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        Arimaa >> General Discussion >> Three-for-one trades
        
(Message started by: aaaa on Aug 30^th, 2008, 7:35am)

Title: Three-for-one trades
Post by aaaa on Aug 30^th, 2008, 7:35am

The Arimaa Wikibook mentions the concept of three-for-one trades. Can anyone give a situation where the evaluation of any such trade is relevant?

Title: Re: Three-for-one trades
Post by omar on Aug 30^th, 2008, 9:23am

Can you give a link to the page.

Title: Re: Three-for-one trades
Post by aaaa on Aug 30^th, 2008, 11:04am

Here you go: http://en.wikibooks.org/wiki/Arimaa/Relative_Value_of_Pieces

Anyway, I think I can answer my own question; it's not that hard to imagine the situation where in response to a capture by, say, Gold, Silver can make a move that guarantees a capture on his or her next move, giving Gold enough time to make two further captures. In this case, it would thus be possible for Gold to have the option of a three-for-one trade ("in gote (http://senseis.xmp.net/?Gote)"), while still not being in the position to capture a lesser amount of pieces for free.

Still, it's interesting to find out whether there ever was a moment in a real game where a consideration of a three-for-one trade would have been relevant to the situation.

Title: Re: Three-for-one trades
Post by chessandgo on Aug 30^th, 2008, 11:11am

I seem to recall a game with megamau in last year's WC where he had DCR for M, or could get it (M should be better usually, but such kind of trade is interesting). I also recall playing with Karl with a H for RRR trade (no idea what this kind of exchange is worth in general). There should be many many more situations, I hope others will recall more such trades.

Title: Re: Three-for-one trades
Post by chessandgo on Aug 30^th, 2008, 11:15am

on 08/30/08 at 11:04:37, aaaa wrote:

Still, it's interesting to find out whether there ever was a moment in a real game where a consideration of a three-for-one trade would have been relevant to the situation.

When there has been a 2 vs 1 trade (say H vs cd for instance) and there is an opportunity for another 2 vs 1 trade (say, M vs hr), this gives a 3 vs 1 question.

Title: Re: Three-for-one trades
Post by aaaa on Aug 30^th, 2008, 11:44am

on 08/30/08 at 11:15:52, chessandgo wrote:

When there has been a 2 vs 1 trade (say H vs cd for instance) and there is an opportunity for another 2 vs 1 trade (say, M vs hr), this gives a 3 vs 1 question.

Unless the whole sequence is forced in some way after the first trade, then the consideration is just of the second trade (with respect to the situation that has arrived after the first) and I wouldn't call this a three-for-one trade.

Title: Re: Three-for-one trades
Post by Fritzlein on Aug 30^th, 2008, 1:26pm

on 08/30/08 at 07:35:45, aaaa wrote:

The Arimaa Wikibook mentions the concept of three-for-one trades. Can anyone give a situation where the evaluation of any such trade is relevant?

Are you asking this question with respect to your material evaluation function? If so, the evaluation of a given material difference is very relevant, even if direct three-for-one-trades rarely happen. It might be that winning M for hc is a favorable trade, and winning H for dr is a favorable trade, but the net of M for dcr is merely equal when a pair of horses is off. You could dismiss the question of whether M for dcr (with a pair of horses off) is a good trade on the grounds that no one ever has the opportunity to directly engineer such a trade, but it is not at all far-fetched that you would need to evaluate the result of a series of trades.

I guess it all depends on what the point of your original post was.

Title: Re: Three-for-one trades
Post by aaaa on Aug 30^th, 2008, 2:38pm

It's true that having absolute evaluation scores for every material imbalance that can exist immediately allows one to assess the soundness of trades (taking only material into account), especially since they depend on what's currently on the board.
However, although that's how bots do it, I don't think that's the way humans think. I think it's rather the case that we have some ideas of what certain particular initial trades are worth and take that as baseline values, which are subject to further, heuristically determined modifications as pieces come off the board. We don't store in our heads that MH for hdcr is about equal, but we rather derive it, amongst others, from the fact that the side with the larger amount of pieces is benefited by equal trades.
So, for that reason, I think it would prove to be very interesting to see real examples of where the opportunity of rare, but still "atomic" trades, could have come up, as they would be quite a tax on one's insight into material evaluation.

Title: Re: Three-for-one trades
Post by mistre on Aug 31^st, 2008, 5:22am

In my postal tournament game vs Adanac - I decided to give up my M for hostage and eventual capture in exchange for H-R-R.