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Initial Piece Values


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#1 The Prof

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Posted 07 May 2015 - 03:40 AM

The goal of this thread is to quantify how much each piece is worth at the beginning of the game.  For example, suppose your opponent offered to play with one less major if you gave up a captain, lieutenant, and scout?  Would you take the deal?  Would you rather give up the major?  Perhaps you feel it is about equal.  If so, we could make the following equation (using the 10 to 2 numbering system).

 

 7 = 6, 5, 2

 

In order to realistically determine equivalences for each rank, suppose that you have to propose the equivalence and then your opponent gets to decide which end of the deal he wants.   This is similar to the classic method used to divide a piece of cake fairly:  One person cuts it in half, and the other gets to choose which half he wants.  If I say 8 = 7, 4 my opponent will surely give up the major and sergeant for the colonel advantage, for I have undervalued my colonel.  If I say 8 = 7, 7, 6, my opponent will want to give up his colonel in exchange for two majors and a captain, and I have valued my colonel too high.  The idea is to try to come up with a satisfying equilibrium for each piece.  Here’s my attempt at this:

 

10 = 9, 7

9 = 8, 7, 4

8 = 7, 6, 4

7 = 6, 6

6 = 5, 5

5 = 4, 4

4 = 3

3 = 2, 2

S = 7

B = 5, 2

 

We could also look at equivalences of more than one piece.  For example, the following would take into account that a general is worth more if both marshals are gone:

 

10, 9 = 10, 8, 8, 5

 

I’m interested to see other people’s piece valuations, so go ahead and propose your own.  I'm hoping this also may generate discussion of what strategies would be optimal for the player with the advantage of having the high piece, and for the player with the advantage in lower pieces.  You can also be creative and think of other combinations to value, like what would all 8 scouts be worth?  


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#2 Midnightguy

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Posted 07 May 2015 - 04:58 AM

Very interesting topic The Prof.

 

You forgot to also make mention what is value of a piece to attacking to known unit to see what is behind it?  Is it worth Colonel taking a Major early in game to see the Marshal or General vs Captain taking a Lieutenant? 

 

Typically any unit I say Major or higher you want to at least capture one rank lower plus another unit (Hopefully not a scout!) to make it worthwhile trade. Such as Major takes a Captain and Lieutenant before he is captured or runs into a bomb.   If you can't capture one rank lower, then you need to at least capture three units no lower than 3 of that unit to make it worthwhile.  Such as Colonel captures say two captains and a Lieutenant.  

 

Sorry I'm a stickler for American units....

 

1 = 2, x      or   1 = 3, 4, 4

2 = 3, x      or   2 = 4, 5, 5

3 = 4, x      or   3 = 5, 6, 6

4 = 5, x      or   4 = 6, 7, 7

 

S = 5

B = 6 or greater

 

Anything Captain or lower if you can take our more than one unit, that is a plus.  

 

Lieutenants or lower are good units to explore for bombs and taking our pesky scouts early.  Captain or lower worthwhile to give up to take out Spy.  

 

Just a thought, though nothing is absolute in Statego.  



#3 Kernel Mustard

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Posted 07 May 2015 - 05:29 AM

Perhaps you could attempt to assign point values to each piece.

 

For example, if 1 major = 2 captains,

 

Than major may be worth 20 points, vs the 10 point captain.

 

 

MG, my guess is that The Prof was intentionally leaving out the "value of information" in these comparisons because it complicates things, although you're right, practically speaking that's something to think about. 



#4 Cannan

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Posted 07 May 2015 - 07:07 AM

For me:

B = 6

S = 6, 2

3 = 2, 2

4 = 3, 2

5 = 4, 2

6 = 5, 4

7 = 6, 5

8 = 6, 6, 6 or 7, 6, 2

9 = 8, 6, 4, 2 if Marshall is known

10 = 9, 7


I was surprised when playing a game to find the opponent's flag in the front row. I would think guarded by bombs in the back row would make more sense.


#5 Napoleon 1er

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Posted 07 May 2015 - 08:30 AM

The only one i can fully agree with i 4=3. For the others i would almost never sacrify 3 lower pieces to get 1 strong. But the whole thing depends a lot on what is your initial situation. Do you have material or info advantage or not? If yes then you are more comfortable to sacrify 2 lower pieces to get 1 stronger. If you don't have material or info advantage is better not. The you have also the case 8=7+info or 7=6+info. If you sacrify a major to get a captain + info on where is the gen the deal is good, and even better if you get the info that the protecting piece was a bluff.
other point to watch is when a level is out all equations shall be revised accordingly. For example if there are no more captains then the equation 6=5+2 becomes 7=5+2 so the higher levels lose power when the game moves forward.
Also the miners get increased power when the proportion of bombs among the remaining pieces becomes substantial (let'say >50%). So the equation 4=3 becomes 5=3 or 6=3 over time.
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#6 The Prof

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Posted 07 May 2015 - 04:57 PM

Thank you all for the responses, but just to clarify, this thread is about the value of a piece at the beginning of the game.  No information can be assumed and no pieces other than those in the equation are lost.  Clearly the values of the pieces changes as the game evolves, so that's why I wanted to control for that variable.  Regarding why it could be an advantage to give up three pieces for one, the player may be able to use his higher piece to capture one or more of those three pieces before the player with more pieces can trade down.  For example, if I trade an 8, 7 and 4 for a 9 before the game starts, then I may be able to use my 9 and 10 to kill some mid to high level pieces of my opponent.



