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Piece value contest


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#61 Napoleon 1er

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Posted 14 November 2018 - 06:37 PM

I'm afraid you may finish at the bottom of the contest with this level of unrealistic values - but you're free to try of cours

ok so do i understand it right that if i make the exact same opposite proposal i will finish on top? :)


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#62 Wogomite

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Posted 14 November 2018 - 07:34 PM

ok so do i understand it right that if i make the exact same opposite proposal i will finish on top? :)

Napo, in the Astros series, I forgot, were you on the clowns or the other team? :)

#63 Nortrom

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Posted 14 November 2018 - 08:20 PM

Other team - the names of the tribe weren't known at the time the players were grouped together.


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#64 Wogomite

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Posted 14 November 2018 - 08:35 PM

Other team - the names of the tribe weren't known at the time the players were grouped together.

If so the players may have been grouped differently eh? :)

#65 Nortrom

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Posted 14 November 2018 - 08:40 PM

It would be impossible to both give people the team they deserve and have equal number of members per team.


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#66 Napoleon 1er

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Posted 14 November 2018 - 08:59 PM

... is it also a contest for who would propose the best relative value of each Astros series team member? :D


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#67 Wogomite

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Posted 14 November 2018 - 10:49 PM

... is it also a contest for who would propose the best relative value of each Astros series team member? :D

I'll give fairway the highest value.

#68 Wogomite

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Posted 14 November 2018 - 10:51 PM

It would be impossible to both give people the team they deserve and have equal number of members per team.

What if the names were different. You could have the clowns and the goonies. Maybe a third team called the 'minorities' with everyone else. There might not be enough people for that team though :).

#69 Nortrom

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Posted 20 November 2018 - 07:09 PM

Astros

Spoiler

 

FKS Tried to submit something, but initially did not succeed understanding the question, his entry was off due to this and will not be posted.

 

 

 

TemplateRex

Spoiler

 

Due to the seemingly low interest, I suggest we leave the topic for what it is.


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#70 TemplateRex

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Posted 20 November 2018 - 08:54 PM

For future readers, here's my explanation (as sent in to Nortrom, reformatted slightly for clarity, with minor edits in red). Comments are welcomed!

 

Basic idea: for piece of rank R, I postulate the equation:

 

[R] = [R-1]+ [R-3],

 

i.e. marshal = general + major, general = colonel + captain etc. 

 

Constraint: proportional scaling between all consecutive ranks, i.e.

 

[R+X] = [R] * (scale to the power of X).

 

This leads to a third-degree polynomial that you can solve with e.g. Wolfram Alpha. Result,

 

[R+1] = 1.46557 * [R].

 

I put the marshal equal to 100, and this fixes the column "known" for each piece.

 

Info: I postulate

 

unknown [R] = 90% * known [R+1],

 

so an unknown general is 90% of a known marshal. This also means (combined with the previous scale factor), that info on rank R is about 24.2% of that piece's base value. In terms of other piece values: info on rank R is almost identical to a known piece of rank R-3. I.e., marshal info is equal to a known major, general info to a known captain. etc.

 

For the spy, I compute its known value equal to 1.46557 times less than a known scout (a spy is a crippled scout) and I postulate that this is 10% of its unknown value, this fixes an unknown spy to 24.3, almost equal to marshal info. I.e., a known marshal + spy is almost exactly equal to an unknown marshal without the spy. The spy is worth a little more than an unknown captain

 

For bombs, I postulate that

 

info on a bomb's location = unknown lieutenant. (edit: slightly than Astros)

 

I don't bother to formulate bomb's actual value, because the info part is the most valuable (probably 90% of a bomb's value). 

 

For pieces with special ability, I value the last two pieces much higher than the earlier pieces. So IMO 

 

last two miners are worth a lieutenant and a captain (edit: Astros has last unknown miner = known colonel),

last two scouts a sergeant and a lieutenant.

last two bomb locations are worth a captain (edit: Astros has front row bomb info = known major)

 

Knowing all 6 bombs is worth as much as giving up the marshal IMO (think of the absolute feast your general could have).

 

Other notes: this problem is seriously hard!! E.g., I think I value info value slightly too low. Do you really want to hit a known major with your unknown marshal? But OTOH, putting too much value on info value, reduces the known piece of rank R compared to an unknown piece of R-1. I don't think an unknown general is more valuable than a known marshal (edit: Astros thinks unknown general is slightly more valuable than known marshal!).

