Tactical Command
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An exercise in game theory - formation cost prediction
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Author:  semajnollissor [ Wed Oct 17, 2012 2:59 pm ]
Post subject:  An exercise in game theory - formation cost prediction
This probably won't go very far, but I have the urge to take on a mathematical challenge.

I want to develop a function to predict the appropriate point cost for a given formation.

To start with, I need to identify the variables that formation cost is a function of.

So far, I have:

Total number of units in the formation
Individual unit abilities (true units point values)
Mix of unit types (infantry/LV/AV/etc)
Army list special rules
+
individual unit size
formation initiative
formation deployment options

So, besides those, is there anything else that you can come up with?
Author:  Dave [ Wed Oct 17, 2012 3:02 pm ]
Post subject:  Re: An exercise in game theory - formation cost prediction
Strategy rating of the army and initiative of the formation.
Author:  madd0ct0r [ Wed Oct 17, 2012 4:37 pm ]
Post subject:  Re: An exercise in game theory - formation cost prediction
Going off a idea Neal explained to me:

value of a unit is the square product of it's root firepower and root resiliance - you can make a tank twice as tough but you have to make it twice as shooty as well before it becomes worth twice the points. - i developed this to include unit speed and range in the 'firepower' part (the area the unit could threaten in a normal move) and a vauge approximation of the affects of void shields, DC and some special rules in the 'resiliance' part. I can email you the spreadsheet if you want.

Something similar ought to be possible for formations.

You might also need to pick some 'classic' enemy formations to be tested against - I used orks, gaurd in cover, rhinos, leman russes and a warhound.
Author:  semajnollissor [ Wed Oct 17, 2012 5:45 pm ]
Post subject:  Re: An exercise in game theory - formation cost prediction
You are right, of course, madd0ct0r, and I will need to address 'true unit point value' when I get into it. But right now I'm looking at what else the formation cost is a function of.

I think I got the big ones so far, but I don't know what I don't know, if you know what I mean.
Author:  madd0ct0r [ Wed Oct 17, 2012 9:27 pm ]
Post subject:  Re: An exercise in game theory - formation cost prediction
sheer size is relevent when you're considering vulnerability to templates.

likewise - line capable of defending at maximum spread.

being able to garrison is worth something, as is cross defense (ie AA AT And AP in one formation is useful to have)
Author:  Ginger [ Wed Oct 17, 2012 9:53 pm ]
Post subject:  Re: An exercise in game theory - formation cost prediction
Activation impact as well. As individual formation costs increase, there is a corresponding impact on the army through the reduced activation count. Not sure how to implement this, though it is some form of inverse rule. Put another way, as formations become cheaper, their ability to 'stall' becomes more important.

And extending Madd0ct0rs point, you need to factor in all the special abilities, extra attacks, transport etc, most of which seem to have different values.

This is appealing though definitely "brave". :D
Author:  semajnollissor [ Thu Oct 18, 2012 1:01 am ]
Post subject:  Re: An exercise in game theory - formation cost prediction
madd0ct0r wrote:
sheer size is relevent when you're considering vulnerability to templates.
this is probably rolled into true unit value. but I'll add it to the list.

Quote:
likewise - line capable of defending at maximum spread.
not sure what you mean here, unless you're referring to the scout ability or WE coherency distance, but both those affect unit value, which is already listed

Quote:
being able to garrison is worth something
added
Quote:
as is cross defense (ie AA AT And AP in one formation is useful to have)
got it

Ginger wrote:
Activation impact as well. As individual formation costs increase, there is a corresponding impact on the army through the reduced activation count. Not sure how to implement this, though it is some form of inverse rule. Put another way, as formations become cheaper, their ability to 'stall' becomes more important.
so the cost of a formation is a function of the cost of the formation. That's cool, I can handle differential equations.

Quote:
And extending Madd0ct0rs point, you need to factor in all the special abilities, extra attacks, transport etc, most of which seem to have different values
its on the list
Author:  Spectrar Ghost [ Thu Oct 18, 2012 1:22 am ]
Post subject:  Re: An exercise in game theory - formation cost prediction
semajnollissor wrote:
Ginger wrote:
Activation impact as well. As individual formation costs increase, there is a corresponding impact on the army through the reduced activation count. Not sure how to implement this, though it is some form of inverse rule. Put another way, as formations become cheaper, their ability to 'stall' becomes more important.
so the cost of a formation is a function of the cost of the formation. That's cool, I can handle differential equations.


More specifically, the cost of the formation is a function of the cost of the formation with respect to army size.

I've tried to do something like this before, though I didn't tie it to points, instead to an arbitrary scale. I hope you like variables - mine was far les complete than what you're trying to do and had at least twelve.
Author:  adam77 [ Thu Oct 18, 2012 2:27 am ]
Post subject:  Re: An exercise in game theory - formation cost prediction
Are you averaging over all possible player-decisions/terrain-configurations/dice-rolls/army-rosters, or making some simplifying assumptions?

If you're just looking at survivability this might be of use...
http://traitor-legion.appspot.com/assaultulator/assaultulator.html
Author:  SpeakerToMachines [ Thu Oct 18, 2012 7:27 am ]
Post subject:  Re: An exercise in game theory - formation cost prediction
Spectrar Ghost wrote:
semajnollissor wrote:
Ginger wrote:
Activation impact as well. As individual formation costs increase, there is a corresponding impact on the army through the reduced activation count. Not sure how to implement this, though it is some form of inverse rule. Put another way, as formations become cheaper, their ability to 'stall' becomes more important.
so the cost of a formation is a function of the cost of the formation. That's cool, I can handle differential equations.


More specifically, the cost of the formation is a function of the cost of the formation with respect to army size.


Um, the simplest formula here would probably be to determine the cost of the activation in isolation from the cost of the formation capabilities. In other words, what would be the value of a formation consisting of a single unit with no combat or movement capability? It's clearly not zero, since it can be used to stall activation.

A similar approach can be used to determine the value of movement capability, though whether value scales with the movement range or perhaps some power of the movement range is not immediately obvious.
Author:  Ginger [ Thu Oct 18, 2012 7:56 am ]
Post subject:  Re: An exercise in game theory - formation cost prediction
SpeakerToMachines wrote:
Spectrar Ghost wrote:
semajnollissor wrote:
Ginger wrote:
Activation impact as well. As individual formation costs increase, there is a corresponding impact on the army through the reduced activation count. Not sure how to implement this, though it is some form of inverse rule. Put another way, as formations become cheaper, their ability to 'stall' becomes more important.
so the cost of a formation is a function of the cost of the formation. That's cool, I can handle differential equations.


More specifically, the cost of the formation is a function of the cost of the formation with respect to army size.


Um, the simplest formula here would probably be to determine the cost of the activation in isolation from the cost of the formation capabilities. In other words, what would be the value of a formation consisting of a single unit with no combat or movement capability? It's clearly not zero, since it can be used to stall activation.

A similar approach can be used to determine the value of movement capability, though whether value scales with the movement range or perhaps some power of the movement range is not immediately obvious.
And extending on this, obviously there are the various threat radii for assaulting (in and out of transports?) and shooting - though I would draw the line at trying to split shooting further.
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