#7 Cannan

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Posted 07 May 2015 - 05:00 PM

That's what I assumed The Prof.

I put in my post what I felt I could win with at the end.

Such as if he had a Sergeant and I had a Miner and Scout, that would be a easy, easy win for me.


I was surprised when playing a game to find the opponent's flag in the front row. I would think guarded by bombs in the back row would make more sense.


#8 Napoleon 1er

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Posted 07 May 2015 - 07:19 PM

...not sure to understand what means "trading a col a major and a sergeant for a gen before the game starts"? ... I understood the question was: is it worth sacrifying a col a major and a sergeant, once you know where your opponent gen is, if your are sure with 100% certainty to then be able to capture this gen with your marsh ... and thus revealing your marsh?

 

on the other side if the goal is only to identify the value of a piece before any capture has been made and before any info is known then i would say that only the front 6 pieces are worth something .... or did I miss something in the question? ... pieces acquire their power only when they are in certain positions. For example a major in diagonal of a captain is worth less than a major "next" to a captain or in direct alignment with him. Also a sergeant sealed behind bombs is worth nothing until a miner would unseal that sergeant, or a major on the right side of the game is worth nothing against a captain on the left side.

 

...or is the question: what would your prefer between starting a game with 39 pieces but no gen or starting a game with 37 pieces but 1 col 1 major and 1 sergeant less?


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#9 The Prof

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Posted 07 May 2015 - 09:40 PM

...or is the question: what would your prefer between starting a game with 39 pieces but no gen or starting a game with 37 pieces but 1 col 1 major and 1 sergeant less?

 

Yes, that's was what I was getting at.  I know it is an abstract question but I think it can be used as a building block in answering more realistic game-related questions.  After figuring out the relative worth of the pieces before the game starts, then we could proceed to work out what pieces you would trade (before the game started) for simply the knowledge of the location of an opponent's piece.  For example, what would you give up to know the location of a enemy general or enemy marshal?  Then you could put all this information together to reason whether it is wise, for example, to take a captain with a colonel if the protecting piece has say a 1/3 probability of being a general, 1/6 probability of marshal, and 1/2 colonel or bluff. 



#10 Midnightguy

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Posted 07 May 2015 - 09:44 PM

Well if we also compare to the game of chess these are the values most players use:

 

Queen = 9

Rook = 5

Bishop = 3

Knight  = 3

Pawn = 1

 

Some players may still believe Queen more powerful than two rooks so they value it a 10 or a player may value a bishop or knight slightly higher than the other pending on their preference towards that unit or what point of the game it is.  The value of the pawn increases when its on 6th or 7th row near the end game and especially if the pawn forces the opponent's King or another chess unit must prevent that Pawn from Queening. 

 

The same could be said for Statego units.  Some players might be more willing to give up that Marshal for a General if he can assure he already captured or can capture another unit or two.  While other players would think of giving up a Marshal for a General (assuming he is guarded by Spy)    Also what point of the game is it like Napoleon suggested also plays a key factor.  

 

Another factor the value of unit changes in other factors such as for example a General is being used to stop a Colonel from captured a Major that is trapped.  The value of the General drops especially if your opponents general is still on the prowl.  

 

My first post was just a suggested value chart for early in a game.


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#11 Enigma

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Posted 08 May 2015 - 12:52 AM

The goal of this thread is to quantify how much each piece is worth at the beginning of the game.  

 

If you're going to do this (and I'm not sure you can), it might be useful to imagine a common end-game scenario that would result in a draw and then work backwards to figure out how you would get there from the beginning with the given piece combinations.  



#12 GaryLShelton

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Posted 08 May 2015 - 02:46 AM

Hey, I know The Prof is going to hate me for making the comparison, but I can't help myself. :)

This subject seems so scarily close to the old superdrew topic of piece values.

You can find that old topic at the following link and read for yourself....

http://forum.strateg...=3354#entry3354
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The complete GS&F Rules can be found here: http://forum.strateg...rum-rules-2016/

Draw Refusal Rules, specifically, can be read here: http://forum.strateg...604#entry339604





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