, which makes it very easy to play for control, but I can see how racing players would prefer the extra dog with a couple of pieces gone.

Title: Re: Material exchanges/control questions
Post by rbarreira on May 8^th, 2011, 1:30pm

I saw a strange behavior by FAME:

Gold has lost MHH, silver has lost DCC. At this point, silver doesn't differ between losing the M or a D.

Both DAPE and HarLog prefer to lose the D.

edit - oh, now I can see this was already discussed:

http://arimaa.com/arimaa/forum/cgi/YaBB.cgi?board=devTalk;action=display;num=1062013358;start=45#45

Title: Re: Material exchanges/control questions
Post by Fritzlein on May 8^th, 2011, 1:43pm

on 05/08/11 at 13:30:16, rbarreira wrote:

I saw a strange behavior by FAME

FAME is obsolete; I'm surprised it is still be used by top-level bots. ;)

Title: Re: Material exchanges/control questions
Post by rbarreira on May 8^th, 2011, 1:54pm

on 05/08/11 at 13:43:00, Fritzlein wrote:

FAME is obsolete; I'm surprised it is still be used by top-level bots. ;)

I think cases like the above are quite rare... I often play around with Janzert's evaluation page while I'm watching games and I've never seen this problem (or any other big problem with it to tell the truth).