 

Some simple sanity checks: hitting a known piece of rank R with an unknown piece of rank R+1 that is being recaptured with an unknown piece of rank R+2 is a losing proposition, but not by much (less than a known lieutenant for an unknown general taking a known colonel, being recaptured by the unknown marshal). This is probably still too optimistic, since having reduced a rank R+1 piece, the remaining rank R pieces should become more valuable.This dynamic re-scaling is not being taken into account here.

 

For future reference, the best way to determine these values is to load all 80,000 Gravon games, convert all the positions with > 30 pieces on the board into a spreadsheet with columns indicating the piece counts and do a regression analysis of the game outcomes with respect to the various pieces counts. This will give statistical estimates (essentially ELO values). This is the approach taken in the seminal work by GM Larry Kaufman for chess.

 

Originality: many ideas have been posted before (Ouwesok, thesis Vincent de Boer). I claim these values are original. I use the idea of proportional scaling from VdB, but with a higher scaling factor (Vdb: 1.45, here: 1.46557) and with a lower value on info (VdB: 33%, here: 24.2%). Also the idea of scaling the last two pieces for special ability pieces is not new (VdB: times (4 - nr_pieces_left), here: rank R + (4 - nr_pieces_left)).


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#71 TemplateRex

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Posted 20 November 2018 - 08:57 PM

Question to Astros: you value a front two rows bomb equal to a known major! Are you really willing to start with a front row major, have it revealed by a scout and then drill it into an unmoved piece behind it? 


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#72 tobermoryx

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Posted 20 November 2018 - 09:17 PM

I do that every game.



#73 TemplateRex

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Posted 20 November 2018 - 09:19 PM

I do that every game.

 

OK, but do you consider it a disadvantage if you hit a bomb, or are you OK with that? If you find captains and lieutenants often enough, it might still be a good move on average, but astros seems to even be OK with the worst case!


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#74 Fks

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Posted 20 November 2018 - 09:21 PM

OK, but do you consider it a disadvantage if you hit a bomb, or are you OK with that? If you find captains and lieutenants often enough, it might still be a good move on average, but astros seems to even be OK with the worst case!

Have you ever seen Astros play? :) Bombs are a disadvantage once they are known, the earlier you know one the more you can start to punish there set up.


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#75 TemplateRex

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Posted 20 November 2018 - 09:24 PM

Have you ever seen Astros play? :) Bombs are a dissadvantage once they are known, the earlier you know one the more yout can start to punish there set up.

 

I played against him once, don't recall specifically any major charges in the opening (or I might have countered them in time before he did too much damage). 

 

Anyway, I agree with you on the principle of finding bombs, but I valued them at a lieutenant, so maybe I'm too stingy!


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#76 tobermoryx

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Posted 20 November 2018 - 09:34 PM

OK, but do you consider it a disadvantage if you hit a bomb, or are you OK with that? If you find captains and lieutenants often enough, it might still be a good move on average, but astros seems to even be OK with the worst case!

 

Of course you'd rather find a front row bomb with a scout, but it's much better to find a front row captain with a major than a scout. On balance it's much more likely that a captain is front row than a bomb so yes, I am OK with it. 



#77 TemplateRex

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Posted 20 November 2018 - 09:43 PM

Of course you'd rather find a front row bomb with a scout, but it's much better to find a front row captain with a major than a scout. On balance it's much more likely that a captain is front row than a bomb so yes, I am OK with it. 

 

Yes, I agree with you that with the usual mix of captains / scouts on the front row, "on balance" it's not bad to start charging with a major from the front row. But Astros front bomb info value is such that he thinks he'll be at least equal, even if he loses the major on a bomb. This is a much stronger statement than yours, namely that the gains outweigh the losses. With Astros' piece values, there is no loss in the first place!


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#78 tobermoryx

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Posted 20 November 2018 - 09:52 PM

I think though that finding a front row bomb on the left is good info as it usually indicates that is going to be the opponents weak side, and that the marshal/general and likely colonels are all in the centre or towards right. They wouldn't likely have a front row bomb in a lane they were planning to attack from. So you would be down a major but immediately can start making a good assessment of their set up. 


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